Evaporation of a Droplet: From physics to applications

Physics Reports 804 (2019) 1–56

Contents lists available at ScienceDirect

Physics Reports journal homepage: www.elsevier.com/locate/physrep

Evaporation of a Droplet: From physics to applications ∗

Duyang Zang a , , Sujata Tarafdar b , Yuri Yu. Tarasevich c , Moutushi Dutta Choudhury b,d , Tapati Dutta b,e a

Functional Soft Matter & Materials Group, MOE Key Laboratory of Material Physics and Chemistry under Extraordinary Conditions, School of Science, Northwestern Polytechnical University, Xi’an, 710129, China b Condensed Matter Physics Research Center (CMPRC), Physics Department, Jadavpur University, Kolkata, 700032, India c Laboratory of Mathematical Modeling, Astrakhan State University, Astrakhan, 414056, Russia d Department of Physical Sciences, Indian Institute of Science Education and Research (IISER-Mohali), Mohali, Punjab, 140306, India e Physics Department, St. Xavier’s College, Kolkata, 700016, India

article

info

Article history: Received 30 November 2018 Received in revised form 24 January 2019 Accepted 30 January 2019 Available online 15 February 2019 Editor: H. Orland Keywords: Drop Evaporation Crust Crack Pattern formation Coffee ring effect Marangoni flow

a b s t r a c t Evaporation of a drop, though a simple everyday observation, provides a fascinating subject for study. Various issues interact here, such as dynamics of the contact line, evaporation-induced phase transitions, and formation of patterns. The explanation of the rich variety of patterns formed is not only an academic challenge, but also a problem of practical importance, as applications are growing in medical diagnosis and improvement of coating/printing technology. The multi-scale aspect of the problem is emphasized in this review. The specific fundamental problem to be solved, related to the system is the investigation of the mass transfer processes, the formation and evolution of phase fronts and the identification of mechanisms of pattern formation. To understand these problems, we introduce the important forces and interactions involved in these processes, and highlight the evaporation-driven phase transitions and flows in the drop. We focus on how the deposited patterns are related to and tuned by important factors, for instance substrate properties and contents of the drop. In addition, the formation of crust and crack patterns are discussed. The simulation and modeling methods, which are often utilized in this topic, are also reviewed. Finally, we summarize the applications of drop evaporation and suggest several potential directions for future research in this area. Exploiting the full potential of this topic in basic science research and applications needs involvement and interaction between scientists and engineers from disciplines of physics, chemistry, biology, medicine and other related fields. © 2019 Elsevier B.V. All rights reserved.

Contents 1.

Introduction............................................................................................................................................................................................... 1.1. Overview ....................................................................................................................................................................................... 1.2. Different types of droplets ......................................................................................................................................................... 1.3. Different modes of drying: Constant Contact Radius (CCR) and Constant Contact Angle (CCA) ....................................... 1.4. Important forces involved in droplet evaporation .................................................................................................................. 1.4.1. Multi-scale nature of a spreading droplet ................................................................................................................ 1.4.2. Forces which control spreading and evaporation and associated characteristic lengths.................................... 1.4.3. Other length scales ......................................................................................................................................................

∗ Corresponding author. E-mail address: [email protected] (D. Zang). https://doi.org/10.1016/j.physrep.2019.01.008 0370-1573/© 2019 Elsevier B.V. All rights reserved.

3 3 3 4 6 6 6 7

2

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

1.5.

2.

3.

4.

5.

6.

7.

8.

9.

Phase transition induced by evaporation ................................................................................................................................. 1.5.1. Sol–gel transition ......................................................................................................................................................... 1.5.2. Crystallization of salt or macromolecules ................................................................................................................. 1.5.3. Crystallization and glass transition in colloidal droplet .......................................................................................... Evaporation driven flow .......................................................................................................................................................................... 2.1. Thermodynamics and evaporation flux..................................................................................................................................... 2.2. Convection: natural convection and capillary flow ................................................................................................................. 2.3. Marangoni flow ............................................................................................................................................................................ 2.4. Recent experiments: thermal imaging to visualize flow ........................................................................................................ Deposited patterns ................................................................................................................................................................................... 3.1. Coffee ring and its regulation .................................................................................................................................................... 3.2. Effects of substrate properties ................................................................................................................................................... 3.2.1. Porous substrates ......................................................................................................................................................... 3.2.2. Substrate orientation ................................................................................................................................................... 3.2.3. Effects of substrate rigidity ......................................................................................................................................... 3.3. Effect of salts ................................................................................................................................................................................ 3.4. Effect of surfactants ..................................................................................................................................................................... 3.5. Effects of macromolecules .......................................................................................................................................................... 3.6. Dried droplets of protein binary mixtures ............................................................................................................................... 3.7. Evaporation under masks ........................................................................................................................................................... Binary/multicomponent fluids ................................................................................................................................................................ 4.1. Miscible binary liquids ................................................................................................................................................................ 4.2. Self-assembly of particles using binary solvents ..................................................................................................................... 4.3. Effect of temperature on binary fluids...................................................................................................................................... 4.4. Evaporation of acoustically levitated droplets of binary liquid mixtures............................................................................. Crust formation......................................................................................................................................................................................... 5.1. Phenomenology............................................................................................................................................................................ 5.2. Crust morphology and buckling instability .............................................................................................................................. 5.3. Cavity formation .......................................................................................................................................................................... Crack patterns ........................................................................................................................................................................................... 6.1. Mechanisms .................................................................................................................................................................................. 6.2. Factors affecting crack morphology........................................................................................................................................... 6.2.1. Cracks under electric field .......................................................................................................................................... 6.2.2. Magnetic field effects................................................................................................................................................... 6.2.3. Effect of salinity............................................................................................................................................................ 6.2.4. Substrate wetting ......................................................................................................................................................... 6.2.5. Substrate heating ......................................................................................................................................................... 6.3. Wavy and spiral cracks ............................................................................................................................................................... 6.4. Propagation dynamics ................................................................................................................................................................. 6.5. Suppression of cracks .................................................................................................................................................................. Simulation and modeling ........................................................................................................................................................................ 7.1. Models of evaporation ................................................................................................................................................................ 7.2. 2D models of mass transfer ....................................................................................................................................................... 7.3. Modeling flow in three dimensions .......................................................................................................................................... 7.4. 3D models of mass transfer ....................................................................................................................................................... 7.5. Crystal growth.............................................................................................................................................................................. Applications............................................................................................................................................................................................... 8.1. Materials science.......................................................................................................................................................................... 8.1.1. Self-assembly: pros and cons of the coffee ring ...................................................................................................... 8.1.2. Self assembled patterns............................................................................................................................................... 8.1.3. Uniform deposition ...................................................................................................................................................... 8.2. Crystallization............................................................................................................................................................................... 8.3. Quantum dots............................................................................................................................................................................... 8.4. Applications in bioscience .......................................................................................................................................................... 8.4.1. Medical diagnosis ......................................................................................................................................................... 8.4.2. Other applications in biosciences............................................................................................................................... Conclusions and future directions ........................................................................................................................................................ Acknowledgments .................................................................................................................................................................................... References .................................................................................................................................................................................................

7 7 7 8 8 8 10 10 11 11 11 13 14 15 15 16 17 19 20 21 22 23 23 25 26 27 27 28 30 31 31 32 32 32 32 33 33 33 34 34 35 35 37 38 39 40 40 40 40 41 41 42 43 43 43 43 44 46 46

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

3

1. Introduction 1.1. Overview The word ‘‘liquid’’ can make us think of the ocean, a glass of milk, a raindrop or the misty spray near a waterfall. What is special about the raindrop or the droplets of dew condensing on a cool surface? While our earliest introduction to liquids told us that they take up the shape of their container, the raindrop or condensed dewdrop has a very typical shape. Obviously competition between surface tension and gravity is responsible for this. The size of the fluid unit is the controlling factor here. The unit must be small enough for the effect of surface tension to be comparable with gravity. This crucial size is quantified by a characteristic length, the capillary length lc and ensures unique boundary conditions at the interfaces of the droplet [1]. The capillary length is defined as

√ lc =

σl v , ρg

(1)

where σlv is the interface tension between the fluid and air/vapor, ρ is the density of the fluid and g is the acceleration due to gravity. A film is a droplet for the limit curvature tending to zero. While in this review our focus shall be mainly confined to droplets, in a few instances we may briefly digress to point out related features in drying films. As compared with fluid-mass of large scale, the characteristic length scale mentioned above, influences the transportation of the droplets, alters the internal flows as well as the heat and mass transfer between droplet and the surroundings. One of the most commonly observed phenomena is the evaporation of droplets [2–4], which plays an important role in spray cooling [5], coating [6], and inkjet printing [7]. It also provides an approach for self-assembly of solid particles, through which a number of functional materials can be fabricated, for instance the colloidal crystals [8], nano-assemblies [9,10] etc. Evaporation of droplets containing non-volatile materials often leads to various dried patterns, which are related to both the internal flow stresses caused by evaporation and the mechanical properties of the contained materials. If the droplets contain biological matter, for instance blood [11–13], the patterns may reflect important biological information. Therefore, droplet evaporation has attracted increasing research interest in the field of soft condensed matter and fluid mechanics. Different methods for controlling drying have been discussed [14], for example, varying temperature [15], relative humidity [16–22], and vibrating the droplet [23]. Several reviews of the droplet problem have been published [11,24–40], which have reviewed some specific aspects of droplet evaporation, for instance coffee ring effect [27,36], pattern formation [30,35], evaporation induced assembly [29]. However, a more complete physical picture, which describes how the thermodynamics of evaporation results in flows and mass transfer inside the drying droplet and in turn various dried patterns, is high desirable, especially for the beginner. The evaporation of a droplet, although ubiquitous in nature, locates at the interface where thermodynamics and mechanics meet. Therefore, the phase transitions and mechanical instabilities strongly couple, and lead to tremendous evaporationinduced phenomena. In this review, we aim to link different aspects of droplet evaporation including phase transitions, the internal flow, pattern formation and the mechanical behavior, thus providing the readers a more complete picture that spans across different length scales ranging from nano-scale to macro-scale. Both experimental results and simulation and modeling are reviewed. The applications of droplet evaporation are also summarized. Finally, we suggest several potential directions for future research on this topic, for example external field influenced evaporation, evaporation of active matter, space station experiments, etc. Drops are formed by droplets. Droplets are much smaller in volume than drops. According to the data-sheet of U.S. Geological Survey on size measurements of raindrops, the diameter of a tiny water droplet varies between 1 and 50 micrometer in diameter. Coalescence occurs when bigger drops ‘‘eat’’ smaller droplets and grow into a drop with diameter 0.5 mm or bigger. If it gets any larger than 4 mm, it will usually split into two separate drops of rain. Therefore, here some time we mention droplets during discussions of the drop characterizations, like when we will discuss about their wetting properties or surface tension but most of the time particularly on pattern discussion part we will talk about drops instead of droplets. 1.2. Different types of droplets A droplet sittings on top of a horizontal solid substrate is termed a sessile drop and exhibits axial symmetry. The substrate can be rotated to vertical position, when the drop will take an asymmetric shape. Vertical drops are also studied and used for diagnostic purposes [41]. If the substrate is further rotated, turning the system upside down so that the drop is suspended downward it is termed a pendant drop. This is illustrated in Fig. 1. For all these cases, the shape of the sessile drops (Fig. 1a left panel) is determined by the wettability of the solid and the competition between liquid surface tension and gravity. For the pendant droplet (Fig. 1a right panel), its profile can be described by the Gauss–Laplace equation of capillarity [42]. For sessile, pendant as well as vertical drops (Fig. 1b), there are Triple-Phase Contact Lines (TPLC), where the solid (substrate), liquid (drop fluid) and gas (ambient air and vapor) meet. To suppress completely the influence of contact line, one way is to levitate the droplets (Fig. 1c) by using ultrasound levitation [43,44] or electrostatic levitation [45]. The levitated droplets may have distinct boundary conditions for their evaporation, because of the different drop shape and avoidance of contact line pinning.

4

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 1. Illustration of different types of droplets. (a) Sessile drop (left) and pendant drop (right) on a flat substrate; (b) Droplets on a vertical wall (left) and on an inclined surface (right); (c) Levitated droplets via acoustic field (left) and electrostatic field (right).

The apparent contact angle θY for the ideal flat surface (Fig. 2) is one of the simplest terms to define the wettability between droplet and the substrate, which can be written as the Young–Dupré equation: cos θY =

σsv − σsl , σl v

where σsv , σsl and σlv are the interfacial tensions for the solid–vapor, solid–liquid and liquid–vapor interfaces. A rough surface modeled in a simplistic manner, may be considered to have closely spaced protrusions as shown in Fig. 2a and b. A fluid, which wets the protrusions completely, will seep into the spaces between them and there will be no gaps between the fluid and substrate, this is represented by the Wenzel model (Fig. 3a). However, a perfectly non-wetting fluid will sit on top of the protrusions, leaving air pockets beneath, this is the Cassie–Baxter model (Fig. 3b). These are the two extreme cases, real situations may be in between. For rough surfaces or surfaces with micro/nanostructures, the apparent contact angle for the Wenzel model is defined as cos θW =

St Sa

cos θY ,

where St /Sa is the roughness ratio, i.e., a measure of how surface roughness affects a homogeneous surface, viz., the ratio of true area of the solid surface, St , to the apparent area, Sa . The apparent contact angle in Cassie model is given by [47] cos θC = φs cos θY + φs − 1. Here, φs is the fraction of solid in contact with the liquid. The equilibrium of the TPCL becomes possible only when the drop sits on solid islands only [48]. 1.3. Different modes of drying: Constant Contact Radius (CCR) and Constant Contact Angle (CCA) The pinning/depinning of the TPCL and contact angle of the drying droplet play very important role in the internal flow and in turn the mass transfer. According to the behavior of the TPCL and the contact angle, in 1977, Picknett and Bexon distinguished these two modes of evaporation in contact with the substrate. i. Constant Contact Radius (CCR) mode where the contact area remains constant though out the drying process and ii. Constant Contact Angle (CCA) mode when contact radius of the drop with the substrate deceases with time but the contact angle remains invariable [49]. They observed it for slow evaporation of methyl acetoacetate drop, which was deposited on a poly (tetrafluoroethylene) (Teflon) surface. They spotted that transition of these two modes during drying leads to the change of the shape of the

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

5

Fig. 2. Illustration of the wetting of sessile droplet and the dominant forces at different regions. The rows of text in the figure represent from top to bottom—the region, characteristic length scale of the region, forces involved, simulation/computation techniques, various pressures involved and the equation for pressure. Source: Image redrawn from Ref. [46]. © 2012 with permission from Science Publisher of China.

Fig. 3. Schematic diagram of (a) Wenzel’s model and (b) Cassie–Baxter model for wetting of a rough surface.

Fig. 4. Schematic diagram of (a) Constant Contact Radius (CCR) and (b) Constant Contact Angle (CCA). The different colors of the substrate indicate that the CCR and CCA mode can be substrate dependent even for same liquid.

liquid drop (Fig. 4). Here the TPCL proceeds in steps, remaining pinned for a short time, then slipping to a new position. At the last stage of drying stick–slip (SS) mode [50,51] dominates the mechanism of evaporation. Birdi et al. found that the evaporation rate for a liquid making angle <90◦ is linear with time whereas the same is non-linear when the liquid drop makes contact angle >90◦ with a substrate [52]. Rowan et al. also observed same kind of evaporation of a water drop from poly(methyl methacrylate) (PMMA) polymer surface in open air and they explained the reason of linearity in evaporation graph in CCR mode [53]. Interestingly all these observations were done considering that the surfaces are microscopically smooth. Meric et al. worked on the similar problem regarding the drop shape. They treated

6

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

the problem considering the drop is a three dimensional spherical cap instead of two parameter spherical cap [54]. Rapid drying as well as slow drying also affect the CCR–CCA mode changing process [55]. Usually CCR mode is found for the cases where a liquid with weak Marangoni number (Section 2.3) is deposited on high energy surfaces and makes contact angle less than 90◦ with the substrate [39,55,56]. The CCR mode is hampered due to various reasons. For examples, substrate temperature affects strongly the modes of drying [51]. In some cases surface roughness increases the pinning of the drop on the substrate [57], i.e in this case CCR mode dominates. Basically roughness changes drying modes since the contact line pins for Wenzel surface or it sticks-and-slips with time in case of Cassie–Baxter surfaces [57] (Fig. 3). Evaporation from superhydrophobic surface takes place in CCA mode until the drop reaches a certain critical height. At the critical thickness, the Gibbs energy is minimized by switching between CCA–CCR modes [2]. 1.4. Important forces involved in droplet evaporation 1.4.1. Multi-scale nature of a spreading droplet In spite of the simplicity in phenomenology, a spreading droplet exhibits a multi-scale dynamics ranging from 10−9 to 10−2 m. Based on the related length scales, the spreading droplet can be divided into three different regions: capillary region, transitional region and molecular region from droplet center to its periphery [46] (Fig. 2). At different regions, different forces dominate. It is difficult to use a uniform theory to describe the entire droplet dynamics instead one uses appropriate theory for different regions. It is important to note that at the periphery of the droplet, outside the apparent contact line, due to the disjoining pressure, a precursor film of nanoscale width can often be observed [58–61]. The presence of precursor film can somewhat eliminate the singularity of energy dissipation at the moving contact lines. 1.4.2. Forces which control spreading and evaporation and associated characteristic lengths Let us try to summarize what happens after a droplet is deposited on a surface, we consider sessile drops for the present. On deposition, the droplet first spreads out, with the initial circular TPCL expanding, until the equilibrium angle of contact is reached. The radius of the TPCL R usually follows the empirical rule, referred to as Tanner’s law [14] R ∝ t 0.1 ,

(2)

where t is the time after deposition. All physical processes ultimately follow from intermolecular forces of electrostatic origin. For interactions between bare charges, we refer to Coulomb’s law, whereas if interactions between dipoles are relevant, the forces are termed van der Waals forces. For practical purposes, physical laws invoking effective interactions between fluids and surfaces are used. In case of droplet physics, the most dominating effect is the interface tension or surface tension, much discussed in elementary physics textbooks. It was first proposed by Hungarian mathematician J. A. von Segner [62]. The presence of two different fluids (say 1 and 2) across an interface makes the interface behave like a membrane in tension. The surface tension σ1,2 is usually measured as the force per unit length (in units of N/m) tangential to the interface, normal to the TPCL for a sessile drop. For small length scales, the tangential component at the TPCL may also be significant in determining the contact angle. This is termed the line tension σl and measured as the total force (in N) on the TPCL. It is estimated as [63]

√ σl ∼ 4δ σsv σlv cot θY .

(3)

σl can be either positive or negative for θY ≤ 90◦ or θY ≥ 90◦ respectively. The ratio between line tension and surface tension lτ =

|σl | σl v

gives the characteristic length for line tension lτ for the droplet. This is the droplet size (of the order ∼ µm) below which it is necessary to modify Young’s equation as cos θ = cos θY −

σl , σlv RB

(4)

where RB is the local radius of curvature of the TPCL. For a curved interface, there is an additional pressure on the concave side of the surface (for a closed surface this would be on the fluid within) due to surface tension, which is termed the Laplace pressure ∆PL

∆PL = σlv

(

1 R1

+

1

)

R2

= σlv κ,

(5)

where R1 , R2 are the principal radii of curvature and κ is the mean curvature. For systems far from thermodynamic equilibrium, use of the term ‘‘surface tension’’ is questionable and it is better to replace it by ‘‘apparent surface tension’’. We shall encounter this situation while discussing liquid marbles [64] in Section 3. In Section 1.4.1, we have seen that there is often an extremely thin (∼ nm) layer outside what is normally considered as the TPCL, called the precursor film. This layer is important in wetting/dewetting problems and the pressure involved here is termed the disjoining pressure Π . In this case the surface potential W (h) is dependent on the thickness h of the film. W (h) and Π (h) are written as [65] W (h) = σlv + σsl − σsv

(6)

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

7

and

Π (h) =

dW (h)

(7) dh Temperature, volume and surface area remaining constant. The precursor layer thickness hp is determined by the competition between van der Waals force and surface tension. It can be considered as a characteristic length scale for the system and is given by

√ hp =

A 6π σlv

,

(8)

where A is the Hamaker constant. The other two forces which play a very important role in droplet drying problems—the Marangoni force and capillary force will be introduced and discussed in greater detail in subsequent sections. 1.4.3. Other length scales Elastocapillarity is often referred to the phenomenon that capillary force induced by wetting interacts with the elasticity of the substrate being wetted. Elastocapillary length, lEC , is a characteristic length scale reflecting the competition between capillarity and elasticity, which can be written as [65]

√ lEC =

B 2(1 + cos θ )σlv

,

(9)

where B = Eh3 / 12(1 − ν 2 ) is the rigidity of the thin film substrate. Here, E is the Young’s modulus, ν is the Poisson ratio, and h is the thickness of the film. In the elastocapillarity phenomena, the vertical component cannot be ignored, and may result in the bending of the film. If its lengthscale is over lEC , droplet wetting will lead to the wrapping of the elastic film, which is often evidenced in capillary origami [66].

(

)

Debye screening length λD . When exposed to ionizing environment, the existence of counter ions has a screening effect to the ‘‘bare’’ Coulomb potential generated by a charged objective. This leads to a length scale related to the electrostatic potential, which is called Debye screening length λD [65].

√ λD =

εε0 kB T ∑ 2

e2 NA

i zi

mi

,

(10)

where ε is the permittivity, NA is the Avogadro constant, ε0 is the electric constant, e is elementary charge, mi is molar concentration, zi is the valence of the ions. λD is an important characteristic length scale in electro wetting as well as in the interactions of colloids. The presence of salt or ionic surfactant could reduce the Debye screening length, thus leading to colloid aggregation. 1.5. Phase transition induced by evaporation Evaporation-driven phase transition mainly arises from the enhanced concentration (accumulation) of the contained materials. However, in a drying droplet, the phase transition is not simply evaporation-driven accumulation. The existence of TPCL, and the coupling with mechanical instabilities could result in very rich phase transition behavior. 1.5.1. Sol–gel transition Gelation, i.e. sol–gel transition often occurs in association with the drying of a droplet containing colloidal particles or polymer solvent. The main driving force for gelation in drying droplets is the enhanced concentration, which may result in the formation of networks of particles or polymer molecules. Gelation leads to significant increase in viscosity and greatly reduces the fluidity; therefore, the evaporation driven mass transfer will be changed upon the occurrence of gelation. For instance, the particle migration is inhibited [67]. However, the diffusion of ions may not be influenced. Furthermore, the mechanical properties of the gel layer/shell (elastic modulus) and its adhesion with substrate may give rise to the buildup of stress field in the drying droplet, thus leading to various instability behavior (wrinkling, buckling, etc.). There are several factors: surrounding temperature, particle shape and type of solvent, which may influence the gelation transition in a drying droplet. 1.5.2. Crystallization of salt or macromolecules For a droplet of salt or macromolecular solution, evaporation results in the oversaturation of solute, thus leading to its crystallization. It is often observed that the salt crystals as well as protein crystals grow in the form of faceted phase (Fig. 5a). However, for the droplet containing a mixture of solute and colloids, the crystal morphology can be significantly changed and various morphologies range from fractal [68], dendrites [69] to seaweed structures [70] have been observed (Fig. 5b–f). The anisotropic growth and in turn the crystal morphologies can be tuned by gelation in the droplet and exhibit rich branching behavior at the contact lines [71], although the underlying physics is not clear yet.

8

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 5. Various crystal morphologies obtained from droplet evaporation. (a) NaCl crystals in dried gelatin droplet, in cubic form. (b) NaCl crystals in dendritic patterns. (c) Lysozyme crystals with 0.50 wt% NaCl. (d) Branched crystal patterns of mixture of sodium oxalate salt and colloidal sulfur particles. (e) Magnified SEM image of a tip of a single branch in (d). (f) Dendritic crystals of Na2 SO4 evaporating on a hydrophilic surface. Source: Image adopted from Refs. [68–71]. With permission from Elsevier.

1.5.3. Crystallization and glass transition in colloidal droplet For the evaporation of colloidal droplet, in addition to gelation, other phase behaviors, namely crystallization and glass transition can occur with the increase of particle fraction caused by evaporation [67]. The transitions are dependent on the interparticle actions and the evaporation rate. Generally, repulsive force between particles often leads to ordered structure (crystallization) whereas attractive force gives rise to disordered-structure (glass transition). Sometimes, it has been observed that crystallization occurs at the contact line, however, glass structure appeared at the central part in a drying droplet [72] (Fig. 6). The order-to-disorder transition is attributed to the rush-hour behavior caused by enhanced deposition rate inside the evaporating droplet at the end of its life. This suggests the flow velocity in the droplet, which can be influenced by contact angle and contact line dynamics, plays important role in the phase behaviors of the drying of colloidal droplets. Due to the sufficient large time scale (as compared with atom systems) and visibility to optical microscope, colloidal systems are often applied as a model platform for the study of nucleation, melting and crystallization [73,74]. Moreover, evaporation induced particles assembly provide an excellent technique for the preparation of optical crystals [75]. 2. Evaporation driven flow As soon as the drop is deposited, prevailing non-equilibrium conditions start to act on it. Firstly, the drop must spread to reach its equilibrium condition, assuming that the drop is sessile and wets the substrate partially. The spreading coefficient [14] (which is essentially W (h) for h → 0) must be negative for partial wetting, i.e. when the contact angle is finite, and vanish for complete wetting. The rate of spreading usually follows Tanner’s law (2) [14]. Secondly, evaporation starts simultaneously with spreading. Since we are interested in drying drops, we assume that the ambient air is not saturated with vapor of the fluid. Evaporation is not uniform due to the shape of the drop, so there is local cooling and temperature gradients are set up. If the drop contains salts, colloids, polymers and/or surfactants, their concentrations change, leading to concentration gradients. Concentration gradients and thermal gradients in case of substrate heating, leads to surface tension gradients that cause Marangoni flow. In short, all kinds of interplay are initiated between different participants in the game. In addition, there may be external agents such as electric, magnetic or acoustic fields or external heating/cooling. Let us try to identify the relevant forces and effects in this extremely complex situation and see how far we can understand what is going on. It should be mentioned that the flows in Leidenfrost drops was not included in the present review, although these flows were also driven by evaporation [76]. 2.1. Thermodynamics and evaporation flux The thermodynamic aspect of the droplet problem arises from the excess free energy per unit area due to new formation or a change in the interface between two different phases, as discussed by Carrier and Bonn in Chapter 1 of [14]. Considering equilibrium thermodynamics, to make the situation simpler, the grand canonical ensemble is an appropriate

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

9

Fig. 6. Order-to-disorder transition in the particle stain left by an evaporating drop. (a) A 3 µL sessile water droplet evaporates from a glass substrate. (b) Ring-shaped stain of red particles after evaporation. (c) Magnified image taken from the white square in (b). (d) Magnified image taken from the red square in (c) with a scanning electron microscope (SEM). Source: Image adopted from Ref. [72] with permission from APS.

formalism here to describe the interface. The number of particles in the interface and the energy may change as particles leave or join the interface from other phases, while maintaining equilibrium with particles of the same phase in the bulk liquid or vapor states. The chemical potential is assumed to be constant. In terms of the grand potential Ω , the surface tension σ can be defined thermodynamically as

σ =

⏐ ∂ Ω ⏐⏐ ∂ A ⏐T ,V ,µ

(11)

A, T , V , and µ being the area, absolute temperature, volume and chemical potential respectively. It may be noted that even for partial wetting a few molecules of the drop fluid may be present on the substrate as a two-dimensional gas as this is favorable from the point of view of entropy. Volume of the evaporated liquid depends on the configuration of the drop, which is considered in most of the studies, as a spherical cap with radius r and contact angle θ with the substrate [77,78]. Based on diffusion equation the drop evaporation rate [49,78] is dV dt

= 2π D∆P

where

M

ρ RT

f (θ )

3V 1/3

πζ

,

(12)

π

r 3ζ , (13) 3 is the volume of the drop, D is the diffusion coefficient of vapor molecules in free air, ∆P is the difference between the saturation vapor pressure around the drop (P0 ) and the vapor pressure far away from the drop surface (P∞ ), ζ = (1 − cos θ )2 (2 + cos θ ). M is the molar mass, T is the temperature of the system and R is the gas constant. θ is considered less than 90◦ . The factor f (θ ) is related to the shape of the isoconcentration curves of water in the air [49]. Basically f (θ ) = 2.7θ 2 + 1.30. But analytically it is not possible to find the exact solution of (12) for CCR mode of evaporation since f and ζ change significantly with the contact angle. Schönfeld et al. [78] modified the equation and found that the volume decreased non-linearly with contact angle value. However for contact angles less than 90◦ , the volume decreased linearly with time [49], to within 3% error, given by a power law with exponent 3/2 [49]. V =

( V (t) = V0

1−

t t0

)3/2

.

Here, t0 is the total time of evaporation, and V0 is the initial volume of the drop.

(14)

10

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

2.2. Convection: natural convection and capillary flow Convection inside drops may be caused by two distinct sources. As a result, buoyancy convection and capillary convection should be distinguished. The origin of the first one is vertical gradient of temperature inside a drop. This kind of convection arises in thick films of liquids. In the case of drops, it may basically occur in pendant [79] or levitating drops [80] or drops on super-hydrophobic surfaces [81]. Rayleigh number is widely used to characterize buoyancy convection Ra =

gβ

να

(Ts − T∞ )l3 ,

(15)

where l is the characteristic length; in context of levitating drops, the drop diameter is the naturally characteristic length; in the case of sessile drops, the height of the drop apex may be considered as this length, g is the acceleration due to gravity, β is the coefficient of thermal expansion, ν = η/ρ is the kinematic viscosity (here, η is the dynamic viscosity), α is the thermal diffusivity, Ts is the surface temperature, T∞ is the temperature far from the surface. Rayleigh numbers for alcohol and alkanes are quoted as < 1 for heptanol and 23000 for pentane by Carle and Brutin in [14, chapter 10]. When the Rayleigh number exceeds a certain value characteristic of that fluid, heat flow through convection dominates over heat flow through conduction. There is an opinion [82] that buoyancy convection is the origin of ‘‘coffee-ring effect’’. The capillary convection may be produced by two distinct effects. First of all, any distortion of equilibrium shape of drop free surface produces a gradient of Laplace pressure (5) (see also [26]). This gradient may produce both outward and inward flows depending of the shape of the free surface [83]. Laplace number La =

ρ lσlv , η2

(16)

is the ratio of surface tension to the momentum-transport (e.g., dissipation) inside a fluid. Deegan [84] showed that the rate of evaporation is maximum near the TPCL as sketched in Fig. 4, where the length of the arrows indicates the evaporation rate. When the contact line of the droplet is pinned on the surface, the evaporative mass loss near the contact line must be balanced by new liquid flowing there from the bulk of the droplet (Fig. 4). Therefore, a capillary flow can exist within an evaporating sessile droplet. This flow is directed radially outward towards the edge of the droplet. The flow velocity near the edge can be several tens of micrometers per second. 2.3. Marangoni flow Another source of the capillary convection is gradient in surface tension. This kind of capillary convection is known as Bénard–Marangoni convection or simply Marangoni flow. In sessile drops of one component liquid, i.e., in pure solvents, this gradient occurs due to non-uniform evaporation flux along the droplet interface [85,86], that causes differential cooling on the surface. Depending on the thermal properties of both substrate and liquid, the hotter part of the drop may be at its edge or its apex [87]. Since surface tension decreases as temperature increases, a gradient along free surface occurs [88–92]. To characterize any convection that may possibly arise, the thermal Marangoni number is used. Thermal Marangoni number is the ratio of surface tension induced by a temperature gradient along the free surface to adhesive force dσlv l∆T . (17) MaT = − dT ηα Surface tension depends as well on concentration of dissolved substances. When a drop of binary mixture or saline solution evaporates, solutal Marangoni effect can be observed [93]. Increasing concentration of an electrolyte (salt) may increase the surface tension. By contrast, increasing concentration of colloids or polymers decreases the surface tension [94]. There already exists substantial review on flow dynamics [30,34,37]. Therefore in this review, only a few recent works on pattern formation concerning (i) capillary flow and (ii) Marangoni flow have been discussed (Fig. 7). Differences in volatility and surface tension in case of a droplet of binary fluids may set up concentration gradients of the components, due to the preferential evaporation of one of the liquid components over the other. This in turn sets up concentration gradients that cause Marangoni convection. The direction of the Marangoni flow in sessile droplets is determined by the ratio of thermal conductivities between the solid substrate and the liquid. If the thermal conductivity of the substrate is at least a factor of 2 greater, than that of the liquid, the droplet is warmest at the contact line and the Marangoni flow is directed radially outward along the substrate. On the other hand, when the thermal conductivity of the substrate is much less than that of the liquid, droplet is coldest near the contact line and the Marangoni flow is directed inward along the substrate to the center of the droplet. The solutal Marangoni effect can be brought about by the presence of different solutes/dispersions, such as electrolyte (salt), colloids or polymers [94], surfactants [86]. To characterize this effect, solutal Marangoni number is useful. Solutal Marangoni number is the ratio of surface tension induced by a concentration gradient to adhesive force. MaC = −

dσlv l∆C dC ηα

,

where C is the concentration. Additional source of Marangoni effect may be due to a presence of surfactants [95].

(18)

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

11

2.4. Recent experiments: thermal imaging to visualize flow Several parameters affect the evaporation rate among which the substrate properties, the moisture of the surrounding air and the heating conditions are important. Therefore, different flow patterns may be observed during the evaporation and they are mainly influenced by the relative importance of the evaporation rate, the thermo-capillarity and the buoyancy. Some recent experiments have been designed to visualize flow and temperature patterns and verify some of the relations involving flow within droplets, which were obtained analytically. Gleason et al. [96] designed a steady-state evaporation experiment by pumping in water through an acrylic substrate, to compensate for the fluid loss by evaporation. The substrate was patterned to pin the TPCL in CCR mode and the contact angle could be accurately controlled. The substrate was heated to a desired temperature and infrared thermography was used observe the temperature distribution during evaporation. The results showed that over a range of contact angles 80◦ –110◦ and for substrate temperatures varying from 22 ◦ C–70 ◦ C, (1) the evaporative mass flux scaled inversely with contact angle and (2) the temperature distribution resulting from evaporative cooling was significantly non uniform. A different scenario was investigated by Chandramohan et al. [97] who also used infrared thermography to monitor temperature distribution across an evaporating droplet. Here the substrate was strongly non-wetting, resulting in a tall droplet, with a nearly spherical vertical contour. The top of the droplet was in this case at a much lower temperature than the base and there was a prominent temperature gradient increasing downward. The base of the droplet, near the substrate was cooler by several degrees compared to the average substrate temperature due to higher evaporation rate near the TPCL, but the effect of evaporative cooling at the droplet apex was predominant. So the thermal gradient is strongly affected by the aspect ratio of the spherical cap-like sessile droplet. Brutin et al. [98] used infrared imaging to study the thermal motion inside droplets evaporating on heated substrates. They recorded thermo-convective instabilities that developed during evaporation, and linked these to the temperature difference between the substrate and the ambient. Marin et al. [72] use micro-particle image velocimetry to show that the particle velocity increases dramatically in the last moments of droplet evaporation. This ‘‘rush-hour’’ for particles occurs when the contact angle and the droplet height tend to zero. As the droplet height decreases with evaporation, the particles still suspended in the droplet, are ‘‘squeezed’’ out radially where they are forced to jostle for space to settle down. These particles are unable to reach the periphery of the droplet due to the reduced angle of contact, and create a random deposition. Magnetic resonance imaging visualization down to nanometric liquid films was used by Thiery et al. [99] to characterize the physical mechanisms of drying in homogeneous porous medium. An initial constant drying rate period was identified in larger pores. This was followed by a falling drying rate period, which was associated with the development of a gradient in saturation underneath the sample free surface. This initiates an inward recession of the contact line. 3. Deposited patterns 3.1. Coffee ring and its regulation We have seen that capillary convection drives fluid towards the TPCL. So if the drop contains dissolved or suspended inclusions, they are driven outward with the fluid, and in CCR mode, they form a ring along TPCL, when the drop is completely dried. This has come to be known as the coffee ring phenomenon [100]. However not every drop that is drying, leaves such a ring pattern. Hu and Larson in 2006 showed that the higher evaporation rate at TPCL makes the TPCL cooler than other parts of the drop. The higher evaporation at the TPCL, results in a greater solute concentration there. This in turn results in a concentration driven surface tension gradient leading to Marangoni flow that drives the solution in a path opposite to the outward capillary flow. So, there is a competition between capillary convection and Solutal Marangoni flow and only a weak Marangoni flow of the solution is able to create a coffee ring [90]. Pinning of the drop at TPCL along with faster evaporation leads to the defined ring structure [101]. Depinning of the drop from the substrate is defined by various factors like solute concentration, particle size, ionic bonding, surfactant concentration, chemical and/or roughness heterogeneity of the substrate, while the depinning time is quite evidently related to the evaporation time [83]. Weon et al. show that particle size greatly affects flow inside the drop and the resulting patterns [102]. The same capillary flow, which forms coffee ring in some cases, can become responsible for different other patterns in some cases. Weon et al. suspended 20 µm diameter polystyrene particles as the solute in a water drop and the drop was deposited on a Petri dish of polystyrene (Fig. 8) to obtain a central deposition of particles. Smaller sizes of the particles however formed coffee ring on the same substrate. An interesting observation was performed by Yunker et al. [103]. They observed that the particle shape influences the pattern of deposition remarkably. They used elliptical particles instead of spherical particles as inclusion, for water based solution and suppressed coffee ring effect by creating uniform deposition through out the drop (Fig. 9). For this kind of deposition the depinning or dewetting does not occur. Here the main factor is the anisotropic shape of the particles that changes the interactions between the particles

12

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 7. Schematic diagram showing (a) Coffee ring formation due to capillary flow, (b) Marangoni flow due to temperature gradient or surface tension gradient. Darker shades represent higher temperature regions generating surface tension gradient.

Fig. 8. Reverse motion of larger polystyrene microspheres suspended in a drying water droplet on a solid substrate. Source: Reproduced from [102] with permission of American Physical Society.

Fig. 9. (a) Coffee ring formed by a drop containing spherical-microparticles (b) Same kind of drop containing elliptical particles. Source: Reproduced from [103] with permission of Springer Nature.

during the flow. Their structures do not allow them to form dense deposition at the air–liquid interface and is responsible for the overall uniform deposition pattern of the drop. Same kind of observations were performed by Dugyala et al. in 2014 [104] and Bhardwaj et al. in 2010 [105]. However, they claimed that the process of deposition was independent of the particle size aspect ratio. DLVO interactions decided the final particle deposition. DLVO interactions can be modified by changing pH of the solution, which was done in their work [105]. Uniform deposition was achieved by controlling pH [104–106]. Similarly substrate temperature is another parameter which changes deposition pattern by generating temperature gradient along the height of the drop. Various kinds of deposition is observed by changing the temperature of substrates [107,108]. Temperature gradients have also been created on evaporating droplets by infrared heating from the top of a droplet [109]. This makes the temperature at

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

13

Fig. 10. Drop containing 2 µm polystyrene beads in water solution deposited on (a) treated glass substrate, (b) PMMA substrate, (c) PS substrate, (d) PDMS substrate. For treated glass substrate, clear coffee ring is noted and the spreading is much higher than other polymer substrates. For other polymer substrates like PMMA, PS or PDMS substrates, final radius of the drop is much lesser than glass and accumulation of particles are high but some particles spread uniformly inside the drop as well. Even cracks are noted for some cases with a particular diameter of beads. Source: Reproduced from [115] with permission of American Chemical Society.

the apex of the droplet higher than at the contact line. A thermal Marangoni flow creates directed loops of flow along the interface from the apex to the contact line and then towards the droplet axis. In this case the deposited pattern is similar to the coffee ring albeit, a different cause. Presence of vapor source changes the Marangoni flow inside the drops. It also affects the evaporation rate, which alters the deposition pattern [110]. Drying patterns of drops can also be modified by changing their flow through the application of external forces. Eral et al. first observed that electro-wetting can suppress coffee stain effect. They were able to deposit a single small patch of solute on the substrate [111] by the eMaldi technique. Here time dependent electrostatic forces was used to counter radial capillary flow. Continuous and periodic mechanical fluctuation at the TPCL withstood particle deposition at the periphery of the drop and settled particles at the center at the end of the evaporation. Simple capillary flow can be interrupted by complex flow inside the fluid when the drop contains polymers or surfactants [77,112]. One of these drop-constitutes may also lead to suppression of the coffee ring. Surfactant affects are briefly discussed in the next sections. Specifically, adding glue like polymers change the viscosity of a fluid. This affects the Marangoni number (17) that changes the flow. During evaporation, polymers compel drops to depin or change their viscosity with time by making long chains and sol to gel transitions, which changes the flow dynamics inside the drop. The effects on the patterns are clear after drying [113]. Similar kind of variations in patterns have been observed by Sowade et al. in inject printing. The self-assembly of the particles is observed by changing the substrate temperature, substrate types (Fig. 10) and adding mild acid base in the ink [114]. These factors affect the particle–particle interactions, which result in several types of pattern formation. Multicomponent drops are used to form uniform deposition to point deposition of the particles by changing the particle’s polarity, the interactions amongst themselves as well as the substrates. These depositions can be tuned by changing the evaporation rate of the volatile base of the solutions too. Faster evaporation of the solution triggers off small Eddie flows throughout the drop resulting in variations in the Marangoni flow [6]. It changes the accumulation pattern of particles. 3.2. Effects of substrate properties The substrate plays one of the most important roles in drying pattern of droplets as the pattern is affected by the adhesion of the liquid drop with the substrate. Roughness, surface energy and thermal conductivity of the substrate decides the molecular interactions between the drops with the surface molecules of the substrate. Most of studies include coffee ring phenomenon for hydrophilic smooth substrates [94,116,117]. Heterogeneity of the substrates due to roughness or composition manifested through Contact Angle Hysteresis (CAH) [118], may affect pattern formation [119].

14

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 11. Deposition morphologies inside colloidal drops dried under 40% relative humidity with 20 nm particles at different particle volume fractions: (a) 0.5%, (b) 0.25%, and (c) 0.1%. Source: Reproduced from [20] with permission of The Royal Society of Chemistry.

Fig. 12. Drop on porous substrate. (i) Spreading of drop, (ii) infiltration of the liquid of the drop inside the pores, (iii) evaporation of the drop after infiltration [127]. Source: Reproduced from [127] with permission of American Chemical Society.

Any heterogeneity of the substrate too may affect adhesion with droplets. With weak CAH, drops usually shrink during evaporation and leave a dot on the substrate, whereas strong CAH substrates usually collect coffee ring stain on them. Most of the polymer substrates usually show high CAH and they exhibit coffee ring deposition when exposed to solutions containing micro-order diameter particles. Transition from CCR mode of drying to CCA mode of drying, deposits solute particles in a different manner. Stick–slip drying occurs when receding angles differ from advancing angle within a certain range during drying [20]. Differences in contact line velocity with the particle deposition growth is the main cause of multi-ring, radial spokes, spider web and foam (Fig. 11). Heating can change the stick or slip behavior of particles in a solution depending on whether the substrate is hydrophilic or hydrophobic [120]. For hydrophilic substrates, peripheral rings with uniform deposition in the center are observed, the latter due to thermal Marangoni effect. With heating of substrate, the rings become thinner as Marangoni effect becomes stronger. For hydrophobic substrates however, higher substrate temperatures and concentration, the pattern changes from a central deposition and depinned contact line, to a pinned contact line with peripheral deposition. The lower temperature at the contact line with respect to the central point of contact with the substrate reverses the surface tension gradient in the droplet causing peripheral deposition. Hydrophobicity of substrates always leads to self cleansing property [121,122]. Particle laden drops leave spots and do not form rings on these kinds of substrates [123,124]. Considerable research has been done on forming hydrophobic substrates by growing nanotubes or nanopillars on substrates, or coating substrates [123,125] by other kind of particles. Lithography is another technique of making hydrophobic substrates by masking the substrates [126] (see also 3.7). All serve the common purpose of reducing the adhesion of the substrate to dirt or oil. 3.2.1. Porous substrates Porous substrates may be considered to be a bundle of capillary tubes. The solution seeps into these tubes and forms intrinsic contact angles with the pores. Let t1 be the time taken by the solution to fill these pores and tEl the time taken for the solution in these pores to evaporate. tEl is found to be greater than the corresponding time for a smooth surface of the same solution–substrate combination (Fig. 12). Particle deposition on a porous substrate totally depends on particle motion, solvent evaporation, and infiltration. If particle motion time to TPCL is tp and tp /t1 > 1, that is solvent infiltration dominates, then coffee ring deposition is suppressed [127,128]. But tp /t1 < 1 leads to the well-known coffee ring along the TPCL. Like-wise, if particle motion time

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

15

Fig. 13. Microscope images of the deposit patterns of (a) a sessile drop drying on a hydrophobic surface and (b) pendant drop. Both were containing 0.01 wt% 40 nm silica particles. The scale bar represents 50 µm. Source: Reproduced from [132] with permission of Elsevier.

is less than evaporation time tp /tEl then particles are more likely to deposit along TPCL. The opposite case suppresses the coffee ring. Chao et al. investigated blood deposition on porous media. They have found that time dependent spreading of the fluid drop shows a universal power law behavior [129,130]. Shear thinning behavior of blood determines the spreading but the porous media absorb blood cells which directly affects spreading compared to a smooth substrate [131]. 3.2.2. Substrate orientation Patterns formed by drying of a sessile drop are quite different from the patterns formed by pendant drops. Pendant drop drying is an important feature for fertilizer deposition on the leaf of tree. The orientation of the leaf determines the pattern of deposition. In 2012, Hampton et al. investigated effects of surface orientations on dried deposition of the particles (Fig. 13). Unlike sessile drop which forms coffee ring at TPCL, pendant drop forms small and dense deposition of the particles at the center of the drop [132]. If a droplet is dried on a vertical surface, radial and axial symmetry are lost. The thickness of the drop increases downward and the same drop displays a wider range of thicknesses compared to the sessile position. This can be utilized to segregate inclusions and their aggregates of different sizes as described in (refer section: applications). Internal flow of the particles under gravity determines this kind of deposition pattern but natural convection or particle instability at the initial concentration does not affect the results. Roughness of the surface and CAH of the substrate determine the shape of the droplet. The effect on drop particles due to presence of gravity matters if vertical temperature flux is not balanced by gravitational field [133]. A nano particle laden droplet is not much affected by gravity, it forms coffee ring instead of central deposition. 3.2.3. Effects of substrate rigidity Due to the vertical component of drop surface tension at the contact line, substrate deformation may appear. This effect becomes noticeable if a drop is deposited on soft substrates, for instance immiscible liquid or gels. For a liquid surface, for example oil drop on water, instead of the Young’s equation, the Neumann’s triangle equation for liquid surface [134] is appropriate (Fig. 14b):

σsv = σsl cos θ2 + σlv cos θ1 , σsl sin θ2 = σlv sin θ1 .

(19)

The same equation takes the form

Σsv cos θs = Σsl cos θ2 + σlv cos θ1 , Σsl sin θ2 + Σsv sin θs = σlv sin θ1

(20)

for gel like polymer substrate (Fig. 14c). When a drop is deposited on a gel or liquid substrate the substrate deforms. At TPCL the local forces balance which includes the surface tension of the corresponding interfaces. These surface tensions of the substrates come up from the elastic stresses, which occur from the corresponding deformations. This additional information of substrate deformation is contained in Σi . The relation between σ and Σ follows Shutterworth equation [135]. For liquid substrate σi = Σi Young’s law is applicable for solid non-deformable substrate where Neumann’s triangle condition is representing another extreme limit that is liquid substrate [136]. Cao et al. claims that substrate modification changes the drop deposition and the elasticity of the substrate changes the dynamics of drying during evaporation [136]. In the context of drying of ink from an elastic substrate, the variation

16

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 14. Water drop on (a) solid substrate, (b) liquid substrate, (c) polymer soft substrate. Drop makes Neumatic triangle with liquid and soft substrates.

Fig. 15. (a) Faster drying of NaCl in gelatin base with RH 45% (b) Same kind of drop containing 0.01 M NaCl, 0.5 g gelatin in 50 ml water dried in RH 35%.

of dynamic contact line increases hugely with increasing order of Young’s modulus [137]. Droplets containing colloidal particles and drying on floating elastomer have been reported by Boulogne et al. [138]. They have observed no shrinking of the substrate initially. However, as drying proceeds, the dispersed particles apply tensile force on the substrate and a wrinkling instability of the membrane is observed. Due to the non-rigid nature of the soft substrates, the drop evaporation on them often leads to various substrate deformation, which is far from fully understood yet. Therefore, researchers put more effort on how the substrate was deformed rather than the pattern formed on the substrate. 3.3. Effect of salts There are many reports that NaCl crystals in simple salt solution drops, grow at the pinned TPCL during drying of the drop [39,71,100,139]. Bonn et al. concluded after observing various experiments that saturated NaCl salt crystals prefer to grow in contact with a non-polar environment. Coffee ring like deposition is observed at the liquid–air interface for hydrophilic low energy surfaces but cauliflower like crystal structures are observed at the solid–liquid interface of hydrophobic surfaces. Deposition of salt crystals on hydrophilic surfaces at the TPCL, slightly enhances the spreading of droplets by lowering interfacial tension during evaporation. Anhydrous Sodium sulfate (Na2 SO4 ) salt crystals creep both inside and outside the drop from TPCL at the final stage of drying. This kind of dendritic growth of anhydrous (Na2 SO4 ) salt is known at ‘‘Thenardite’’. The remaining hydrated crystals of (Na2 SO4 ) accumulate at the TPCL. They are cubic in nature like NaCl. Changes of interfacial properties are behind these kinds of growth and they cause two kinds of damages inside the material or at the surface of the material. One is known as the subflorescence, where the salts accumulate at the pores and another kind is efflorescence, when crystallization occurs on the exterior surface of the body [140]. Now if any of the drying conditions change, for example, temperature of solution or humidity of the environment, the crystalline patterns change drastically. It is shown by Dutta Choudhury et al. that with increased humidity, the crystal growth is more regular and symmetric in shape. Slower evaporation gives the ion more time to look for the position where energy is minimum. Since such positions correspond to sites of the perfect crystal structure, slow growth makes the deposit grow as a perfect crystal. Otherwise, the ion would attach at random positions, resulting in amorphous or imperfect crystal structure [139,141,142] (Fig. 15). Shahidzadeh et al. claimed after a series of observations on drying Ca2 SO4 and NaCl salts solutions that salt stains on substrates were initiated by the different wetting behavior of growing crystals on the substrates. Initially NaCl solute concentration becomes high at the edge of the drop, but because of their very small size at the initial times, they flow towards the center. The liquid carrying Na+ Cl− ions continues convection flow until crystal size becomes large enough to be confined to the surface. Since the outward convection flow has the tendency to move the crystals to the liquid–air

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

17

interface, they stop moving when they reach the TPCL at this stage of drying [4]. For the crystal to just fit into the wedge shaped vertical profile of the sessile drop, displacement of the crystals from the edge towards the center at the initial stages of drying is given by L(t) = d(t)/tan θ ,

(21)

where d(t) is the crystal size and θ is the contact angle of the solution with the substrate. A drop is allowed to shrink under the influence of the surface energy of the substrate and adhesive force experienced by the molecules at the TPCL. Variation in the adhesive property of a saline water drop can be achieved through surface modification as well as by changing the concentration of the solutes inside the drop. On silica wafer and PMMA substrates, drops experience depinning unlike lifelong pinning experienced on soda–lime glass substrate. On such partially hydrophobic substrates, the Péclet number (22) is less than unity. This is because r, the radius of the circular TPCL is small and the diffusion coefficient of Na+ ions is high [143]. The Péclet number in this context can be defined as Pe = v r /D,

(22)

where D is the diffusion coefficient. Diffusion is more dominant than the convective outward flow. These are the reasons of formation of big NaCl crystals at the center of the drops on PMMA or silica substrates. Similar kind of studies were done by McBride et al. Calcium sulfate Ca2 SO4 on super hydrophobic Cassie type substrate with minimal contact angle hysteresis and liquid impregnated surface. Oil impregnated surface prevents nucleation and pinning of the salt crystals at the TPCL [144]. The capillary flow inside the drop could be manipulated by applying external fields on the drop. Molecular dynamical studies of the evaporating drop of saline nano-droplets under alternating (AC) external electric fields revealed [111] that continuous pinning–depinning of a drop at TPCL produces a clump of salt near the middle of the drop instead of a coffee ring stain, the DC field presented ribbon like salt deposition throughout the drop [145]. To get a crystal clump, electric field should suppress the pinning adhesive force due to CAH Fp = σlv (cos θa − cos θr ).

(23)

The addition of salt reduces the electric double layer (EDL) between colloidal particles in solution [146,147]. This enhances flocculation about the particles resulting in a decrease of their radial velocity towards the contact line. The final deposited pattern is determined by the competition between the capillary flow and solutal Marangoni effect that drives the particles towards the droplet center. This effect has been studied on polymer and salt solutions [142,148], human serum albumin (HSA) and salt solutions [149,150]. Increasing the salt concentration increases the crystalline property of the polymers in solution by absorbing ions on the macromolecules, and affects the distribution of the deposits. The rings are also formed for drops of protein–salt solutions but in this case Yakhno et al. claimed that if the surface tension exceeds the force of adhesion at TPCL, the drops shrink. During shrinking, they leave concentric circles of deposition [151]. Varying humidity during drying changes the salt crystallization and aggregations in the protein drops [152]. Dried drop of plasma from a healthy individual reveals dendritic patterns and fractals [11,153]. Studies on various protein and salt containing drops have been reported, showing similar results [68,69,149,154–156]. 3.4. Effect of surfactants It is observed that when micelle concentration increases a normal anionic surfactant drop makes transition from nonspreading to spreading on hydrophobic surface [157,158]. There are some superspreading surfactants, like trisiloxane, whose spreading dynamics are quite different from ‘‘normal’’ surfactant on the same surface. For the substrate, this kind of spreading determines the pattern formation inside the dried drops. Since the affinity of the liquid changes with the addition of the surfactant, it affects some crystal growth phenomena too. For example, Yan et al. observed crystal growths of hydroxyapatites nanorods. The growth patterns can be modified using different surfactants like Teigen (CTAB) [159], polyvinyl alcohol (PVA) surfactant and Sodium dodecyl sulfate (SDS). These surfactants are used as regulators in crystal growths because of their surface active properties and the ionic affinity towards certain crystal faces [160]. Kilpatrick et al. in 1985 showed that surfactant–water solutions left finger like stains in presence of Uranyl acetate (UA). They observed triangular shaped crystals along the TPCL of the dried drop along with birefringent textures inside the surfactant induced UA drop whereas simple aqueous solution of the surfactant, sodium 4-(l’-heptylnonyl)benzenesulfonate (SHBS), generates needle like structures after drying [161]. Basically surfactant type (anionic or cationic) and their concentrations control the surface tension gradient within a drop which in turn controls the Marangoni flow inside the drop [89]. Nguyen et al. studied a drop of HCl containing 0.01 w/v % solid amidine- or sulfate-functionalized microspheres [162,163]. Along with Marangoni flow, here Marangoni– Bénard convection occurs. They observed that surfactant takes three states of arrangements: The surface gaseous state (G) arises when number of surfactant molecules can barely interact due to the low number of molecules present per unit area, if tails of the surfactant orient randomly out of the interface then the state is ‘‘surface liquid expanded state’’ (LE) and with highly ordered chain of surfactants forms ‘‘liquid condensed states’’ (LC). At G–LC interface capillarity takes place and at LE–LC interface, where periodic hexagonal network forms, Marangoni–Bénard convection occurred (Fig. 16). Controlling drop patterns is an important factor for inkjet printing [164]. Ordered array of organic nanoparticles at the rim of the droplet could be controlled by the evaporation of the microemulsion in the droplets [165] which

18

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 16. Microscopic images of different stages of a drying-drop, containing sulfate functionalized microspheres. (a) A monolayer at its interface in LE–LC coexistence with very weak coffee ring deposition, (b) Microspheres which were circulating in Bénard convection deposited on the surface and periodic hexagonal structured formed [163], (c) Residual of dried particles forming a connected network of polygons with a coffee ring. Source: Reproduced from [163] with permission of American Chemical Society.

contains gemini-type surfactant. In a similar kind of study, Small et al. found that single-walled carbon nanotube (SWNT) networks can be modified by using the evaporation dynamics of a drop of SDS–SWNT [166]. In brief, adding surfactant helps nanofluid drops to form ‘‘coffee ring’’ instead of uniform or semi-uniform nanoparticle distribution inside the drop. In mathematical modeling of drop drying, Crivoi and Duan showed that the sticking factor of the particles at the TPCL is considered to be the most important parameter to determine the patterns followed by surfactant induced nano particle [167] flow. Surfactant also suppresses edge depositions for colloidal particles [168] and long chain polymers [112,169] (Fig. 17), colloidal particles [106,170] and living bacterial systems [171]. For anionic particles with anionic surfactants interaction always forms coffee ring at the edge whereas with cationic surfactants the same anionic particles give homogeneous patterns in a certain range of concentration of micelles (below critical micelle concentration) [106]. A fingering instability at pinned TPCL is reported by Dier et al. [172]. They claimed that thermocapillarity as well as surfactant induced Marangoni flow are behind this pattern. When the drop is pinned, convection flow increases the number of surfactant molecules and the particles along TPCL. Surfactant molecules at the liquid–air interface near TPCL decrease the local interfacial tension and generate ‘‘Marangoni vortex’’ or ‘‘Marangoni eddies’’ there. It produces Marangoni flow just opposite to the ‘‘coffee ring’’ and provides ‘‘levelling effect’’ in a drop with fixed TPCL during drying [169]. Jung et al. showed using Monte Carlo simulation that if the absorption rate of the surfactant to the particles is slow and initial surfactant particle number increases, the coffee ring pattern transforms into multi-ring pattern. However, for the case of fast absorption rate, the uniform pattern could be achieved with a small outer ring deposition [173].

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

19

Fig. 17. (a) Schematic description of the Marangoni eddy: SDS molecules from the bulk are pushed to the pinned contact line, they locally decrease the interfacial tension which produces a surface Marangoni flow towards the center of the drop. (b–f) The flow of the particles from the edge deposition towards the center due to Maragoni eddy for a sample containing 0.5 wt% PS particles (1330 nm) and 0.5 wt% SDS at different stages in the evaporation [168]. Source: Reproduced from [168] with permission of American Chemical Society.

3.5. Effects of macromolecules It is already discussed in previous sections that mono-dispersed particles in a solution accumulate at the TPCL when the drop is pinned at TPCL. But what happens when a macromolecular solution is deposited on a substrate in the form of drop? How do the macromolecules arrange themselves during free evaporation? What are the effects of ions on the patterns of dried macromolecules? In this section, we will briefly go into the subject of pattern formation by macromolecular solution drops. At the initial time of evaporation, polymer drops have the tendency to be pinned on homogeneous substrates [139]. This kind of drop introduces radial convection flow as well as Marangoni instability because of the changing viscosity of the liquid with time. For smaller size of drop, TPCL shrinks because of the decrease of concentration gradient in the drop [174,175]. Marangoni convection forms dot like feature whereas larger drop of the same material forms concentric ring depositions during drying. During drying, initially, polymer concentration is higher along TPCL and glass transition occurs [176]. Since the medium is non-volatile wrinkling or cracks form due to pinning of the polymers to the substrate. At a particular concentration of the drop containing polymer and dispersed colloidal particles, a sudden rise in the middle of the drop is noticed, which the authors named as ‘‘Mexican hat’’. Similar kind of central buckling occurs in drying of sessile droplets of poly (ethylene oxide) (PEO) [147,177–179]. Baldwin et al. explained the accumulation of polymer pillar at the center of the drop in terms of the droplet’s initial Péclet number [180] (Eq. (26)). Increasing height determines the final pillar-shaped deposition (Fig. 18). Polymer drops show some mesmerizing features when ions are added to the solutions [139,141,148]. Different polymers give different patterns because of their chain length. Salt interaction with these polymers gives fractal patterns, for example, when gelatin sol is made on the basis of NaCl salt, multifractal growth of salt is observed [68,182]. The sol– gel transformation and flocculation of polymer occur during drying of the drop [139,182]. Changing polymer produces different features including DLA, faceted crystals, dendritic crystals, concentric rings with different patterns [139,141]. Interestingly changing salts in gelatin gel solution gives more variations too [22,148]. These different patterns arise because of different dynamics of drying. Electrostatic force plays an important role due to the presence of ions in the solution. The frictional forces rise in the presence of salts and ‘‘slip–stick drying mechanism’’ gives rise to concentric rings.

20

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 18. (a) Mexican hat [181] (b) Polymer pillars with varying concentration of the polymer (c0 = 3, 5, 10, 15, 20, and 25%), size of the drop (V0 = 0.4, 5, 10, 20, 30, and 50 µl), humidity (RH = 25, 55, 75, 80%) and pressure (P = 20, 50, 100, 200 mbar). The bar size is 1 mm. The thin outline shows the initial drop profile. Source: Reproduced from [180] with permission of Royal Society of Chemistry.

Fig. 19. Circular structures formed by dried droplets of various protein binary solutions. Source: Reproduced from [189] with permission of Elsevier.

3.6. Dried droplets of protein binary mixtures The formation of patterns produced by the evaporation of drops containing bio-fluids is a topic of great relevance due to its potential use for diagnostic purposes and screening of pathologies. For example, blood serum droplets of patients with leukemia, anemia, viral hepatitis type B, tuberculosis, burn disease and breast cancer produce complex and well-differentiated patterns [183–185]. The formation of protein deposits strongly depend on concentration, relative humidity, the size of the drop and contact angle [24,94,186–188]. Natural body fluids obviously contain various different components. Laboratory experiments on judiciously designed mixtures of proteins and salts dried under controlled conditions are expected to be useful in understanding this area. Carreon et al. [189] reported the study of pattern formation in a binary solution of two proteins, bovine serum albumin (BSA) and lysozyme. The morphology of the deposit of a protein mixture solution is a consequence of the competition between gelation and desiccation kinetics [187]. Faster evaporation at the droplet periphery produces a coffee ring, which gels and cracks soon after. The fluid moves inwards towards the droplet center where it finally forms a grainy deposit. The aggregation occurs when the hydrophobic side chains of an unfolded protein are distributed randomly in small structural subunits, which interact intermolecularly with other subunits of hydrophobic surfaces of neighboring molecules forming small groups [190]. If a protein of smaller size intervenes during this process, it is trapped within these interactions, resulting in the formation of complex aggregates of small crystal aggregates, dendritic structures, undulated branches, and interlocked chains; as well as cavities [191–193] (Fig. 19). In another work on binary fluid of BSA–lysosome together with the salt NaCl, Carreon et al. [194] used first-order statistics (FOS) and gray level co-occurrence matrix (GLCM) to characterize the complex texture of deposit patterns. The FOS and GLCM are complementary measures for the assessment of texture of an object. They showed that the FOS texture

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

21

Fig. 20. Optical images of colloidal films under masks of varying design: (a) a hexagonal array of circular holes and (b) a parallel array of open lines. Source: Reproduced from [211] with permission of American Chemical Society.

parameter had an exponential dependency on the salt concentration and was a useful tool to characterize the complex aggregates that arose due to the protein–protein interaction that was enabled through the different flow dynamics in the evaporating droplet. 3.7. Evaporation under masks Patterned colloidal depositions find wide applications in coatings, metalized ceramic layers and high throughput DNA screening, to name a few [195–198]. In most patterning approaches, colloidal assembly is guided through chemical [199– 201] or topographical modifications of the substrate [202–204] or by the application of suitable external fields [205–207]. Other experimental techniques include Infrared radiation-assisted evaporative lithography (IRAEL) [208], and convective gas flow experiments of [209]. Simulation studies [210] have also been performed that give a good agreement with experimental results. However all these works are confined to patterning evaporating colloidal films. Very little of these techniques have been extended to evaporating droplets, perhaps the greatest challenge being the size of a droplet! We discuss the few works that deal with evaporation of droplets under masks. Harris and Lewis [211] developed a new method for patterning colloidal films through evaporative lithography by making use of Marangoni stresses that develop in evaporating droplets of ∼2 cm diameter and films. Evaporative cooling and inefficient heat transfer through a drying drop induces a temperature gradient, which in turn leads to a gradient in surface tension across the drops surface such that the temperature is lowest and surface tension highest at the center of the drop. This generates recirculating fluid flow from the regions of lower surface tension to the regions of higher surface tension. The majority of particles are now driven to the center of the droplet where they deposit. A broad range of patterned colloidal films could be generated simply by tuning the initial colloid volume fraction and mask design. The size, shape, and arrangement of the recirculating cells are determined by the design of the mask, which controls the evaporation profile and resulting temperature gradient across the film. Evaporative cooling in the unmasked regions creates a film surface that is cooler than the masked, non-evaporating regions. The final deposited pattern can be easily controlled by modifying the mask design as shown in Fig. 20. In another study, Harris et al. [212] used a binary colloidal mixture containing microspheres and nanoparticles. On evaporation, these components were segregated into a pattern of discrete nanoparticle assemblies separated by a continuous network formed by the microspheres. Evaporation of droplets under suitably designed masks were simulated by Tarasevich et al. [213,214] using a finite element method. The authors simulated the experimental findings of [211] in which a thin colloidal sessile droplet was allowed to dry out on a horizontal hydrophilic surface with a mask just above the droplet. Only one particular case was considered where the center-to-center spacing between the holes was much less than the drop diameter. In their model, advection, diffusion, and sedimentation were taken into account by the authors. The simulation demonstrated that the colloidal particles accumulated below the holes as the solvent evaporated as was observed experimentally. Moreover, diffusion was found to reduce this accumulation of particles. Lin et al. [215] prepared a layer of polystyrene (PS) beads of monolayer thickness, that acted as a mask for the deposition of Au nanoparticles on a fused silica substrate. Microliter sized droplets of PS solution were placed in microwells of PDMS created on the substrate. Surface tension creates a concave profile when the droplet height is decreased below the wall height during the evaporation, as shown in Fig. 21. At some point, the film might rupture, and a monolayer of the solute forms at the center, Fig. 21b. After the PS beads were deposited as a mask, Au particles were sprayed on the system, to get a uniform array of Au after the PS mask was removed Fig. 21c. Evaporation of droplets under a ‘‘mask’’ of particles is utilized to form ‘‘liquid marbles’’. Several studies have exploited ‘‘liquid marbles’’ for transporting small volumes of high surface tension liquids [216], storing water in a powdered form [217], and for the encapsulation and delivery of active (water soluble) ingredients [218]. Liquid cannot penetrate

22

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 21. (a) A schematic cross-sectional view of a micro-evaporative droplet on wall-structured surfaces. (b) A schematic diagram of the droplet-deposition scheme in microwells. (c) Scheme of nano-sphere deposition of Au. Source: Figure adapted from [215] with permission of IEEE.

Fig. 22. Schematic of ethanol–water droplets (10 µL in volume) on packed beds of hydrophobic glass spheres (98 µm in diameter). (a) Ethanol-rich drops wet the particles and penetrate into the packed bed within seconds, leaving a circular depression on the bed surface. (b) Water-rich drops wet the particles only partially and remain trapped on the packed beds; they evaporate over a few hours. (c) Water drops rolled over the packed bed surface become encapsulated by a layer of particles, i.e., form liquid marbles. The particle shell is robust and the liquid marble can be rolled onto other surfaces without breaking or leaking. (d) A water marble sitting on the packed bed. Source: Figure adapted from [220] with permission of Royal Society of Chemistry.

into powders that consist of poorly wetting particles. The particles may encapsulate drops that are rolled across the bed, forming liquid core-particle shell structures (liquid marbles) [216,219]. Laborie et al. [221] and Bhosale et al. [222] have showed in their studies that contrary to expectations, ‘‘liquid marble’’ surfaces coated with a single layer of densely packed particles dry at a greater speed than the bare liquid droplets (see Fig. 22). 4. Binary/multicomponent fluids In this section, we focus on how the mixture of two or more liquids (solvents) influence evaporation. We have discussed in Section 2 how capillary and Marangoni effects compete and combine to drive the droplet fluid along different paths. The fluid carries along the suspended and dissolved inclusions which deposit on the substrate forming a wide variety of patterns as we have seen in Section 3. Of course, the wetting behavior of the fluid–substrate system and other external factors like temperature and humidity all affect the end result. In this section, we concentrate on the composition of the

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

23

suspending fluid. We discuss how a mixture of more than one miscible fluids, can be cleverly utilized to engineer specific deposition patterns as desired. The situation, as can be imagined, is becoming more and more complex as we go on introducing additional diversity in the picture. However it is important to decode each effect on the evaporation dynamics, mass transfer processes and hence on the end result to successfully apply this technology in industry, medicine, environmental problems and other fields. The fluid components may have contrasting or similar properties of volatility, boiling point, diffusion coefficient, thermal diffusivity, surface tension and viscosity. Therefore, they interact differently with substrate properties of roughness, wetting and spreading coefficients, surface energies and hydrophilicity or hydrophobicity resulting in complex droplet evaporation dynamics. 4.1. Miscible binary liquids Miscible liquids are those that mix in any proportion to form a homogeneous solution. In such mixtures, the component with lower boiling point and higher volatility will evaporate faster in contrast to another liquid of higher boiling point and lower volatility. The preferential evaporation may give rise to solutal Marangoni effect due to concentration gradients of the faster evaporating liquid. The flow pattern inside the droplet is decided by the competition between the evaporation flux and the rate of diffusion of this fluid to the liquid gas interface. Thermal gradients that develop in the droplet due to such preferential evaporation is usually very weak especially for micro-, nano- or picolitre droplets [223]. Of course, heated substrates can set up strong thermal Marangoni effects even for very small droplets that can play a significant role in the flow dynamics. By contrast, substances are said to be immiscible if there are certain proportions in which the mixture does not form a solution. For example, butanone is significantly soluble in water, but these two solvents are not miscible because they are not soluble in all proportions. In organic compounds, the weight percent of hydrocarbon chain often determines the compound’s miscibility with water. For example, among the alcohols, ethanol has two carbon atoms and is miscible with water, whereas 1-butanol with four carbons is not; octanol, with eight carbons, is practically insoluble in water. Immiscible fluid mixtures are not normally used in droplet drying studies. The last decade has seen a volume of research on droplets formed from binary mixtures, especially for mixtures on the water-rich side of any binary azeotrope, for example, an alcohol and water [224–226]. Hamamoto et al. [227] compared and reported experimental results of the spatial and temporal velocity field within pure water and ethanol–water mixture droplets, a miscible binary, evaporating on a glass substrate. They investigated the overall drop profile variation and surface temperature map of the evaporating drops and tried to correlate these with the velocity field within the drop. The presence of multiple vortices in the initial phase of evaporation was driven by concentration gradients set up by the preferential evaporation of ethanol and could not be explained by capillary convection alone. An exponential decay in vorticity was observed soon after as the ethanol evaporated. The droplet apex got completely depleted of ethanol. This set up a large concentration difference of ethanol from the contact line to the apex resulting in the formation of one large toroidal vortex. The last stage of evaporation was characterized by radial flow towards the contact line, which matched the evaporative flux and flow measurements for pure water, indicating the complete depletion of ethanol at this stage. Initial multiple vortices driven by solutal Marangoni effects caused by a concentration variation because of the evaporation of ethanol was also reported by Christy et al. [228] and Bennacer et al. [229]. 4.2. Self-assembly of particles using binary solvents A homogeneous 2D self-assembled colloidal monolayer without segregation of particles is extremely important for the fabrication of nano/microperiodic structures to be utilized for nanostructure fabrication such as etch masks, biochemical and catalytic supports, and photonic crystals, to name a few. Uniform coating of particles was observed by Kim et al. [6] by evaporating a whiskey drop which is a mixture of ethanol, water and some surfactants. The uniform deposition obtained after the whiskey drops evaporated could not be explained by surfactant driven Marangoni flow alone. Working with a model liquid which consisted of a binary mixture, surface-active surfactant, and surface adsorbed polymer, the authors established that particle-surface interactions affected by surface-adsorbed macromolecules [230,231], was sufficient to achieve a uniform deposition pattern. They investigated the flow field inside the droplet by using particle image velocimetry and recorded images of the final particle deposits to establish their results. Park and Moon [232] demonstrated that homogeneous dot like patterns were obtained from the evaporation of droplets of the mixed-solvent-based inks with judicious contrasts in their boiling points and surface tension values. Dual solventbased inks in which the high-boiling-point solvent as a minor component, had a lower surface tension compared to the lower-boiling-point major solvent of higher surface tension, were suitable candidates. By adding drying control agents of high boiling point to water based inks, a concentration gradient of the drying agent quickly develops along the air–droplet interface as the water rapidly evaporates. The faster rate of evaporation is facilitated by the smaller contact angle of mixedsolvent-based ink droplets than that of water based ink droplets due to reduced surface tension. Since low-boiling-point water had a higher surface tension than both the drying agents used by the authors, a Marangoni flow starts from the

24

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 23. SEM of deposit patterns composed of the silica microspheres produced by ink-jet printing a single ink-jet droplet of varying ink compositions: (a) water-based ink (b) water/DEG-based ink and (c) water/FA-based ink. The substrate was a hydrophilic Si wafer. Source: Reproduced from [232] with permission of American Chemical Society.

Fig. 24. Deposits from 10–70 vol% ethylene glycol–water, containing 1 vol% nanometer spheres. Source: Reproduced from [233] with permission of Ingenta.

droplet apex and flows towards the TPCL along the droplet–air interface, in the direction opposite to convective flow. If the drying agent had a surface tension higher than that of water, the solutal Marangoni flow would have flowed from the TPCL to the droplet apex along the interface. As the droplet dried, a diminished outward convective flow concurrent with Marangoni flow, allowed the suspended particles to self-assemble into homogeneous 2D colloidal crystals without distinct ring-shaped deposition, Fig. 23. Talbot et al. [233] demonstrated that uniform deposition of nanoparticles, was possible by judiciously adjusting the fraction of a liquid less volatile than water, in a binary composition with water. Ring deposits were observed for high volume percentage of the less volatile liquid component (e.g., ethylene glycol) in the mixture whereas a lower volume fraction (10%–30%), gave more uniform deposits. A thick raised edge was observed for the 50% composition, Fig. 24c. After most of the water evaporates, the initial convective flow towards the contact line gets arrested, and the suspended nanoparticles settle as a deposit if the remaining liquid with its low volatility, is unable to generate a convective flux. A greater volume fraction of water enables the convective flow to sustain for a longer time leading to a more uniform deposition of particles, Fig. 24. Similar experiments with a liquid of higher volatility than water, e.g., ethanol, showed ring deposition for all volume fractions. Self-assembly of colloidal particles in dual-droplet inkjet printing was demonstrated by Al-Milaji et al. [234] in order to produce a nearly monolayer of closely packed deposition of colloidal particles that exhibited colorful reflection. A microdroplet of the wetting liquid (water ethanol mixture) was placed on a supporting sessile droplet of deionized water

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

25

Fig. 25. Dried deposits of 0.05 wt% binary-based CuO nanofluid droplets on heated substrates at 47, 64, and 81 ◦ C. Source: Reproduced from [236] with permission from Springer.

with the essential condition that wetting droplet should have a surface tension smaller than that of the supporting droplet. This enables the spreading of the wetting droplet on the entire surface of the supporting droplet. The two liquids were miscible in the experiment conducted by the authors. Weber number We = ρ V 2 l/σlv ,

(24)

that compares the inertial energy of the wetting droplet to the deformation energy of the supporting droplet surface, determines the efficiency of spreading of the wetting droplet on the supporting droplet. A smaller We favors spreading of the wetting droplets, and a larger We tends to bring the wetting droplet into the supporting droplet and enhances chaotic mixing of the wetting and supporting droplets. Nanoparticles were initially mixed with the supporting droplet liquid. Immediately after the wetting droplet impact, the nanoparticles on the supporting droplet surface move along with the Marangoni flow created by the ethanol/water surface tension gradient. Individual nanoparticles collide and assemble into larger islands and monolayer networks at the interface by particle–interface interactions, which are trapped at the air–water interface in an energetically favorable state due to the interfacial deformation caused by the fractal shape of the agglomerates [235]. In addition, the quick evaporation of ethanol solvent in the wetting droplet also contributes to the network formation on the supporting droplet surface. During evaporation of the supporting droplet, the particle film is maintained at the air–water interface, being further compressed by the reduced surface area. When the water solvent in the supporting droplet completely evaporates, a deposition of nanoparticles forms. The nanoparticles formed a ring at the TPCL, which the authors attributed to DLVO interactions between the particles and the substrate and not the usual coffee-ring effect. Depending on the functional group of the nanoparticles, skin formation, wrinkling or even buckling may be observed during evaporation. 4.3. Effect of temperature on binary fluids The role of temperature on evaporation of binary-based sessile droplets of water and 1-butanol mixture containing CuO nanoparticles placed on silicon substrates, was investigated by Parsa et al. [236] for a substrate temperature variation of 47, 64, 81 and 99 ◦ C. Butanol is a ‘‘self-rewetting’’ fluid that shows inverse Marangoni effect [237], i.e., beyond a certain temperature, its surface tension increases with temperature instead of decreasing. Different deposition patterns were observed depending on substrate temperature. At temperatures of 47 and 64 ◦ C, a vigorous chaotic flow was observed at first, followed by an outward capillary flow that drove the nanoparticles towards the triple line and stopped at the edge. With increase in the temperature difference between the substrate and the drop apex, thermal Marangoni became stronger than capillary effect and the nanoparticles moved back radially to the top surface of the drying droplet where they formed a ring-like cluster. This ring-cluster descended towards the substrate with further drying as the droplet height decreased. At the final stage of the evaporation, the triple line depinned and the nanoparticle cluster moved towards the depinned triple line, leading to the deposition of a secondary ring on the substrate, Fig. 25(b and c). Pinning allows more nanoparticles to deposit at the TPCL of an evaporating droplet, acting as a potential energy barrier preventing the depinning of the droplet [238]. The droplet depins when this energy barrier is overcome by an excess of free energy arisen from changes in the shape of the droplet [239]. Increasing the substrate temperature and hence enhancing the evaporation rate causes higher accumulation of nanoparticles at the triple line. As the value of the excess free energy is an increasing function of nanoparticle concentration more liable to cause droplet deformation, in some cases with a high evaporation rate, the excess free energy can be equivalent to the energy barrier causing the slip of the TPCL. The depinning triple line tends to reach a more energetically favorable position. Parsa et al. [240] had reported that the higher evaporation rate enhanced nanoparticle velocity, which arrived more rapidly at the depinned triple line, leading to a larger secondary ring. Accordingly, in this case too, the higher the substrate temperature, the larger was the secondary ring observed.

26

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 26. SEM of dried particles removed from the levitator chamber at the end of single-droplet drying (a) 3.7 wt% itraconazole + 4.7 wt% PVP in DCM/Ethanol (90:10). (b) 3.1 wt% itraconazole + 4.7 wt% PVP in DCM/Ethanol (30:70). (c) 4.7 wt% PVP in DCM/Ethanol (30:70). (d) 3.7 wt% itraconazole+ 4.7 wt% HPMC in DCM/Ethanol (70:30). (e) 3.1 wt% itraconazole + 4.7 wt% HPMC in DCM/Ethanol (40:60). (f) 4.7 wt% HPMC in DCM/Ethanol (70:30). Source: Reproduced from [242] with permission of Elsevier.

At higher temperatures of 81 and 99 ◦ C, transition from an initial chaotic flow to slower and regular flow occurred, accompanied by two distinctive counter-rotating vortices. The inverse Marangoni effect shown by butanol, comes into play increasing the surface tension at the TPCL where temperature is higher than at the apex. This is responsible for the thermal Marangoni flow that is generated from apex to TPCL along the air–droplet interface. The competition between the capillary convection and the inverse Marangoni flows is responsible for the stick–slip deposition pattern observed at 81 and 99 ◦ . The ring-like cluster on the top of the evaporating droplet at 99 ◦ C did not deposit the secondary ring on the substrate, as a part of the triple line pinned and depinned several times leading to the slip–stick pattern, Fig. 25c. 4.4. Evaporation of acoustically levitated droplets of binary liquid mixtures The evaporation of a multicomponent droplet in stagnant, convective, or acoustic environment inevitably results in heat transfer and diffusion of components inside the droplet. Yarin et al. [241] investigated both theoretically and experimentally, the evaporation of acoustically levitated droplets of binary liquid mixtures. The theoretical description of the mass transfer, the diffusion equation inside the droplet was solved by the authors. Experiments on the evaporation of single droplets levitated in an ultrasonic levitator were carried out. For the theoretical description of the mass transfer, the diffusion equation inside the droplet is solved. The authors measured the temporal evolutions of the drop surface and the aspect ratio of the drop contour, along with the temporal derivative of these parameters. These measurements gave the of mass flow rate from the droplet surface. Comparison of the theoretical and experimental results yielded reasonably satisfactory agreement. Wulsten et al. [242] used the single-droplet drying levitator using two solutes – a drug and a polymer, in a binary mixture of Dichloromethane (DCM) and ethanol – to determine how the solvent system influenced the drying rate and dried particle morphology. The polymeric component determined the drying rate, whereas the drug determined the end particle morphology. Since DCM evaporates preferentially at early times, the droplet surface temperature changed during drying as the composition of the binary mixture moved towards that of the less-volatile component ethanol. High fractions of DCM produced a smooth particle surface, while the surface became more structured with an increase in the fraction of ethanol in solution, Fig. 26 (a and b). The polymers studied were polyvinylpyrrolidon (PVP)/hydroxypropyle methylcellulose (HPMC), while the drug was itraconazole. Though the drug did not affect the precipitation time, its absence from the solution changed the appearance of the dried drop, (Fig. 26c). The particle collapsed and had a smooth surface that no longer showed the structured appearance seen with the drug formulation. When the same series of experiments were performed with a polymer of lower solubility in the solvent, skin formation was observed in the early drying stage itself, leading to rapid precipitation. The absence of the drug from the solution changed the dried drop appearance to a smooth collapsed state as before, (Fig. 26d–f).

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

27

Fig. 27. Sketch of the colloidal array accumulated at the free surface due to solvent evaporation. (a)–(c) a film: (a) initial stage of the film: colloidal particles are homogeneously distributed inside the solution; (b) and (c) about a half of the solvent has evaporated; (b) diffusion dominates: colloidal particles are homogeneously distributed inside the solution; (c) evaporation dominates: the colloidal array accumulated at the free surface of the film. (d) and (e) a sessile droplet: (d) particles accumulate near the drop edge due to the outward flow; (e) due to high evaporation, the particles accumulate at the drop free surface forming a skin.

5. Crust formation We are all familiar with skin formation on a drying viscous emulsion or suspension. A drop of paint spilt while painting the window, or a cup of creamy milk or thick soup left to cool soon forms a semi-solid wrinkled layer on the surface. ‘‘Skin’’ and ‘‘crust’’ refer to hard/solid layers formed on top of drying suspensions or concentrated solutions. The terms are essentially synonymous and have been used interchangeably by different authors. Wrinkling or buckling is a characteristic of elastic materials, so skin formation implies a transition from viscous to elastic behavior. ‘‘Wrinkling’’ and ‘‘buckling’’ both refer to a deviation of a smooth flat surface to a more complex morphology. However, whereas ‘‘wrinkling’’ indicates transformation to a corrugated rough surface, ‘‘buckling’’ usually refers to the instability behavior of elastic materials that a sudden change in curvature is caused by a critical lateral compression. In this section the crust/skin formation and the associated buckling instability are discussed in some detail. 5.1. Phenomenology The drying of complex fluids involves a large number of microscopic phenomena including emergence of concentration gradients [243]. These gradients may lead to formation of a glassy, gelled or porous skin (also denoted as a crust or an envelope) subjected to mechanical stress. When the initial concentration of solute is high enough or when evaporationinduced increase of the solute concentration dominates over its diffusional relaxation, desiccation leads to a skin formation at the free surface of drying solution [38] (Fig. 27). Usually, the skin hinders further solvent evaporation and slows down the entire film formation process. Moreover, buckling instability may occur due to presence of the skin [176,181,244,245]. A comprehensive review of both experimental and theoretical work has been presented by Routh [246]. The recently published review [37] is partially devoted to vertical and horizontal drying of droplets, including skin formation. We start our consideration with films, since flat surfaces are simpler for discussion. The model [247] utilized the concept that strong diffusion of the solute leads to a uniform film profile, whilst weak diffusion of the solute leads to skin formation. A simple model has been proposed for the skin formation in the evaporation process of a polymer solution at a free surface [248]. In this model the skin was regarded as a gel phase formed near the free surface. The dynamics was described by a diffusion equation for the polymer concentration with moving boundaries. It was shown that the skin phase appears when the evaporation rate is high or when the initial polymer concentration is high. An analytical expression was given for the criterion for the skin phase to be formed. The well-structured skin phase could be observed when Pe >

φg − φ0 (1 − φ0 )φ0

,

(25)

where the Péclet number is defined is this context as Pe =

h0 J D

,

(26)

where h0 is initial thickness of the layer of polymer solution, J is the evaporation rate, D is the diffusion coefficient, φg is the critical volume fraction of polymers when the polymer solution becomes a gel and a skin phase is formed, φ0 is the initial volume fraction of polymers [248].

28

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

In fact, the Péclet number is the ratio of two characteristic times, viz., the time of diffusion relaxation, td , and the time of evaporation, te . The first one is td =

h20

.

D The second one may be estimated as initial height of the film divided by the rate of the free surface decreasing te =

h0 J

.

When Pe < 1, the drying process is regarded as a slow process and the evaporation-induced concentration gradient can be flattened by diffusion, leading to a uniform concentration profile. When Pe > 1, the drying is fast enough and the concentration gradient increases with time and the solute accumulates near the solution–air interface. These two distinct scenarios are sketched in Fig. 27(b) and (c). The rate of drying is as well a key feature in the case of drop drying. In the case of drops, the Péclet number (Pe) is defined as the ratio of R2 and Dτ , where R is the radius of the droplets, D is the diffusion coefficient of the colloidal particles in the droplet, and τ is the time of drying. When the droplet dries rapidly enough, particles tend to accumulate at the air–liquid interface rather than at the drop edge [249] (compare Fig. 27(d) and (e)). Recently, a minimal model of solvent evaporation and absorption in thin films consisting of a volatile solvent and non-volatile solutes has been presented [250]. The model can predict the dynamics of drying and film formation, as well as sorption/desorption, over a wide range of experimental conditions. It is worthwhile to mention that the evaporation-driven accumulation and the diffusion relaxation are not sole mechanisms of the spatio-temporal redistribution of the particles inside evaporating drops. Another important mechanism is the advection, i.e., outward flow leading, particularly, to the coffee ring formation. Skin formation is hardly possible when the outward flow makes the main contribution in particle redistribution. In this way, skin formation is mainly associated with uniform evaporation, examples including drying in a thin-film geometry [247], evaporating a spherical droplet on a superhydrophobic surface [251], during spray drying [252], and in levitated drops (e.g., Leidenfrost drops [253] and in acoustically levitated drops [254]). In these cases, the evaporation is uniform, hence, the outward flow induced by nonuniform drying cannot arise. Consequently, redistribution of the particles takes place in the direction of the evaporation. 5.2. Crust morphology and buckling instability The crust may become unstable due to the evaporation stress acting against its mechanical properties. The instability may lead to various crust morphologies, wrinkles [255], buckling [3], bowl shape and donut [254]. This is attributed to the elastocapillarity behavior [256] in the drying droplet which is similar to the phenomena observed in other soft materials [257–259]. The morphology and surface properties of crusts of drying of suspensions are strongly influenced by the general dynamics of the drying process, interplay between several physico-chemical parameters, such as operating conditions (e.g., temperature), initial particle concentration, and material properties [260–264]. The final structure of the skin depends on the evaporation rate [251]. When the evaporation is slow, the solutes have enough time to adjust and form an ordered structure. When the evaporation rate is high, disordered structure forms. This behavior resembles formation of wellordered and disordered annular structures near the drop edge [72,265,266]. Sen et al. [252] investigated the effect of the concentration of suspended particles on the morphological transition in spray drying. Low particle concentrations led to the creation of a donut-like grain as a result of droplet drying, whereas, increasing particle concentration resulted in the formation of spherical grains due to reduction of deformation during drying. The importance of competition between diffusion and convection during the formation of large porous grains formed during the drying of suspensions was illustrated by Tsapis et al. [267]. Although initially the droplets behave like pure liquids and shrink isotropically, eventually the formation of a viscoelastic shell of densely packed particles forms at its surface. This occurs due to a thermophoretic force, which originates from the temperature gradient at the surface of the droplet and moves the colloids to the air–water interface. Such a shell is produced initially and gets thicker as the droplet shrinks. However, at a certain instant, the capillary forces driving the deformation of the shell overcome the electrostatic forces stabilizing the colloidal particles. The shell becomes elastic and undergoes a sol–gel type transition and then buckles. This gives rise to donut-like particles with a central hole. Moreover, this process depends significantly on the volume fraction of particles in the droplets. If the number density of particles is less, the above process becomes more favorable than the situation where the number density of the colloidal particles is more. A high particle concentration significantly hinders the buckling process because of the inherent constraints of availability of space. A model balancing particulate diffusion with the evaporation rate during drying, with careful control of the drying dynamics, was used by Trueman et al. [268], to manipulate film morphology in the presence of different sized particles. This led to stratification in the drying films. Osman et al. [269] tracked the temporal development of the aspect ratio of droplets containing micro- and nanosized dispersions. The micro-particulate droplets showed apricot-like morphology,

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

29

Fig. 28. Characteristic diagram showing the aspect ratio of particles versus Péclet number (Pe) obtained from the drying of suspensions of different particle sizes, initial volumes, and initial particle concentrations. Source: Reproduced from [269] with permission of the American Chemical Society.

with cavities inside the shell. On the other hand, the nano-particulate droplets shrunk to dense spherical grains. The authors show that the drying behavior and the assembly of the final grains are significantly influenced by the particle size, particle concentration, and initial droplet volume. The observed morphological difference was shown to be the result of the competition between diffusion and convection during drying. The authors proposed a characteristic curve that showed the variation of the aspect ratio of particles, with a Péclet number that encompassed all the above mentioned parameters (Fig. 28). Kumar et al. [270] studied the structural morphology of acoustically levitated and heated nano-silica droplet. For all particle concentrations, they reported three phases: solvent evaporation, surface agglomeration, and precipitation that lead to bowl or ring shaped structures. The rate at which the temperature rose in the droplet, was governed by the structure geometry, position with respect to the heating source and speed of rotation induced by the acoustic field of the levitator. With non-uniform particle distribution, these structures experienced rupture that in turn modified the droplet rotational speed. Buckling typically occurs in elastic systems. A flat spring compressed from both ends, can become unstable at a critical stress and take a curved shape, storing the excess energy as elastic energy. Buckled donut grains have been observed in the case of dried droplets of colloidal silica nanoparticles by Bahadur et al. [10], which was explained in terms of a theory of homogeneous elastic shell under capillary pressure. The authors demonstrated that the shell formed during drying of colloidal droplet in the presence of a polymer of high molecular weight, became inhomogeneous due to the presence of soft polymer rich zones on the shell. These zones acted as buckling centers, resulting in bucky-ball type grains. A bucky-ball is the geometric structure of the C60 molecule resembling a soccer ball. Bansal et al. [271] investigated vaporization, self-assembly, agglomeration, and buckling kinetics of sessile nanofluid droplets of aqueous Ludox TM-40 colloidal silica suspension, on a hydrophobic substrate. Droplet lifetime started with evaporation-induced preferential agglomeration that leads to the formation of a unique dome-shaped inhomogeneous shell with a stratified varying-density liquid core. Capillary-pressure-initiated shell buckling and stress-induced shell rupture followed, with rupture-induced cavity inception and growth during the last phase of the droplet lifetime. Chen and Evans [272] have also shown that if two droplets are placed in close proximity to each other the air in their vicinity quickly gets saturated with vapor, thereby leading to local suppression of evaporation. This alters both the location of the buckling site and the buckling pathway. Fu et al. [273] proposed a differential shrinkage approach to describe the particle formation behavior of different materials, by evaluating how the droplet shrinkage kinetics of a material deviates from the ideal shrinkage. For drying of droplets with low solid content, shrinkage kinetics is commonly assumed as ideal shrinkage [274,275]. However, this assumption may considerably deviate when drying process is dominated by the solid fraction, specially at the later stage of drying or during drying of droplets with a high solid content. Using sucrose as the reference material to establish ideal shrinkage kinetics, the authors compared the differential shrinkage kinetics of sucrose, lactose, and mannitol to show that a strong crust-forming tendency, cannot be explained by difference in the solubility of the three materials. By establishing a differential shrinkage curve for each material, they offered a method to evaluate the particle formation property of the material at various initial concentrations. Simulation models for the study of the morphology of crusts in drying droplets have also been developed by several groups [276,277]. When a solid envelope is formed at a drop surface, the mechanical instabilities induced by the drying result in different drop shapes [176,181,244,245,253,278,279]. Detailed description of mechanical instabilities occurring when drops containing solutes desiccate is presented in the recently published review [37]. For instance, final shape of a desiccated sessile droplet may be like a ‘‘pancake’’ (Fig. 29a) or ‘‘Mexican hat’’ (Fig. 29b) [181], moreover, for a large contact angle a complex pattern progressively builds up involving a cascade of buckling that breaks the drop axial symmetry (Fig. 29c) [176,244]. During spray drying, the final shape of a drop may be spherical or donut-like (Fig. 29d) [252,280].

30

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 29. (a) and (b) Top: Evolution of dimensionless profiles of sessile drops of dextran solutions. Bottom: Side views of the drops at the end of the desiccation: the drop forms (a) a flat ‘‘pancake’’ and (b) a typical ‘‘Mexican hat’’ [176] (with permission of the American Chemical Society or American Chemical Society or American Physical Society or Elsevier); (c) the drop with broken axial symmetry [244] (with permission of the American Chemical Society or American Physical Society or Elsevier); (d) final shape of drop during spray drying is donut-like [252] (with permission of the American Chemical Society or American Physical Society or Elsevier).

Fig. 30. Sketch of hollow sphere formation during spray drying of a droplet [282] (with permission of the American Chemical Society or American Physical Society or Elsevier).

The final droplet volume and the radius of curvature at the buckling onset were found to be universal functions of particle concentration [279]. Recently, detailed analysis of the conditions for buckling of drying colloidal spherical drop has been presented [281]. The fundamental mechanism responsible for buckling in drying drops of colloidal dispersions has been elucidated. 5.3. Cavity formation There is another way of storing energy besides elastic energy through buckling and that is by creating excess surface area which stores surface energy. This is what leads to cavitation. The new surface can have different forms. It may be spherical, like a bubble or a disc shaped particle can develop depressions on both sides, which merge, turning the disc into a donut. Further details are discussed in this section. Crust formation is often accompanied by a cavity (vacuole) formation. Different situations can be distinguished. During spray drying, evolution of a droplet of a soft matter solution is completed as a hollow sphere [282–284] (Fig. 30). Similar behavior can be observed when droplets are drying out on superhydrophobic surfaces [279] and for pendant drops [285]. Post-buckling cavity growth was established to be evaporation-driven regardless of the substrate [279]. When a film evaporates, bubbles often appear in the solution after the skin is formed [286]. Bubble formation depends on the evaporation rate. Thus, no bubbles appear at low evaporation rate; isolated bubbles appear at moderate evaporation rate; many bubbles form at high evaporation rate [286]. A theoretical model is given for this phenomenon. It is shown that the formation of a gel-like layer (skin layer), which has a finite shear modulus, is essential for the phenomenon to take place. The condition for cavity formation (how it depends on the shear modulus and thickness of the skin layer), and the variation of the droplet volume and cavity volume after cavity formation are examined [282].

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

31

Fig. 31. Radial cracks in drying colloidal PTFE droplet [255]. The scale bars represent 200 µm. Source: Reproduced from [255] with permission of Springer Nature.

6. Crack patterns We have discussed some phenomena such as buckling and wrinkling in Section 5, which arise during droplet drying and add to the richness in the variety of patterns formed. In this section, we discuss another type of instability: the formation of cracks in the residue left on a substrate after drying. Although the residual crack patterns are quasi-two dimensional morphologically, the third dimension (thickness, which varies in a sessile drop from the TCL to the drying front) of the drying layer plays an important role in determining both the crack dynamics and its patterns. Crack formation due to desiccation is an active research topic in its own right [287] but drying of a sessile droplet has special features not observed in a thin flat colloidal layer. The typical shape of the drying interface usually resembles a section of a sphere. This imposes the symmetry of the interface on the pattern, resulting in the predominance of radial or orthoradial symmetry in the cracks formed. In several examples discussed below, we find crossover behavior between these two principal crack geometries, attributed to various factors such as droplet composition, substrate wetting [288] and ambient conditions, principally temperature and humidity [35,289]. The study of crack formation in multi-component droplets has become particularly important, because of its practical applications. Study of patterns formed on the residue of dried biological fluids has long been an economical and simple method for medical diagnosis [290]. In Section 8.4.1, we shall describe in detail how the morphology of crystals and crystal aggregates of chemical constituents in biological fluids, such as blood, plasma, tear-drops and saliva serve as a guide to medical diagnostics. Cracks in the deposit are a part of this morphology. In this section, we discuss the formation of cracks observed in dried droplets. 6.1. Mechanisms The evaporation-induced stress is compression because it results in a negative pressure inside the gelled film. However, the gelled film usually adheres to the substrate. This leads to the build up of tensile stress in the deposited film. Once the tensile stress exceeds its mechanical strength, a crack emerges. It should be noted the substrate adhesion plays a very important role in crack formation and propagation. If the substrate is extremely slippery, the gelled film would shrink uniformly, therefore suffering no tensile stress. During drying of a droplet with colloidal particles suspended in a solvent, the Péclet number Pe (26) plays an important role [287]. The solid particles tend to be driven to the surface by the process of advection, while the solvent diffuses through the particles and leaves the droplet by evaporation. If diffusion is fast, the composition of the fluid remains uniform throughout, but if it is slow, the colloidal particles tend to aggregate at the surface and form a solid skin Section 5. If the particles interact strongly, sufficient energy is not available to break the skin and form cracks. The skin, being a section of a sphere has an area larger than the flat contact area between fluid and substrate. As the remaining fluid below it dries out slowly, the skin collapses onto the substrate like a loose cover, forming folds and wrinkles. In the opposite case of fast diffusion and evaporation of the solvent, a continuous unbroken skin cannot form. However, if the concentration of solute particles is high, the particles form weak aggregates, which the solvent can ‘‘crack’’ while escaping. The solvent is drawn to the surface through pores between the particles, by capillary action as described in [287] as solvent escapes, negative pressure i.e., compression results within the drop. If the drop material slips against the substrate, i.e. gel–substrate adhesion is very weak, the gel can shrink without deformation. However, if the gel adheres strongly to the substrate, stress builds up, which may ultimately cause cracking of the surface. We discuss some typical crack geometries, which have been observed, in the next section. Zhang et al. [255] studied crack formation in a suspension of PTFE droplets with varying particle concentration (Fig. 31). They show that crack formation is preceded by wrinkles forming in a radial pattern and the cracks appear along the ridges. It is well known that in layers containing granular material a critical cracking thickness hcct is required for crack formation [291]. Thinner layers do not crack, but above hcct crack spacing increases with the layer thickness. Roughly,

32

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 32. Crack formation in clay droplet under DC field. On the left with the central electrode positive, a few cracks appear at the center. On the right, with center negative a large number of cracks appear at the periphery [292]. Diameter of the ring is 1.8 cm. Source: Photo courtesy Somasri Hazra.

the average spacing between adjacent cracks is proportional to the thickness. This principle works for droplets as well, remembering that in the droplet the height of the fluid layer increases from the periphery to the center, this however may be reversed in a dried residue exhibiting coffee ring effect. 6.2. Factors affecting crack morphology 6.2.1. Cracks under electric field Another area of study on cracks formed in drying drops is the effect produced by applying an electric field while the drop dries. We discuss this in some detail. Aqueous slurries of various clays carry charge, as the clay particles become negatively charged due to positive cations leaving the clay platelets and forming a double layer. The response of clay suspensions to an external electric field thus becomes an interesting subject for study. Khatun et al. [292,293] have dried drops of clay slurry, placed in a cylindrical DC(direct current) field. The crack patterns are strongly affected by the direction and magnitude of the field. The synthetic R clay Laponite⃝ with disc-shaped monodisperse and nanosized particles has been used in these experiments. The drops are ∼1 cm in radius with a circular ring-shaped electrode at the periphery. The counter electrode is a thin wire placed at the center of the drop. When a DC voltage of the order of 4–10 V is applied, cracks appear at the positive electrode (Fig. 32). When the central electrode is positive, the number of cracks is 3–4, but when the peripheral electrode is positive, the number of cracks increases and the time of first crack appearance decreases as the applied voltage is increased. Another interesting feature is noted, which can be interpreted as a memory of the field retained by the drop. In this case, the applied voltage is switched off after a time interval of the order of seconds before cracks appear. The appearance of cracks is then delayed. Scaling relations have been obtained connecting the number and time of appearance of the cracks with the time of exposure to the electric field. Hazra et al. [293] later showed that the memory effect can be interpreted by modeling the gelled drop as a leaky capacitor, utilizing generalized calculus. Additional information regarding formation of desiccation crack patterns in electric fields can be found in a just published review [294]. 6.2.2. Magnetic field effects Magnetic fields affect the desiccation residue and crack patterns formed, when the droplet contains magnetic particles. Lama et al. [289] subjected droplets containing anisotropic hematite particles to magnetic fields during drying. They observed competition between the hydrodynamic torque acting on the particles and the applied magnetic field causing the cracks to switch direction. In a subsequent paper [295] they showed that thermal effect on the cracks can be reversed by application of a magnetic field. Pauchard et al. [296] had shown the crack patterns in the drying of a ferrofluid drop can be varied using external magnetic field which can modified the stress in the gel zone. Based on the shape analysis of the cracks, it is possible to obtain an estimation of the Young’s modulus of the gel. 6.2.3. Effect of salinity It has been demonstrated that the effect of adding salt to a colloidal droplet causes remarkable changes in the desiccation crack patterns [297]. This effect occurs because excess salt tends to screen the charges on colloidal particles causing coagulation and gel formation. It is well known that suspensions, which gel give, rise to three typical crack morphologies during drying (Fig. 33). (i) For very low salt content, the outer part of the circular drop, near the periphery gels faster forming the so-called foot, while the inner circular region, termed the cap is still fluid. Cracks now start at periphery, which has gelled and then proceed radially inward, up to the end of the foot. The resulting crack pattern looks like regularly spaced petals of a flower.

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

33

Fig. 33. The effect of varying salinity [297]. Source: Reproduced from [297] with permission of American Physical Society.

(ii) On slightly increasing the salt content, the inner cap region forms a skin, which may buckle inward. For such intermediate salinities, a crack starts at the periphery, but proceeds right across the center, then loops back. Random cracks appear later. (iii) When salt content is still higher, such that the whole drop gels rapidly, a single circular crack is formed, close to the drop periphery. Similar patterns may appear in dried blood droplets. Development of radial and orthoradial cracks in biological fluids is discussed in further detail in Section 8.4.1. 6.2.4. Substrate wetting McQuade and Vuong [298] recently studied the effect of substrate wetting on crack morphology in dried drops of the polymer PEDOT:PSS, which changes the solvent retention and hence drying kinetics. According to this study, a poorly wetted substrate leads to a film thicker than the critical cracking thickness [291], where radial cracks predominate. Orthoradial cracks are the result of stick–slip motion at the periphery, for small contact angle between the drop and substrate. Intermediate patterns with both radial and orthoradial cracks have also been observed. Therefore, the contact angle is another feature that can be used to design cracks for particular applications. 6.2.5. Substrate heating Heating the substrate during droplet drying has also demonstrated interesting changes in the crack patterns. When the temperature between substrate and ambient is considerable, the temperature at the TPCL is at the surface temperature while the temperature at the drop center is at the ambient temperature. This temperature gradient sets up thermal Marangoni flows inside the drying droplet, the direction of the flow decided by whether the substrate temperature is higher or lower than the ambient. In colloidal droplets, the effect of buoyancy driven flows is also important and mass transfer of the colloidal particles is finally determined by a competition between Marangoni, viscosity and gravity effects. While the accumulation of the colloidal particles are determined by the internal flow patterns, the ratio of desiccation and gelling times of the colloid generate stress within the drying droplet that fructify into cracks. It is important to note that a liquid of low thermal conductivity compared to that of the substrate is important in order to observe the effect of substrate temperature in drying droplets. Lama et al. [289] dried aqueous dispersions of negatively charged silica nanoparticles with substrate temperature varying from 25 to 70 ◦ C. For low temperature, they find disordered cracks around the periphery, as temperature is increased to 50 ◦ C, peripheral cracks organize to the regular flower-petal like pattern observed by [297]. This is also attributed to gel-like aggregation around the TPCL due to enhanced capillary flow. In addition there appears a central aggregate which has been named as the coffee-eye by Li et al. [299]. Although, the authors conjectured that the disorder in crack patterns is mainly due to the increased height gradient of the particulate deposit near the TPCL, this effect can be understood in terms of desiccation and gelation times [297]. 6.3. Wavy and spiral cracks Cracks normally tend to grow straight, but Goehring et al. [287] have discussed several instances, where instabilities lead to interesting deviations from the straight path. Sinusoidal cracks are seen to grow in the gaps between a set of parallel cracks [300]. The earlier formed straight cracks have released the parallel stress close to it, so a new crack developing in between two such cracks tends to approach one of

34

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 34. Wavy and spiral cracks in droplets of egg white [301]. Source: Reproduced from [301] with permission of Springer Nature.

the straight cracks normally and bends towards it. However, when it moves closer to a straight crack, the central region between the parallel pair appears more stressed and thus the crack bends back across the central region and moves towards the other parallel crack. The process now repeats, so the new crack moves in a sinusoidally varying pattern as discussed in [287]. In drying droplets and films, once the thick coffee ring has formed, a similar process may occur if a crack initiates between the inner and outer periphery of the coffee ring. Such cracks have been studied by Gao et al. [301] who call them ‘‘wavy-ring cracks’’. Another interesting formation reported long ago [302] in egg albumin is the pattern of spiral cracks. These are easily observed by allowing egg-white to dry in a Petri dish [287]. The film first cracks into polygonal segments, then a spiral appears in the center of each segment. A drying droplet of aqueous egg-white also shows this behavior on a smaller scale [301]. The spirals form as the polygonal segment starts to delaminate from the edges, with the central portion still attached to the substrate (see Fig. 34). 6.4. Propagation dynamics Our field of study being droplets, the system size is small—of the order of cm or mm to µm or even nm length scales. Observing and measuring crack propagation dynamics at these scales is a problem not addressed by many investigators. At larger scales, one usually relies on LEFM (linear elastic fracture mechanics) [303] to understand crack propagation. When instabilities take over, deviating the crack from a straight path to more exotic shapes LEFM may be inadequate. General discussions on crack propagation dynamics in presence of instabilities are reviewed by Bouchbinder et al. [304]. They point out that the crack propagation velocity depends on the magnitude of the elastic modulus of the material, so in normal brittle solids, the crack velocity needed to trigger unstable behavior is extremely high. This makes study of softer materials, such as gels much more amenable to observation and analysis since instability sets in at much lower crack propagation velocities due to the elastic modulus being lower by several orders of magnitude. The fact that drying droplets and gels belong to this regime of soft materials, makes the study of crack dynamics with instabilities very relevant to the area of this review. We may hope that more work in this area will be coming soon. Some studies where the dynamics of crack propagation in droplets has been addressed are, e.g., work by Zhang et al. [255], who observed that the radial cracks propagate towards the center with a velocity v depending on the thickness of the film H as V ∝ H 3/5 .

(27)

It should be noted that H is not uniform over the whole area for a sessile droplet. Therefore, the crack propagation velocity would be spatially dependent. It has also been found that the crack propagation direction can be reversed by using an appropriate amount of surfactant. In another paper interface crack dynamics has been studied using traction force microscopy by Xu et al. [305], from which the spatial distribution of the stress near the tip of a propagating crack can be obtained. 6.5. Suppression of cracks We will see in Section 8.4.1 that cracks in dried droplets can be useful for diagnostic or analytical purposes and even as templates for nano-patterning. However, in many applications utilizing drying fluid droplets or films, such as inkjet printing or applying a thin coating of paint or protective material one ideally hopes for a uniform and continuous distribution. Presence of cracks or non-uniformities such as the coffee ring or coffee-eye are to be avoided. Therefore, techniques for suppressing crack formation are in great demand and research continues to look for such methods. General principles for crack reduction in thin films are of course applicable in case of dried droplets as well. The following methods of crack reduction are expected, in general, to work

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

(i) (ii) (iii) (iv)

35

keeping the thickness of the dried layer below the critical cracking thickness [291], ensuring good spreading by choice of an appropriate fluid–substrate combination or adding a surfactant, adjusting ambient conditions for slow drying, increasing mechanical strength of system by a suitable additive, e.g., a polymer.

These approaches can either reduce the evaporation stress (using surfactant additives to lower the surface tension) or enhance the mechanical strength of the deposited film (for instance adding polymers in colloidal drops). Crack suppression techniques specific for dried droplets have been discussed by Kim et al. [306]. They use confocal microscopy to show that adding the non-adsorbing polymer, polystyrene (PS) to a colloidal suspension of polymethyl methacrylate (PMMA) particles induces gelation and suppresses crack formation, reversing the coffee ring effect in droplets. The underlying principle is the same as demonstrated by Nag et al. [307] for crack suppression in thin layers of clay on adding a polymer. Zhang et al. [255] show that the surfactant SDS can be used to reduce and even fully suppress crack formation in colloidal droplets with PTFE particles. This results from Marangoni flow, which competes with the capillary flow. 7. Simulation and modeling For droplets containing complex fluids with soluble and insoluble solid inclusions, a full mathematical analysis of processes, leading up to the completely dried pattern, is extremely difficult, if not impossible. Attempts at understanding or predicting the outcome in various situations are therefore heavily dependent on ‘‘computer experiments’’ and numerical simulations. We present here an outline of the methodology and summarize work in this direction. 7.1. Models of evaporation In this subsection, we will pay attention only to evaporation of sessile drops; we refer the readers to the review [308] devoted to the evaporation of spherical droplets. Additional information on evaporation of both spherical and sessile drops may be found in the reviews [26,28]. Several reviews are devoted primarily to the evaporation of sessile drops [31,34,35]. Several distinct situations should be considered separately. The simplest case is evaporation of the sessile drop of a pure liquid when its contact line is pinned during the entire time of evaporation. Even in this simplest case, two assumptions are made in most calculations: the evaporation process is treated as a quasi-steady state, and vapor is transported solely by diffusion (convection is neglected) [32]. Diffusion of vapor into the ambient space obeys the diffusion equation [83,100]

∂u = ∇J, ∂t

J = −Dv ∇ u,

(28)

where u is the concentration of vapor, Dv is the diffusivity of the vapor in air, J is the evaporating flux. Since the evaporation is assumed to be a steady state process, i.e., ∂t u = 0, Eq. (28) reduces to the Laplace equation

∇ (Dv ∇ u) = 0.

(29)

Both Eq. (28) and Eq. (29) are subject to the boundary conditions, viz., far from the drop free surface, the concentration of the vapor corresponds to the ambient vapor concentration u(∞) = u∞ and, just above the liquid–air interface, the density of the vapor equals the density of saturated vapor ufree surf. = us . The latter assumption needs to be additionally explained. First of all, the shape of the drop should be stated. For a drop of capillary size, i.e., when the surface tension dominates over gravitational effects, the shape is assumed to be a spherical cap. This assumption is valid when the Eötvös number (Eo) also known as the Bond number (Bo) Eo = Bo =

ρ gR2 σ

(30)

is small. Here, g is the gravitational acceleration, ρ is the density of the fluid, R is the contact radius, and σ is the surface tension. Moreover, this shape is assumed to be insensitive to any flow inside the drop. Therefore, the viscous forces should be smaller than the surface forces, i.e., the capillary number Ca =

vη σ

(31)

should be small. Here, η is the dynamic viscosity and v is some characteristic value of the flow velocity. Examples of distortion of the shape of the drop at different evaporation modes can be found in Ref. [309]. When all above assumptions are valid, the Laplace equation may be solved using the electrostatic analogy (see [310] and correction [311]). The exact analytical expression obtained for the absolute value of the evaporation rate, J, as a function of radial coordinate, r, for arbitrary contact angle, θ , is rather complicated J(r) =

Dv (us − u∞ ) R

×

36

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 35. Sketch of possible drop shapes near the contact line.

(

1

sin θ +

2

√

2(cosh α + cos θ )3/2

∞

∫ 0

cosh θτ cosh πτ

tanh[(π − θ )τ ]P−1/2+iτ (cosh α )τ dτ

)

,

(32)

where P−1/2+iτ are the Legendre functions of the first kind. The toroidal coordinate α is uniquely related to the polar coordinate r on the surface of the drop as r =

R sinh α cosh α + cos θ

.

(33)

Nevertheless, the formula (32) reduces to simple and compact form in two limiting cases [311], viz., J(r) =

Dv (us − u∞ ) 2

√

R2 − r 2

π

,

if θ → 0,

(34)

,

if θ → π/2.

(35)

and J(r) =

Dv (us − u∞ ) 2

π

R

Naturally, evaporative flux is independent of the radial coordinate, r, in the case of a hemispherical drop Eq. (35). By contrast, due to the assumption that the drop is a spherical cap, i.e., its edge is infinitely sharp (Fig. 35), a singularity of the vapor flux arises when r = R both in the exact solution (32) and in the simplified one (34). This physical inconsistency may be eliminated by introducing a correcting factor [312,313]. For the arbitrary angles, the evaporative flux is well fitted by the formula [83] J ∝ (R − r)−λ ,

λ=

π − 2θ 2π − 2θ

.

(36)

A possible way of considering a more realistic situation is taking into account a precursor film (Fig. 35). Recently, more accurate calculations of the evaporation rate of sessile drops has been presented [314]. The proposed fitting formula is valid for a practical range of contact angles 8◦ ≤ θ ≤ 131◦ . An additional source of the drop shape distortion is Marangoni or thermocapillary flow [315]. We briefly recapitulate the basic facts described in Section 2.3. Due to evaporative cooling produced by nonuniform evaporative flux, thermal gradients appear along the interface. These thermal gradients induce surface tension variations with the surface tension being lower where the temperature is higher and vice versa. As a result of such surface tension gradients, a surface flow may occur. The flow goes from regions with lower surface tension to regions of higher surface tension, i.e., from warmer parts to colder ones. The temperature of the free surface is determined not only by the evaporative flux but also by the thermal properties of a substrate [87]. That is, the direction of the flow depends on the relative thermal conductivities of the substrate, kS , and liquid, kL , reversing direction at a critical contact angle, θc , kcrit = tanh θc cot R

(

θc 2

+

θc2 π

)

,

(37)

over the range 1.45 < kR < 2, where kR = kS /kL . We should recall (see Section 2.3) that, in the case of binary mixtures or solutions, Marangoni flow may be also produced by concentration gradients (solutal Marangoni effect) [93]. Competition between solutal and thermal Marangoni flows is also possible [94]. The process of diffusion-driven evaporation of sessile droplets on a solid planar surface has been re-considered and modeled by taking into account the interface cooling which changes the saturated vapor density at the droplet surface and corrections to the available models for predicting the evaporation process were presented [316,317]. The analysis shows a significant effect of interface cooling [316,317]. When the rate-limiting step for evaporation is the transfer of molecules across the interface, evaporating flux may be estimated as follows J ∝

1 h+K +W

,

(38)

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

37

where h is the height of film or drop, K corresponds to the heat transfer through the liquid and W through the solid [26]. Here, all quantities are dimensionless. Another approach is based on molecular dynamic simulations [318]. Three evaporating modes were classified, viz., (i) the diffusion dominant mode, (ii) the substrate heating mode, and (iii) the environment heating mode. Both hydrophilic and hydrophobic substrates were considered. Unstable deposition patterns in an evaporating droplet were simulated within the model that includes both evaporative convection and the Brownian motion of weakly interacting particles by [319]. Modeling the self-assembly of nanoparticles into branched aggregates from a sessile nanofluid droplet was performed to simulate the drying process of a nanofluid droplet in a circular domain [320]. Both of these works exploited and developed the kinetic Monte Carlo approach based on the 2D Ising model proposed by Rabani et al. [321]. Summarizing the foregoing, we can conclude that the simplest approaches, which, naturally, are only the zeroth order approximations, are clear and fruitful. By contrast, sophisticated approaches must take into account simultaneously a large number of various effects, the mutual influence of which are not always completely understandable. Moreover, to the best of our knowledge, no theoretically grounded models of evaporation have yet been proposed for the drops of interest, such as particle-laden drops, drops of colloidal and polymer solutions or multicomponent drops. 7.2. 2D models of mass transfer The simplest models of mass transfer within evaporating sessile drops are based on the assumption that the drops are thin. In this case, height averaged quantities can be considered, e.g., the height averaged velocity can be considered instead of the 3D velocity field. Since the axial symmetry of the drop is often assumed, height averaged quantities, in fact, reduce the problem to a quasi-one-dimensional one, insofar as all quantities are dependent solely on one spatial coordinate, viz., on the radial distance. For a sessile drop consisting solely of a solvent, the conservation of fluid determines the relation between the vertically averaged radial flow of the fluid, v , the position of the air–liquid interface, h, and the vapor flux, i.e., the rate of mass loss per unit surface area per unit time from the drop by evaporation, J, [83]

√ ( )2 ∂h ρ ∂ (rhv ) ∂h ρ =− − J(r , t) 1 + , ∂t r r ∂r

(39)

where t is time and ρ is the density of the liquid. The equation should be rewritten in integral form to find the height averaged velocity

v (r , t) = −

1

ρ rh

r

∫

⎛

√

⎝J(r , t) 1 + 0

(

∂h ∂r

)2

⎞ ∂h ⎠ +ρ r dr . ∂t

(40)

When the shape of the drop and evaporative flux are known, the velocity can be obtained either analytically or numerically. The shape of the drop is often assumed to be a spherical cap while the evaporative flux is assumed to obey Eq. (36). In this case, edge-enhanced evaporation induces the outward flow within the drop. This outward flow is caused by the loss of solvent by evaporation. The velocity inevitably diverges at the drop edge since it inherits this behavior from the evaporative flux having a singularity at the drop edge. We should emphasize that this approach is purely kinematic since no forces are involved here. The real force driving the flow within the drop is, in fact, the surface tension (Section 2). It arises due to deviation of the free surface from the steady-state shape. This deviation leads to different curvatures along the free surface and, hence, to different values of the Laplace pressure. One of the possible ways to involve the dynamics is through the lubrication approximation or long-wave approximation [309]. Assumption that the drop is thin allows simplification of the Navier–Stokes equations and one can calculate the shape of the drop and the flow within it simultaneously when the evaporative flux is known; moreover, this approach accounts for the effect of viscosity both on the shape and the flow. When the drop is particle-laden or it contains a solute, some additional assumptions are needed to describe mass transfer of these particles or dissolved substances. The basic concept is that the admixture is passive, i.e., it has no effect on shape of the drop, internal flows, and evaporation of solvent. The solute conservation reads [83]

∂ (ch) 1 ∂ (rchv ) + = 0, ∂t r ∂r

(41)

where the concentration of solute, c, depends solely on radial distance, r. In fact, Eq. (41) is hardly applicable to solutes because diffusion is completely ignored in that approach. Absence of diffusion is reasonable when the suspended particles are large enough, however, the diffusion may be significant, e.g., for dissolved salts [322]. Diffusion can be easily accounted since the total velocity of the solute transfer is v˜ = va + vd ,

(42)

38

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

where va is the velocity of the advective transfer (transfer by the outward flow (40)) of the solute and D vd = − ∇ c (43) c is the velocity of its transfer by diffusion [322]. Competition between advection and diffusion may lead to less pronounced coffee ring effect in the case of highly diffusive solute when evaporation is slow. A model accounting for the finite spatial dimensions of the deposit patterns in evaporating sessile drops of a colloidal solution on a plane substrate has been proposed [311]. The model is based on several assumptions, particularly, (i) (ii) (iii) (iv)

the the the the

evaporation-limiting process is the diffusion; solute particles occupy finite volume; free-surface slope between the liquid and the deposit phases is continuous; evaporation from the free surface is independent of presence of the solute inside the drop.

The conditions for the applicability of these assumptions were analyzed in detail. Effect of solute on the evaporation rate has been accounted in [309,323–328]. All these approaches assume that solute suppresses the evaporation but in different manners. Moreover, impact of solute on the viscosity has been accounted in some approaches [323–326,329] using Mooney’s, Krieger–Dougherty or a fitting formula. An examination of the important groups controlling the final shape of evaporating pinned droplets containing a polymer has been performed [329]. Different additional effects can be taken into consideration. For instance, contact angle hysteresis and finite solubility have been accounted for in a model for pattern deposition from an evaporating solution [330]; particle adsorption and coagulation have been accounted for in models of deposition of colloidal particles from a sessile drop of a volatile suspension [331,332]. Summarizing, we may conclude that 2D models are useful to understand the basic mechanisms of mass transfer within evaporating drops, to capture the main effects, nevertheless, quantitative description is valid only for restricted cases, primarily, for thin sessile drops where using height averaged quantities is reasonable, and for low concentrations of solute or suspended particles. 7.3. Modeling flow in three dimensions In this subsection, we will focus our attention only on sessile drops with pinned TPCL. Some information regarding modeling flows inside drops with moving contact lines can be found, e.g., in [333]. One of the simplest models of evaporation-driven flow within a sessile drop [334] deals with a hemispherical drop. In this case, the evaporation flux is uniform over the free surface (see Eq. (35)). Inviscid flow inside such the droplet is potential (∇ × v = 0) and analytical solution of the Laplace equation can be obtained. The velocity field within a hemispherical droplet is qualitatively similar to the field in the case of a very thin drop obtained within the lubrication approximation which takes account of the viscosity [309]. Analytical solution for inviscid flow inside an evaporating sessile drop was obtained for an arbitrary contact angle and distribution of evaporative flux along the free boundary [335,336]. In all cases, the capillary flow carries a fluid from the drop apex to the contact line when the vapor flux over the free surface is uniform or edge-enhanced. Comparison of the published calculations performed using different approximations suggests that the qualitative picture of the capillary flow is almost insensitive to the ratio of the initial drop height to the drop radius and the viscosity of the fluid [336]. Effects of Marangoni stresses on the flow in an evaporating sessile droplet were investigated within the lubrication approximation [88,310]. Accounting for the Marangoni stress led to the circular flow inside the sessile evaporating drop. The evaporation rate and internal convective flows of a sessile droplet with a pinned contact line were formulated and investigated numerically for different contact angles [337]. The evaporative cooling of the free surface was accounted for. This cooling produces a temperature gradient along the free surface causing a Marangoni flow. Effect of this flow depends upon thermal Marangoni number (17). As the droplet volume decreases, the thermal gradient becomes smaller, the Marangoni flow becomes negligible, and circular evaporation-induced flow transforms into an outward flow. Different flow patterns were found during the evaporation of the drop on a solid surface by means of numerical solutions of coupled Navier–Stokes, energy and mass diffusion equations [338]. Both buoyancy and thermo-capillary (Marangoni) effects were taken into consideration. For some sets of parameters, multi-cellular convection was observed. Multi-cellular convection and its evolution to a single convection vortex has been studied within an approach which takes into account the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the drop, and the diffusion of vapor in air. A shape of the rotationally symmetric drop was determined within the quasistationary approximation. Nonstationary effects in the diffusion of the vapor were also taken into account [339]. Further studies of the vortex structures in an evaporating sessile droplet were reported in [340,341]. Particularly, the detailed description of the fluid flows was presented for a wide range of contact angles [341]. Marangoni instability was also observed during modeling the evaporation of sessile multi-component droplets [342,343]. Summarizing, we can conclude that evaporation-driven flows inside evaporating single-component drops can be described in a qualitatively correct manner even within the simplest approaches (cf. different parts in Fig. 36). Up to

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

39

Fig. 36. Example of velocity fields obtained within different approaches. (a) Potential flow inside a hemispherical drop [334] (with permission of the American Chemical Society or American Physical Society or Elsevier). (b) Flow inside a thin drop; viscosity has been accounted; the lubrication approximation [309] (with permission of the American Chemical Society or American Physical Society or Elsevier). (c) Internal flows as a result of Marangoni stresses and evaporation (with permission of the American Chemical Society or American Physical Society or Elsevier). (d) Streamlines in liquid phase, iso-concentrations in gas phase, and isotherms in both liquid and gas phases. From left to right: without thermo-capillary and buoyancy effects, without buoyancy effect, all effects considered [338] (with permission of the American Chemical Society or American Physical Society or Elsevier).

now, crust and coffee ring formation were ignored in the velocity field computations to the best of our knowledge. In the case of multi-component fluids, reasonable approaches have to account for a large number of interconnected processes of different nature and can hardly be based on hydrodynamics alone. 7.4. 3D models of mass transfer We should emphasize that, in the hydrodynamics-based models, drops are assumed to possess axial symmetry about an axis perpendicular to the substrate and going through the drop apex. Hence, any quantity of interest depends only on two spatial coordinates and is independent of the polar angle. Thus, 3D models are, in fact, 2D models. The main idea of such 3D models is very close to that which was utilized in 2D models, namely, that particles have negligible effect on hydrodynamics. The shape of a drop, evaporative flux, and flows within the drop are calculated using one of the above methods postulated. Dynamics of the particles is described by convection–diffusion equation (see, e.g., [344,345]) or Brownian particles are imposed on the flow (see, e.g., [346,347]). Presence of the particles may be accounted for in different ways, e.g., both diffusivity and sedimentation of particles have been taken into consideration in [345], effect of gravity has been accounted for in [348], whilst Marangoni effect was studied in [349]. A level-set method was applied for analysis of particle motion in an evaporating microdroplet [350,351]. Particle transport as well as the effects of evaporation, mass and heat transfer, and dynamic contact angles were taken into consideration. An alternative mechanism for coffee ring deposition based on the active role of the free surface was recently proposed [352]. The simulation demonstrated that the bulk flow within the drop may carry particles to the vapor–liquid interface. They are captured by the receding free surface. Further particle transport takes place along the interface until they are deposited near the contact line. The models based on lattice Boltzmann method [353] and molecular dynamics [354] may be treated as the real 3D models.

40

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

A three-dimensional Monte Carlo model of the coffee ring effect in evaporating colloidal droplets based on the biased random walk was proposed by [355]. Several assumptions were used, viz., (i) the shape of a pinned sessile droplet is a spherical cap with a pre-defined initial contact angle value and apex height, (ii) the droplet apex height reduces linearly with time due to evaporation, (iii) during evaporation, this shape remains a spherical cap, whilst the contact angle value continuously decreases, (iv) velocities of the particles were calculated from the analytical expressions [88,90], and (v) the computational 3D domain has a cubical lattice structure. A computational approach for estimating the ring-like deposition of nanoparticles contained in a drying liquid droplet was proposed [356]. The proposed method involves a Monte Carlo scheme, based on three independent probabilistic processes, viz., (i) evaporation at the liquid surface, (ii) convective motion of nanoparticles to the contact line, and (iii) treatment of the nanoparticles floating in the air. The computational approach achieves a morphological and kinematic description of nanoparticle-suspended liquid droplet drying. 7.5. Crystal growth We start with pure salt solutions. When evaporation is slow, the equilibrium shape of crystals is observed. Dendritic crystals may be observed when evaporation is fast, e.g., in dilute solutions at final stages of evaporation. In both cases, crystal growth simulations can be performed in the framework of conventional approaches (see, e.g., [357,358]). The situation is much more complicated in the case of multicomponent solutions, e.g., colloids with salt admixtures. Since theoretical background of the observed processes is weak, the known approaches should be treated as semi-empirical. The models often are based on the lattice approach [141,359] or on diffusion equation [182,360]. 8. Applications We have seen that drying droplets with added salts or colloidal particles create varied and interesting patterns. The kinetics of evaporation, composition of the drop and substrate, the ambient conditions and presence of other drops nearby, all have a role to play in deciding the pattern morphology. Study of the subject provides scope for development of new directions in physical science, biological science, chemical engineering and other fields. But has droplet research led to new technology and methods which are actually useful in practical situations? We have already hinted that there are several such instances. In this section, we try to identify the areas and discuss the applications in some detail. 8.1. Materials science The interdisciplinary subject of materials science has made tremendous progress in the last few decades. Most of the techniques necessary to fabricate and characterize new ‘‘smart’’ and ‘‘exotic’’ materials require specialized and expensive equipment. The droplet evaporation technique offers an inexpensive and simple process with several useful applications. 8.1.1. Self-assembly: pros and cons of the coffee ring The renewed interest in droplet evaporation research started with the work of Deegan et al. [100] and the name ‘‘coffee ring’’ became a scientific term. As we have discussed in Section 3.1, the coffee ring creates problems in processes involving spraying of a fluid suspension onto a solid substrate. If a uniform distribution of the suspended solid is desired, such as in ink-jet printing or spraying a pesticide, the coffee ring is to be avoided and research focuses on methods for suppressing its formation [36,361,362]. However, Shlomo Magdassi and his group [363,364] discovered an ingenious way to make use of the coffee ring. Transparent conductive coatings are in great demand for extensive use in everyday devices such as touch screens, LCD displays, OLED and many others. Indium Tin Oxide (ITO) and Indium Tin Fluoride (ITF) are expensive and difficult to manufacture. A fine metallic wire mesh fused into a glass sheet is a possible alternative. But here the conducting wires will normally be visible and reduce the transparency of the glass, whereas very thin and widely spaced wires will reduce conductivity. A similar idea has been implemented in an elegant way using the coffee ring effect, by drying a suspension of conducting solute particles such as silver nanoparticles or carbon nanotubes (CNT) on a transparent substrate. The substrate may be a flexible polymer sheet if desired, leading to a wider range of applications. Inkjet printing is used to deposit an array of micro-sized droplets on the surface forming a disconnected set of narrow micro- or nanosize conducting rings. To create the connected network necessary for conduction across the surface a second set of rings is deposited which cover the gaps in the first array (see Fig. 37). The ring thickness and spacing have to be worked out to optimize the maximum conductivity together with the maximum transparency.

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

41

Fig. 37. Using the coffee-ring to fabricate transparent conductive coatings. (a) On the left are shown a vertical and a horizontal set of overlapping conducting coffee rings forming a square mesh, a zoomed in view is shown in the right side. (b) details of the ring show the silver nanoparticles deposited and the height profile of the ring is shown in the inset. Source: Adopted from [364] Permissions Royal Society of Chemistry.

Another interesting application of the coffee ring has been suggested by Wong et al. [365]. They demonstrate that a suspension containing solid inclusions of varying size can be separated into rings of different radius. They demonstrate this through nano-chromatography separating a mixture of proteins, micro-organisms and mammalian cells (Fig. 38a) which have sizes varying in the range of ∼10 nm to ∼10 µm. The technique can be used for cell separation in bio-medical field. Moreover, it has great potential for the fabrication of gradient functional materials as particles of varied sizes can be arranged according to expected orders. 8.1.2. Self assembled patterns Nanoparticle assemblies with specific patterns can be created by droplet evaporation as shown by Cai and Newby [366]. They have assembled carboxylated PS nanoparticles, suspended in ethanol and water, into hexagonal or striped assemblies depending on the wettability on the substrate. Marangoni flow of ethanol into water and viscous fingering effects [367] lead to the hexagonal pattern for the silica surface with contact angle 32◦ , whereas stripes are formed on a surface with contact angle approaching to 0◦ . In brief, the mechanism for the non-wetting substrate is as follows: ethanol, being more volatile, evaporates faster at the droplet contact line, reducing the substrate temperature here. This makes water condense into a thin film surrounding the droplet. The water enters the droplet from the boundary as fingers, carrying the nanoparticles along. The elongated fingers pinch off and dry, leaving the nanoparticles as a hexagonal array of dots on the substrate as shown in Fig. 38b. On a wetting substrate the dots form striped patterns (Fig. 38c). Such techniques may be useful for creating nano-patterned surfaces for technological applications. In a related study, Jorsten et al. [368] have reported superlattice growth during evaporation induced self-assembly of nano-particles. One of the possible applications of the skin formation during droplet drying is supraball production [369]. A supraball is a particle composed of colloids. Drying of drops of aqueous colloidal dispersions on superhydrophobic surfaces can be utilized to fabricate supraballs of various sizes and compositions. The shape, crystallinity, porosity, and mechanical properties of the supraballs could be controlled by pH [369]. Supraballs are used to produce colors and have applications in photonics [370] and phononics [371]. 8.1.3. Uniform deposition It emerges from the preceding sections that producing a uniform surface by spraying droplets is not simple, as solute tends to aggregate in a peripheral ring (coffee stain) or multiple rings [148], at the center (due to Marangoni effect) or

42

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 38. Formation of transparent conductive coating via coffee ring effect. (a) Demonstrates separation of different sized inclusions using coffee ring formation [365]. (b) and (c) show respectively self-assembled hexagonal and linear striped arrays [366] formed by evaporation as described in the text. Source: Permissions of American Chemical Society.

in more exotic patterns [366]. Therefore, a lot of research focuses on creating uniform films. Kim et al. [6] noticed that a drop of whiskey spilt on a surface dries to give a nearly uniform stain. Whiskey contains, water, alcohol and particles from cereals. This led them to concoct a model fluid, which would mimic the composition of whiskey. As discussed in Section 4.2, they found that addition of a surfactant and surface-adsorbed polymer gave nearly uniform stains, and hence may be useful for controlling uniformity of commercial coatings. Other researchers have found similar results [372]. 8.2. Crystallization Crystallization of inorganic salt or macromolecules itself is of great importance in many fields ranging from Condensed Matter Physics to Structural Biology. One of the standard methods for growing crystals is to let a saturated solution dry. Crystallization in a drying droplet exhibits tremendously varied behavior as compared with drying from bulk solution, for instance, an aqueous solution of NaCl in a Petri dish will lead to formation of the familiar cubic crystals whereas a small drop of NaCl solution will on drying, give similar crystals arranged in coffee ring like pattern [139]. These differences mainly arise due to the existence of TPCL and the complex droplet-substrate interactions, which determine the heat and mass transfer inside droplet through either convection or diffusion. Therefore, the crystallization can be tuned through the factors that influence the convection and diffusion, such as substrate wettability, topological patterns on the substrate, etc. Crystals with different structure are obtained when the suspending fluid is a complex fluid like carboxy methyl cellulose (CMC), gelatinized potato starch or gelatin [139]. The details of the structure depend on the salt concentration, substrate and ambient conditions. Fractal structures and dendrites have been observed [139] and a gelatin drop with NaCl gives beautiful multifractal aggregates [182]. Recently Ahmed et al. [373] reported a new acoustomicrofluidic nebulization technique, which produced various crystal shapes by utilizing an evaporation rate intermediate between slow evaporation and spray drying. Crystallization in gel medium is known to produce larger crystals and more varied crystal aggregates [374,375], because gelation slows down diffusion. In droplets, the drop composition and ambient temperature, pressure and relative humidity lead to NaCl crystals with stepped pyramid shape, empty-box like hopper crystals, fern-shaped aggregates and other interesting forms. Droplets provide a system with varying height and evaporation rate over different positions of the drop, so different morphologies can be observed in a single drop. The substrate with the drop can be tilted to a vertical position enhancing this effect [41]. The most important application of crystal growth in droplets is in medical diagnostics. Components of biological fluids carry information about health parameters and the presence of diseases. These can be

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

43

easily identified by their characteristic morphology in dried residues of the drops. Examples will be discussed in the subsequent Section 8.4. 8.3. Quantum dots Droplet evaporation technique can be used as an alternative to or in conjunction with standard molecular beam epitaxy (MBE) for producing quantum dots (QD) [376]. This technique has the added advantage that different structured confined deposits can be obtained by varying experimental conditions. These include ring-shaped dots [377] and ‘‘inverted dots’’, which are nanoholes filled with low band-gap material [376]. Nemcsics [376] discusses QD of group III and group V materials, GaAs with AlGaAs as barrier material being a typical example. The basic principle consists of two steps. The first is generation of metallic nano-sized droplets on the surface. This is followed by crystallization to GaAs QD in arsenic atmosphere. QD with super-paramagnetic and fluorescent properties have also been prepared. These have been suggested to be useful for bio-medical applications [378]. Carbon QD are suggested to be useful in eye drops for treatment of bacterial keratitis [379]. 8.4. Applications in bioscience 8.4.1. Medical diagnosis One of the most important and well-known areas of droplet evaporation research is its application in medical diagnosis which started as early as the 1950s. With renewed interest in the coffee ring and related observations, this has become a fast developing field. Older references can be found in several review articles [11,39,40,380]. Here we focus on more recent work in this area. Body fluids, which leave dried residues having the potential for use as a diagnostic tool, are mainly the following: blood plasma, whole blood, saliva, amniotic fluid, tear drops and so on. The technique provides a cheap and easy method for a preliminary diagnosis in remote and inaccessible areas with little or no infrastructure. The signatures to look for in the dried stain may be the shape and size of crystals formed, morphology of crystal aggregates or morphology of crack patterns in the residue left after drying. We discuss some recent observations. D. Brutin and his group have been working on characterization of dried blood drops for many years. Much of their results have been discussed in the earlier mentioned reviews. Current work from this group includes: influence of evaporation rate [381], folds and delamination study [382], effect of the substrate [131] and influence of relative humidity [18,19]. While earlier studies on blood drops mainly focused on differentiation between patients with and without anemia and hyper-lipidaemia, recently diagnosis of other diseases have been discussed. Yakhno and Yakhno [25] show that a dried drop of blood serum of a patient with hepatitis B shows folds. Bahmani et al. [12] try to differentiate blood drop stains from patients with jaundice from healthy patients (Fig. 39). Bilirubin levels are found to be related to the presence of prominent cracks. Hurth et al. [383] report a technique that may lead to rapid imaging-based diagnosis of biomarkers relevant to diagnosis of several types of cancers. They discuss a model to study the possibility for characterization of a known single Nucleotide Polymorphism in the epidermal growth factor receptor gene (dbSNP ID: rs1050171). Tear drop analysis has long been a tool for diagnosing dry-eye type diseases. Usually tear drops are dried on horizontal surfaces, but López-Solís et al. [41] suggest that drying on a vertical surface will be more effective. Very intricate ferning patterns are formed in tear desiccates. The different regions are better separated and observed in a vertically dried drop by comparing horizontal and vertical stains of tear drops from the same subject (Fig. 40). Ferning patterns in other biofluids are also used as indicators of health parameters. Dried saliva patterns have been suggested for measuring level of intoxication [384] and ferning in amniotic fluid drops may be a reliable indicator of contamination [385]. 8.4.2. Other applications in biosciences Many researchers have worked on drying droplets of samples of biological origin, not directly related to medical applications. We briefly discuss some such recent studies. Alberts et al. [386] attempt to utilize the coffee ring effect for biomaterial synthesis using genetically tunable bacteriophage. The effect of temperature and surface chemistry is studied in this work. Kasyap et al. [387] have dried drops containing live E-coli bacteria. They report formation of the usual coffee ring, but as long as there is enough fluid, they observe spurts or jets along the ring. According to the authors, this is due to bacteria swimming in presence of a concentration driven instability. Another study on drying drops containing E-coli is reported by Thokchom et al. [388]. They study chemotaxis induced by presence or absence of nutrients. Live bacteria are found to respond differently from dead bacteria to the presence of sugar. There are many studies on drying drops of proteins [189,194]. Carreon et al. [189] studied protein solutions. Whereas usually proteins in saline solutions are dried to crystallize, this study on binary mixtures of proteins without salts has the potential to identify protein structures like folded and unfolded proteins. Texture analysis of protein mixtures is reported by the same group [194] in a later work. Glibitskiy et al. [389] found zigzag patterns on films of dried bovine serum albumin. However the samples here are 2 cm × 2 cm films, not exactly droplets.

44

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

Fig. 39. Crack patterns in dried blood drops from patients with different levels of bilirubin [12]. Source: Permission of Elsevier.

Smalyukh et al. [390] used droplet drying to show that the liquid crystal matrix of concentrated DNA generate elastic forces that can order rod-shaped bacteria. Roy et al. [391] also observed liquid crystalline ordering forming interesting patterns in drying droplets of CTAB, with and without added salt. Droplet evaporation technique is also being applied in food technology. Quality of wheat grains [392] and carrot roots [393,394] and alcoholic drinks [395] are assessed on the basis of such studies. Brutin et al. suggested application on forensics [38,396–399]. Drying process of blood pools have been studied by Laan et al. [396] where the authors show that the mass of the blood pools diminish similarly and in a reproducible way for blood pools created under various conditions. They verify that the size of the blood pools is directly related to its volume and the wettability of the surface. Such studies may lead to a time-line reconstruction of events in forensic investigation. 9. Conclusions and future directions To summarize, we have reviewed various aspects concerned with evaporation of a droplet. We emphasize once more that the complexity in this problem arises from the multi-scale nature of the process, where the evaporation of molecules occurs at lengthscales of nanometer range and is determined by the thermodynamics of the system; whereas the flow and the instabilities are at the macroscopic scale and dominated by continuum mechanics. Therefore, to understand the evaporation process completely our knowledge needs to be multi-disciplinary, encompassing thermodynamics and surface science to mechanics including phase transitions, flow convection, crust formation, instabilities and crack patterns. In the past decades, researchers have put much effort into study of deposited patterns, crack formation and morphologies and tried to elucidate their underlying physico-mechanical origin, for instance the evaporation-driven flow, the mechanical instability causing wrinkling or buckling, and related phenomena. The boundary conditions for the droplet,

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

45

Fig. 40. Ferning patterns in tear drops dried on horizontal (left) and vertical (right) surfaces [41]. Different constituents are better separated and distinguishable on the vertical surface. Source: Permission of Wolters Kluwer.

such as the contact angle on the substrate, pinning or depinning condition of the contact line, the effect of a topological mask over the droplet, and so on, have been shown to play an important role in drop evaporation and in turn on the final residues. Experimental techniques ranging from in situ optical microscope and confocal microscope observations to in situ X-ray scattering, have been applied to accomplish direct observations of evaporating droplets. Moreover, several simulation and modeling approaches have been exploited to capture both the flow and mass transfer associated with droplet evaporation based either on Monte Carlo models or Lattice Boltzmann methods. Analytical models have also been developed based on the Onsager principle [400]. We have tried to present a state of the art review of this varied body of work. The evaporation of a droplet is intrinsically a highly complex phenomenon, although it is such a common occurrence in our daily life. After hundreds of years of investigation, there still remain rich opportunities and new challenges in this field. A tentative list promising new avenues to explore is given below. 1. Evaporation under external fields. External fields – magnetic, electrostatic, acoustic – can be utilized to change the substrate wetting and flow of the droplet and in turn the mass transfer upon evaporation, as well as the stress field in the residue. For instance, by using acoustic levitation, the coffee ring effect can be significantly suppressed [401]. It would be interesting to look for specific tailored and tunable patterns or structures via different external fields. 2. Evaporation of biological fluids. Although tremendous work has already been done in this area, the understanding is still far from clear regarding pattern formation in drying droplets containing biological matter. The biological fluid can be blood [402], protein [186], bacteria [387], virus [403] etc. An intriguing but challenging question is do the special microorganisms in liquor or wine influence the drying patterns of its droplet? On the basis of this, simple but efficient techniques may be developed for the quality evaluation of foods, tea etc. 3. Evaporation of active colloids. An active colloid itself stands as a hot topic in the field of soft matter. It is highly desirable to gain new insight on how evaporation leads to unique phase behavior and mechanical properties in droplets containing active colloids. 4. Evaporation in space station. To elucidate the effect of gravity on the flow convection and the mass transfer inside a drying droplet, it is highly desirable to perform droplet evaporation study in space stations that can provide a long-term microgravity condition. This will be of great help in understanding the emergence of crust, formation of cavity, buckling of crust, and elucidating the effect of gravity on these processes. 5. As a model system for complex science. Upon evaporation, particularly for a colloidal droplet, the interparticle interactions are varied by particle density. This often brings the system far from equilibrium and leads to complex patterns, fractal or dendritic, analogous to the structure obtained in the solidification of alloys. These may be dominated by similar non-linear mechanisms. Drying droplets provide an ideal model platform for the study of these situations involving non-linear physics.

46

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

In conclusion we expect that, in the apparently mundane drying droplet problem, if researchers from physics, chemistry, material science, mechanics and biology put in a cooperative effort, more exciting secrets of nature can be unlocked. Acknowledgments D.Y. Zang thanks the National Natural Science Foundation of China (No. U1732129) and Fundamental Research Funds for the Central Universities for financial support. Yu.Yu. Tarasevich acknowledge the funding from the Ministry of Science and Higher Education of the Russian Federation, Russia, Project No. 3.959.2017/4.6. M. Dutta Choudhury, T. Dutta and S. Tarafdar are grateful to the Condensed Matter Physics Research Centre, Jadavpur University for providing a forum for interaction and discussion between scientists from different institutions. References [1] J.H. Snoeijer, B. Andreotti, Moving contact lines scales, regimes and dynamical transitions, Annu. Rev. Fluid Mech. 45 (2013) 269–292, http://dx.doi.org/10.1146/annurev-fluid-011212-140734. [2] A. Amini, G.M. Homsy, Evaporation of liquid droplets on solid substrates. I. Flat substrate with pinned or moving contact line, Phys. Rev. Fluids 2 (2017) 043603, http://dx.doi.org/10.1103/PhysRevFluids.2.043603. [3] A. Amini, G.M. Homsy, Evaporation of liquid droplets on solid substrates. II. Periodic substrates with moving contact lines, Phys. Rev. Fluids 2 (2017) 043604, http://dx.doi.org/10.1103/PhysRevFluids.2.043604. [4] N. Shahidzadeh, M.F.L. Schut, J. Desarnaud, M. Prat, D. Bonn, Salt stains from evaporating droplets, Sci. Rep. 5 (1) (2015) 10335, http: //dx.doi.org/10.1038/srep10335. [5] S. Semenov, V.M. Starov, M.G. Velarde, R.G. Rubio, Droplets evaporation: Problems and solutions, Eur. Phys. J. Spec. Top. 197 (2011) 265–278, http://dx.doi.org/10.1140/epjst/e2011-01468-1. [6] H. Kim, F. Boulogne, E. Um, I. Jacobi, E. Button, H.A. Stone, Controlled uniform coating from the interplay of Marangoni flows and surface-adsorbed macromolecules, Phys. Rev. Lett. 116 (2016) 124501, http://dx.doi.org/10.1103/PhysRevLett.116.124501. [7] H. Yoo, C. Kim, Experimental studies on formation, spreading and drying of inkjet drop of colloidal suspensions, Colloids Surf. A 468 (2015) 234–245, http://dx.doi.org/10.1016/j.colsurfa.2014.12.032. [8] T. Kanai, T. Sawada, New route to produce dry colloidal crystals without cracks, Langmuir 25 (2009) 13315–13317, http://dx.doi.org/10.1021/ la9033854. [9] D. Dong, L.W. Yap, D.M. Smilgies, K.J. Si, Q. Shi, W. Cheng, Two-dimensional gold trisoctahedron nanoparticle superlattice sheets: self-assembly, characterization and immunosensing applications, Nanoscale 10 (11) (2018) 5065–5071, http://dx.doi.org/10.1039/c7nr09443d. [10] J. Bahadur, D. Sen, S. Mazumder, B. Paul, H. Bhatt, S.G. Singh, Control of buckling in colloidal droplets during evaporation-induced assembly of nanoparticles, Langmuir 28 (3) (2012) 1914–1923, http://dx.doi.org/10.1021/la204161d. [11] R. Chen, L. Zhang, D. Zang, W. Shen, Blood drop patterns: Formation and applications, Adv. Colloid Interface Sci. 231 (2016) 1–14, http://dx.doi.org/10.1016/j.cis.2016.01.008. [12] L. Bahmani, M. Neysari, M. Maleki, The study of drying and pattern formation of whole human blood drops and the effect of thalassaemia and neonatal jaundice on the patterns, Colloids Surf. A 513 (2017) 66–75, http://dx.doi.org/10.1016/j.colsurfa.2016.10.065. [13] D. Brutin, B. Sobac, B. Loquet, J. Sampol, Pattern formation in drying drops of blood, J. Fluid Mech. 667 (2011) 85–95, http://dx.doi.org/10. 1017/S0022112010005070. [14] D. Brutin (Ed.), Droplet Wetting and Evaporation, Academic Press, Oxford, 2015. [15] B. Sobac, D. Brutin, Thermocapillary instabilities in an evaporating drop deposited onto a heated substrate, Phys. Fluids 24 (3) (2012) 032103, http://dx.doi.org/10.1063/1.3692267. [16] B.D. Caddock, D. Hull, Influence of humidity on the cracking patterns formed during the drying of sol–gel drops, J. Mater. Sci. 37 (4) (2002) 825–834, http://dx.doi.org/10.1023/A:1013808402289. [17] V.H. Chhasatia, A.S. Joshi, Y. Sun, Effect of relative humidity on contact angle and particle deposition morphology of an evaporating colloidal drop, Appl. Phys. Lett. 97 (23) (2010) 231909, http://dx.doi.org/10.1063/1.3525167. [18] W. Bou Zeid, D. Brutin, Influence of relative humidity on spreading, pattern formation and adhesion of a drying drop of whole blood, Colloids Surf. A 430 (2013) 1–7, http://dx.doi.org/10.1016/j.colsurfa.2013.03.019. [19] W. Bou-Zeid, D. Brutin, Effect of relative humidity on the spreading dynamics of sessile drops of blood, Colloids Surf. A 456 (2014) 273–285, http://dx.doi.org/10.1016/j.colsurfa.2014.05.004. [20] X. Yang, C.Y. Li, Y. Sun, From multi-ring to spider web and radial spoke: competition between the receding contact line and particle deposition in a drying colloidal drop, Soft Matter 10 (2014) 4458–4463, http://dx.doi.org/10.1039/C4SM00497C. [21] S. Shin, I. Jacobi, H.A. Stone, Bénard–Marangoni Instability driven by moisture absorption, Europhys. Lett. 113 (2) (2016) 24002, http: //dx.doi.org/10.1209/0295-5075/113/24002. [22] S. Bhattacharyya, B. Roy, M. Dutta Choudhury, Pattern formation in drying drops of colloidal copper sulphate solution on glass surface, J. Surf. Sci. Technol. 32 (3–4) (2017) 79–84, http://dx.doi.org/10.18311/jsst/2016/7752. [23] A. Sanyal, S. Basu, S. Chowdhuri, P. Kabi, S. Chaudhuri, Precision control of drying using rhythmic dancing of sessile nanoparticle laden droplets, Appl. Phys. Lett. 104 (16) (2014) 163108, http://dx.doi.org/10.1063/1.4873394. [24] Y.Y. Tarasevich, Mechanisms and models of the dehydration self-organization in biological fluids, Phys.-Usp. 47 (7) (2004) 717–728, http: //dx.doi.org/10.1070/PU2004v047n07ABEH001758. [25] T.A. Yakhno, V.G. Yakhno, Structural evolution of drying drops of biological fluids, Tech. Phys. 54 (2009) 1219–1227, http://dx.doi.org/10.1134/ S1063784209080210. [26] A.-M. Cazabat, G. Guéna, Evaporation of macroscopic sessile droplets, Soft Matter 6 (2010) 2591–2612, http://dx.doi.org/10.1039/B924477H. [27] W. Han, Z. Lin, Learning from coffee rings: Ordered structures enabled by controlled evaporative self-assembly, Angew. Chem. Int. Ed. 51 (7) (2012) 1534–1546, http://dx.doi.org/10.1002/anie.201104454. [28] H.Y. Erbil, Evaporation of pure liquid sessile and spherical suspended drops: A review, Adv. Colloid Interface Sci. 170 (1–2) (2012) 67–86, http://dx.doi.org/10.1016/j.cis.2011.12.006. [29] T. Brugarolas, F. Tu, D. Lee, Directed assembly of particles using microfluidic droplets and bubbles, Soft Matter 9 (2013) 9046–9058, http://dx.doi.org/10.1039/C3SM50888A. [30] K. Sefiane, Patterns from drying drops, Adv. Colloid Interface Sci. 206 (Suppl. C) (2014) 372–381, http://dx.doi.org/10.1016/j.cis.2013.05.002.

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

47

[31] N.M. Kovalchuk, A. Trybala, V.M. Starov, Evaporation of sessile droplets, Curr. Opin. Colloid Interface Sci. 19 (4) (2014) 336–342, http: //dx.doi.org/10.1016/j.cocis.2014.07.005. [32] X. Zhong, A. Crivoi, F. Duan, Sessile nanofluid droplet drying, Adv. Colloid Interface Sci. 217 (Suppl. C) (2015) 13–30, http://dx.doi.org/10.1016/ j.cis.2014.12.003. [33] H.M. van der Kooij, G.T. van de Kerkhof, J. Sprakel, A mechanistic view of drying suspension droplets, Soft Matter 12 (2016) 2858–2867, http://dx.doi.org/10.1039/C5SM02406D. [34] D. Brutin, V. Starov, Recent advances in droplet wetting and evaporation, Chem. Soc. Rev. 47 (2018) 558–585, http://dx.doi.org/10.1039/ C6CS00902F. [35] M. Parsa, S. Harmand, K. Sefiane, Mechanisms of pattern formation from dried sessile drops, Adv. Colloid Interface 254 (2018) 22–47, http://dx.doi.org/10.1016/j.cis.2018.03.007. [36] D. Mampallil, H.B. Eral, A review on suppression and utilization of the coffee-ring effect, Adv. Colloid Interface Sci. 252 (2018) 38–54, http://dx.doi.org/10.1016/j.cis.2017.12.008. [37] F. Giorgiutti-Dauphiné, L. Pauchard, Drying drops, Eur. Phys. J. E 41 (3) (2018) 32, http://dx.doi.org/10.1140/epje/i2018-11639-2. [38] P. Bacchin, D. Brutin, A. Davaille, E. Di Giuseppe, X.D. Chen, I. Gergianakis, F. Giorgiutti-Dauphiné, L. Goehring, Y. Hallez, R. Heyd, R. Jeantet, C. Le Floch-Fouéré, M. Meireles, E. Mittelstaedt, C. Nicloux, L. Pauchard, M.-L. Saboungi, Drying colloidal systems: Laboratory models for a wide range of applications, Eur. Phys. J. E 41 (8) (2018) 94, http://dx.doi.org/10.1140/epje/i2018-11712-x. [39] S. Tarafdar, Y.Y. Tarasevich, M. Dutta Choudhury, T. Dutta, D. Zang, Droplet drying patterns on solid substrates: From hydrophilic to superhydrophobic contact to levitating drops, Adv. Cond. Matter Phys. 2018 (2018) 1–24, http://dx.doi.org/10.1155/2018/5214924. [40] J.M. Cameron, H.J. Butler, D.S. Palmer, M.J. Baker, Biofluid spectroscopic disease diagnostics: A review on the processes and spectral impact of drying, J. Biophotonics 11 (4) (2018) e201700299, http://dx.doi.org/10.1002/jbio.201700299. [41] R. López-Solís, D. Salinas-Toro, D. López, C. Segovia, K. Villar, P. Agüero, F. Valenzuela, L. Traipe-Castro, Stratification of tear components during tear microdesiccation on vertical glass surfaces: A novel approach in tear fluid assessment, Cornea 34 (8) (2015) 959–966, http: //dx.doi.org/10.1097/ICO.0000000000000467. [42] F. Ravera, G. Loglio, V.I. Kovalchuk, Interfacial dilational rheology by oscillating bubble/drop methods, Curr. Opin. Colloid Interface Sci. 15 (4) (2010) 217–228, http://dx.doi.org/10.1016/j.cocis.2010.04.001. [43] D. Zang, L. Li, W. Di, Z. Zhang, C. Ding, Z. Chen, W. Shen, B.P. Binks, X. Geng, Inducing drop to bubble transformation via resonance in ultrasound, Nature Commun. 9 (1) (2018) 3546, http://dx.doi.org/10.1038/s41467-018-05949-0. [44] D. Zang, Y. Yu, Z. Chen, X. Li, H. Wu, X. Geng, Acoustic levitation of liquid drops: Dynamics, manipulation and phase transitions, Adv. Colloid. Interface Sci. 243 (2017) 77–85, http://dx.doi.org/10.1016/j.cis.2017.03.003. [45] J.T. Okada, T. Ishikawa, Y. Watanabe, P.-F. Paradis, Surface tension and viscosity of molten vanadium measured with an electrostatic levitation furnace, J. Chem. Thermodyn. 42 (7) (2010) 856–859, http://dx.doi.org/10.1016/j.jct.2010.02.008. [46] Y. Zhao, Physical Mechanics of Surfaces and Interfaces, Science Publisher, Beijing, 2012. [47] A. Lafuma, D. Quéré, Superhydrophobic states, Nature Mater. 2 (2003) 457–460, http://dx.doi.org/10.1038/nmat924. [48] G. Whyman, E. Bormashenko, T. Stein, The rigorous derivation of Young, Cassie–Baxter and Wenzel equations and the analysis of the contact angle hysteresis phenomenon, Chem. Phys. Lett. 450 (4) (2008) 355–359, http://dx.doi.org/10.1016/j.cplett.2007.11.033. [49] R.G. Picknett, R. Bexon, The evaporation of sessile or pendant drops in still air, J. Colloid Interface Sci. 61 (2) (1977) 336–350, http: //dx.doi.org/10.1016/0021-9797(77)90396-4. [50] A.J.D. Shaikeea, S. Basu, A. Tyagi, S. Sharma, R. Hans, L. Bansal, Universal representations of evaporation modes in sessile droplets, PLoS One 12 (9) (2017) e0184997, http://dx.doi.org/10.1371/journal.pone.0184997. [51] E.Y. Gatapova, A. Semenov, D.V. Zaitsev, O.A. Kabov, Evaporation of a sessile water drop on a heated surface with controlled wettability, Colloids Surf. A 441 (2014) 776–785, http://dx.doi.org/10.1016/j.colsurfa.2013.05.046. [52] K.S. Birdi, D.T. Vu, Wettability and the evaporation rates of fluids from solid surfaces, J. Adhes. Sci. Technol. 7 (6) (1993) 485–493, http://dx.doi.org/10.1163/156856193X00808. [53] S.M. Rowan, M.I. Newton, G. McHale, Evaporation of microdroplets and the wetting of solid surfaces, J. Phys. Chem. 99 (35) (1995) 13268–13271, http://dx.doi.org/10.1021/j100035a034. [54] R.A. Meric, H.Y. Erbil, Evaporation of sessile drops on solid surfaces: Pseudospherical cap geometry, Langmuir 14 (7) (1998) 1915–1920, http://dx.doi.org/10.1021/la970147c. [55] H.Y. Erbil, G. McHale, M.I. Newton, Drop evaporation on solid surfaces: Constant contact angle mode, Langmuir 18 (7) (2002) 2636–2641, http://dx.doi.org/10.1021/la011470p. [56] M.E.R. Shanahan, C. Bourgès, Effects of evaporation on contact angles on polymer surfaces, Int. J. Adhes. Adhes. 14 (3) (1994) 201–205, http://dx.doi.org/10.1016/0143-7496(94)90031-0. [57] T.-S. Lin, Y.-H. Zeng, R.-Y. Tsay, S.-Y. Lin, Roughness-induced strong pinning for drops evaporating from polymeric surfaces, J. Taiwan. Inst. Chem. E 62 (2016) 54–59, http://dx.doi.org/10.1016/j.jtice.2016.02.015. [58] A. Hoang, H.P. Kavehpour, Dynamics of nanoscale precursor film near a moving contact line of spreading drops, Phys. Rev. Lett. 106 (2011) 254501, http://dx.doi.org/10.1103/PhysRevLett.106.254501. [59] L. Leger, M. Erman, A.M. Guinet-Picard, D. Ausserre, C. Strazielle, Precursor film profiles of spreading liquid drops, Phys. Rev. Lett. 60 (23) (1988) 2390–2393, http://dx.doi.org/10.1103/PhysRevLett.60.2390. [60] H. Xu, D. Shirvanyants, K. Beers, K. Matyjaszewski, M. Rubinstein, S.S. Sheiko, Molecular motion in a spreading precursor film, Phys. Rev. Lett. 93 (20) (2004) 206103, http://dx.doi.org/10.1103/PhysRevLett.93.206103. [61] Q. Yuan, Y.P. Zhao, Precursor film in dynamic wetting, electrowetting, and electro-elasto-capillarity, Phys. Rev. Lett. 104 (24) (2010) 246101, http://dx.doi.org/10.1103/PhysRevLett.104.246101. [62] Y. Pomeau, E. Villermaux, Two hundred years of capillarity research, Phys. Today 59 (2006) 39–44, http://dx.doi.org/10.1063/1.2195314. [63] A. Marmur, Line tension and the intrinsic contact angle in solid–liquid–fluid systems, J. Colloid Interface Sci. 186 (2) (1997) 462–466, http://dx.doi.org/10.1006/jcis.1996.4666. [64] E. Bormashenko, New insights into liquid marbles, Soft Matter 8 (2012) 11018–11021, http://dx.doi.org/10.1039/C2SM26189H. [65] J.N. Israelachvili, Intermolecular and Surface Forces, third ed., Elsevier, New York, 2011. [66] C. Py, P. Reverdy, L. Doppler, J. Bico, B. Roman, C.N. Baroud, CaPillary origami: spontaneous wrapping of a droplet with an elastic sheet, Phys. Rev. Lett. 98 (15) (2007) 156103, http://dx.doi.org/10.1103/PhysRevLett.98.156103. [67] P.J. Lu, D.A. Weitz, Colloidal particles: Crystals, glasses, and gels, Annu. Rev. Condens. Matter Phys. 4 (1) (2013) 217–233, http://dx.doi.org/10. 1146/annurev-conmatphys-030212-184213. [68] A. Giri, M. Dutta Choudhury, T. Dutta, S. Tarafdar, Multifractal growth of crystalline NaCl aggregates in a gelatin medium, Cryst. Growth Des. 13 (1) (2013) 341–345, http://dx.doi.org/10.1021/cg301499b. [69] H.M. Gorr, J.M. Zueger, D.R. McAdams, J.A. Barnard, Salt-induced pattern formation in evaporating droplets of lysozyme solutions, Colloids Surf. B 103 (2013) 59–66, http://dx.doi.org/10.1016/j.colsurfb.2012.09.043.

48

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

[70] N.N. Jason, R.G. Chaudhuri, S. Paria, Self-assembly of colloidal sulfur particles influenced by sodium oxalate salt on glass surface from evaporating drops, Soft Matter 8 (14) (2012) 3771–3780, http://dx.doi.org/10.1039/c2sm07136c. [71] N. Shahidzadeh-Bonn, S. Rafaï, D. Bonn, G. Wegdam, Salt crystallization during evaporation: Impact of interfacial properties, Langmuir 24 (16) (2008) 8599–8605, http://dx.doi.org/10.1021/la8005629. [72] A.G. Marín, H. Gelderblom, D. Lohse, J.H. Snoeijer, Order-to-disorder transition in ring-shaped colloidal stains, Phys. Rev. Lett. 107 (2011) 085502, http://dx.doi.org/10.1103/PhysRevLett.107.085502. [73] D.M. Herlach, I. Klassen, P. Wette, D. Holland-Moritz, Colloids as model systems for metals and alloys: a case study of crystallization, J. Phys. Condens. Matter 22 (15) (2010) 153101, http://dx.doi.org/10.1088/0953-8984/22/15/153101. [74] C. Eisenmann, P. Keim, U. Gasser, G. Maret, Melting of anisotropic colloidal crystals in two dimensions, J. Phys. Condens. Matter 16 (38) (2004) S4095–S4102, http://dx.doi.org/10.1088/0953-8984/16/38/024. [75] J. Zhang, Z. Sun, B. Yang, Self-assembly of photonic crystals from polymer colloids, Curr. Opin. Colloid Interface Sci. 14 (2) (2009) 103–114, http://dx.doi.org/10.1016/j.cocis.2008.09.001. [76] D. Quéré, Leidenfrost dynamics, Annu. Rev. Fluid Mech. 45 (1) (2013) 197–215, http://dx.doi.org/10.1146/annurev-fluid-011212-140709. [77] H.Y. Erbil, Control of stain geometry by drop evaporation of surfactant containing dispersions, Adv. Colloid Interface Sci. 222 (Suppl. C) (2015) 275–290, http://dx.doi.org/10.1016/j.cis.2014.08.004, Reinhard Miller, Honorary Issue. [78] F. Schönfeld, K.-H. Graf, S. Hardt, H.-J. Butt, Evaporation dynamics of sessile liquid drops in still air with constant contact radius, Int. J. Heat Mass Transfer 51 (13) (2008) 3696–3699, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.12.027. [79] J.J. Hegseth, N. Rashidnia, A. Chai, Natural convection in droplet evaporation, Phys. Rev. E 54 (1996) 1640–1644, http://dx.doi.org/10.1103/ PhysRevE.54.1640. [80] R.W. Hyers, Fluid flow effects in levitated droplets, Meas. Sci. Technol. 16 (2) (2005) 394, http://dx.doi.org/10.1088/0957-0233/16/2/010. [81] L. Chen, J.R.G. Evans, Drying of colloidal droplets on superhydrophobic surfaces, J. Colloid Interface Sci. 351 (1) (2010) 283–287, http: //dx.doi.org/10.1016/j.jcis.2010.07.037. [82] A.V. Kistovich, Y.D. Chashechkin, V.V. Shabalin, Formation mechanism of a circumferential roller in a drying biofluid drop, Tech. Phys. 55 (2010) 473–478, http://dx.doi.org/10.1134/S1063784210040067. [83] R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, T.A. Witten, Contact line deposits in an evaporating drop, Phys. Rev. E 62 (1) (2000) 756–765, http://dx.doi.org/10.1103/PhysRevE.62.756. [84] R.D. Deegan, Pattern formation in drying drops, Phys. Rev. E 61 (1) (2000) 475–485, http://dx.doi.org/10.1103/PhysRevE.61.475. [85] T.A. Yakhno, O.A. Sanina, M.G. Volovik, A.G. Sanin, V.G. Yakhno, Thermographic investigation of the temperature field dynamics at the liquid-air interface in drops of water solutions drying on a glass substrate, Tech. Phys. 57 (7) (2012) 915–922, http://dx.doi.org/10.1134/ S1063784212070262. [86] F. Girard, M. Antoni, K. Sefiane, Infrared thermography investigation of an evaporating sessile water droplet on heated substrates, Langmuir 26 (7) (2010) 4576–4580, http://dx.doi.org/10.1021/la9048659. [87] W.D. Ristenpart, P.G. Kim, C. Domingues, J. Wan, H.A. Stone, Influence of substrate conductivity on circulation reversal in evaporating drops, Phys. Rev. Lett. 99 (2007) 234502, http://dx.doi.org/10.1103/PhysRevLett.99.234502. [88] H. Hu, R.G. Larson, Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet, Langmuir 21 (9) (2005) 3972–3980, http://dx.doi.org/10.1021/la0475270. [89] H. Hu, R.G. Larson, Analysis of the microfluid flow in an evaporating sessile droplet, Langmuir 21 (9) (2005) 3963–3971, http://dx.doi.org/10. 1021/la047528s. [90] H. Hu, R.G. Larson, Marangoni effect reverses coffee-ring depositions, J. Phys. Chem. B 110 (14) (2006) 7090–7094, http://dx.doi.org/10.1021/ jp0609232. [91] X. Xu, J. Luo, Marangoni flow in an evaporating water droplet, Appl. Phys. Lett. 91 (12) (2007) 124102, http://dx.doi.org/10.1063/1.2789402. [92] B. Sobac, D. Brutin, Thermal effects of the substrate on water droplet evaporation, Phys. Rev. E 86 (2012) 021602, http://dx.doi.org/10.1103/ PhysRevE.86.021602. [93] S. Karpitschka, F. Liebig, H. Riegler, Marangoni contraction of evaporating sessile droplets of binary mixtures, Langmuir 33 (19) (2017) 4682–4687, http://dx.doi.org/10.1021/acs.langmuir.7b00740. [94] P. Takhistov, H.-C. Chang, Complex stain morphologies, Ind. Eng. Chem. Res. 41 (25) (2002) 6256–6269, http://dx.doi.org/10.1021/ie010788+. [95] F. Girard, M. Antoni, S. Faure, A. Steinchen, Evaporation and Marangoni driven convection in small heated water droplets, Langmuir 22 (26) (2006) 11085–11091, http://dx.doi.org/10.1021/la061572l. [96] K. Gleason, H. Voota, S.A. Putnam, Steady-state droplet evaporation: Contact angle influence on the evaporation efficiency, Int. J. Heat Mass Transfer 101 (2016) 418–426, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.04.075. [97] A. Chandramohan, J.A. Weibel, S.V. Garimella, Spatiotemporal infrared measurement of interface temperatures during water droplet evaporation on a nonwetting substrate, Appl. Phys. Lett. 110 (4) (2017) 041605, http://dx.doi.org/10.1063/1.4975003. [98] D. Brutin, B. Sobac, F. Rigollet, C. Le Niliot, Infrared visualization of thermal motion inside a sessile drop deposited onto a heated surface, Exp. Therm Fluid Sci. 35 (3) (2011) 521–530, http://dx.doi.org/10.1016/j.expthermflusci.2010.12.004. [99] J. Thiery, S. Rodts, D.A. Weitz, P. Coussot, Drying regimes in homogeneous porous media from macro- to nanoscale, Phys. Rev. Fluids 2 (2017) 074201, http://dx.doi.org/10.1103/PhysRevFluids.2.074201. [100] R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, T.A. Witten, Capillary flow as the cause of ring stains from dried liquid drops, Nature 389 (6653) (1997) 827–829, http://dx.doi.org/10.1038/39827. [101] W. Zhang, T. Yu, L. Liao, Z. Cao, Ring formation from a drying sessile colloidal droplet, AIP Adv. 3 (10) (2013) 102109, http://dx.doi.org/10. 1063/1.4824741. [102] B.M. Weon, J.H. Je, Capillary force repels coffee-ring effect, Phys. Rev. E 82 (2010) 015305, http://dx.doi.org/10.1103/PhysRevE.82.015305. [103] P.J. Yunker, T. Still, M.A. Lohr, A.G. Yodh, Suppression of the coffee-ring effect by shape-dependent capillary interactions, Nature 476 (7360) (2011) 308–311, http://dx.doi.org/10.1038/nature10344. [104] V.R. Dugyala, M.G. Basavaraj, Control over coffee-ring formation in evaporating liquid drops containing ellipsoids, Langmuir 30 (29) (2014) 8680–8686, http://dx.doi.org/10.1021/la500803h. [105] R. Bhardwaj, X. Fang, P. Somasundaran, D. Attinger, Self-assembly of colloidal particles from evaporating droplets: Role of DLVO interactions and proposition of a phase diagram, Langmuir 26 (11) (2010) 7833–7842, http://dx.doi.org/10.1021/la9047227. [106] M. Anyfantakis, Z. Geng, M. Morel, S. Rudiuk, D. Baigl, Modulation of the coffee-ring effect in particle/surfactant mixtures: the importance of particle–interface interactions, Langmuir 31 (14) (2015) 4113–4120, http://dx.doi.org/10.1021/acs.langmuir.5b00453. [107] R. Malinowski, G. Volpe, I.P. Parkin, G. Volpe, Dynamic control of particle deposition in evaporating droplets by an external point source of vapor, J. Phys. Chem. Lett. 9 (3) (2018) 659–664, http://dx.doi.org/10.1021/acs.jpclett.7b02831. [108] J.M. Baek, C. Yi, J.Y. Rhee, Central spot formed in dried coffee-water-mixture droplets: Inverse coffee-ring effect, Curr. Appl. Phys. 18 (4) (2018) 477–483, http://dx.doi.org/10.1016/j.cap.2018.01.007. [109] A.K. Thokchom, A. Gupta, P.J. Jaijus, A. Singh, Analysis of fluid flow and particle transport in evaporating droplets exposed to infrared heating, Int. J. Heat Mass Transfer 68 (2014) 67–77, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.09.012.

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

49

[110] Z.S. Davidson, Y. Huang, A. Gross, A. Martinez, T. Still, C. Zhou, P.J. Collings, R.D. Kamien, A.G. Yodh, Deposition and drying dynamics of liquid crystal droplets, Nature Commun. 8 (2017) 15642, http://dx.doi.org/10.1038/ncomms15642. [111] H.B. Eral, D.M. Augustine, M.H.G. Duits, F. Mugele, Suppressing the coffee stain effect: how to control colloidal self-assembly in evaporating drops using electrowetting, Soft Matter 7 (2011) 4954–4958, http://dx.doi.org/10.1039/C1SM05183K. [112] C. Seo, D. Jang, J. Chae, S. Shin, Altering the coffee-ring effect by adding a surfactant-like viscous polymer solution, Sci. Rep. 7 (1) (2017) 500, http://dx.doi.org/10.1038/s41598-017-00497-x. [113] L. Cui, J. Zhang, X. Zhang, L. Huang, Z. Wang, Y. Li, H. Gao, S. Zhu, T. Wang, B. Yang, Suppression of the coffee ring effect by hydrosoluble polymer additives, ACS Appl. Mater. Interfaces 4 (5) (2012) 2775–2780, http://dx.doi.org/10.1021/am300423p. [114] E. Sowade, T. Blaudeck, R.R. Baumann, Inkjet printing of colloidal nanospheres: Engineering the evaporation-driven self-assembly process to form defined layer morphologies, Nanoscale Res. Lett. 10 (1) (2015) 362, http://dx.doi.org/10.1186/s11671-015-1065-2. [115] D. Lohani, S. Sarkar, Nanoscale topographical fluctuations: A key factor for evaporative colloidal self-assembly, Langmuir 34 (43) (2018) 12751–12758, http://dx.doi.org/10.1021/acs.langmuir.8b02409. [116] E. Kočišová, M. Petr, H. Šípová, O. Kylián, M. Procházka, Drop coating deposition of a liposome suspension on surfaces with different wettabilities: ‘‘coffee ring’’ formation and suspension preconcentration, Phys. Chem. Chem. Phys. 19 (2017) 388–393, http://dx.doi.org/10. 1039/C6CP07606H. [117] T. Cuk, S.M. Troian, C.M. Hong, S. Wagner, Using convective flow splitting for the direct printing of fine copper lines, Appl. Phys. Lett. 77 (13) (2000) 2063–2065, http://dx.doi.org/10.1063/1.1311954. [118] H.B. Eral, D.J.C.M. ’t Mannetje, J.M. Oh, Contact angle hysteresis: a review of fundamentals and applications, Colloid Polymer Sci. 291 (2) (2013) 247–260, http://dx.doi.org/10.1007/s00396-012-2796-6. [119] Y.-F. Li, Y.-J. Sheng, H.-K. Tsao, Evaporation stains: Suppressing the coffee-ring effect by contact angle hysteresis, Langmuir 29 (25) (2013) 7802–7811, http://dx.doi.org/10.1021/la400948e. [120] N.D. Patil, P.G. Bange, R. Bhardwaj, A. Sharma, Effects of substrate heating and wettability on evaporation dynamics and deposition patterns for a sessile water droplet containing colloidal particles, Langmuir 32 (45) (2016) 11958–11972, http://dx.doi.org/10.1021/acs.langmuir.6b02769. [121] B. Sharma, R. Verma, C. Baur, J. Bykova, J.M. Mabry, D.W. Smith, Ultra low dielectric self-cleansing and highly oleophobic POSS-PFCP aryl ether polymer composites, J. Mater. Chem. C 1 (2013) 7222–7227, http://dx.doi.org/10.1039/C3TC31161A. [122] F. Pacheco-Torgal, S. Jalali, Nanotechnology: Advantages and drawbacks in the field of construction and building materials, Constr. Build. Mater. 25 (2) (2011) 582–590, Composite materials and adhesive bonding technology, http://dx.doi.org/10.1016/j.conbuildmat.2010.07.009. [123] J. Lee, P.K. Duy, S.C. Park, H. Chung, Development of hydrophobic surface substrates enabling reproducible drop-and-dry spectroscopic measurements, Talanta 153 (2016) 31–37, http://dx.doi.org/10.1016/j.talanta.2016.02.053. [124] K. Uno, K. Hayashi, T. Hayashi, K. Ito, H. Kitano, Particle adsorption in evaporating droplets of polymer latex dispersions on hydrophilic and hydrophobic surfaces, Colloid Polymer Sci. 276 (9) (1998) 810–815, http://dx.doi.org/10.1007/s003960050314. [125] E. Kočišová, M. Procházka, H. Šípová, Thiol-modified gold-coated glass as an efficient hydrophobic substrate for drop coating deposition Raman (DCDR) technique, J. Raman Spectrosc. 47 (11) (2016) 1394–1396, http://dx.doi.org/10.1002/jrs.4961. [126] P. Fantinel, O. Borgman, R. Holtzman, L. Goehring, Drying in a microfluidic chip: experiments and simulations, Sci. Rep. 7 (1) (2017) 15572, http://dx.doi.org/10.1038/s41598-017-15718-6. [127] M. Pack, H. Hu, D.-O. Kim, X. Yang, Y. Sun, Colloidal drop deposition on porous substrates: Competition among particle motion, evaporation, and infiltration, Langmuir 31 (29) (2015) 7953–7961, http://dx.doi.org/10.1021/acs.langmuir.5b01846. [128] R. Dou, B. Derby, Formation of coffee stains on porous surfaces, Langmuir 28 (12) (2012) 5331–5338, http://dx.doi.org/10.1021/la204440w. [129] T.C. Chao, A. Trybala, V. Starov, D.B. Das, Influence of haematocrit level on the kinetics of blood spreading on thin porous medium during dried blood spot sampling, Colloids Surf. A 451 (2014) 38–47, http://dx.doi.org/10.1016/j.colsurfa.2014.03.033. [130] T.C. Chao, O. Arjmandi-Tash, D.B. Das, V.M. Starov, Spreading of blood drops over dry porous substrate: Complete wetting case, J. Colloid Interface Sci. 446 (2015) 218–225, http://dx.doi.org/10.1016/j.jcis.2015.01.054. [131] D. Brutin, B. Sobac, C. Nicloux, Influence of substrate nature on the evaporation of a sessile drop of blood, J. Heat Transfer 134 (6) (2012) 061101, http://dx.doi.org/10.1115/1.4006033. [132] M.A. Hampton, T.A.H. Nguyen, A.V. Nguyen, Z.P. Xu, L. Huang, V. Rudolph, Influence of surface orientation on the organization of nanoparticles in drying nanofluid droplets, J. Colloid Interface Sci. 377 (1) (2012) 456–462, http://dx.doi.org/10.1016/j.jcis.2012.03.024. [133] A.P. Sommer, Limits of the impact of gravity on self-organizing nanospheres, J. Phys. Chem. B 108 (24) (2004) 8096–8098, http://dx.doi.org/ 10.1021/jp0487049. [134] P.-G. de Gennes, F. Brochard-Wyart, D. Quere, Capillarity and Wetting Phenomena, first ed., Springer-Verlag, New York, 2004, http://dx.doi. org/10.1007/978-0-387-21656-0. [135] R. Pericet-Camara, G.K. Auernhammer, K. Koynov, S. Lorenzoni, R. Raiteri, E. Bonaccurso, Solid-supported thin elastomer films deformed by microdrops, Soft Matter 5 (2009) 3611–3617, http://dx.doi.org/10.1039/B907212H. [136] Z. Cao, A.V. Dobrynin, Polymeric droplets on soft surfaces: From Neumann’s triangle to Young’s law, Macromolecules 48 (2) (2015) 443–451, http://dx.doi.org/10.1021/ma501672p. [137] N. Saengchairat, A.T. Tran, Ink evaporation on soft substrates for stretchable electronics applications, 2018, http://dx.doi.org/10.25341/d46k5d. [138] F. Boulogne, Y.L. Kong, J.K. Nunes, H.A. Stone, Effect of the polydispersity of a colloidal drop on drying induced stress as measured by the buckling of a floating sheet, Phys. Rev. Lett. 116 (2016) 238001, http://dx.doi.org/10.1103/PhysRevLett.116.238001. [139] M. Dutta Choudhury, T. Dutta, S. Tarafdar, Pattern formation in droplets of starch gels containing NaCl dried on different surfaces, Colloids Surf. A 432 (2013) 110–118, Wetting and evaporation: Droplets of pure and complex fluids. http://dx.doi.org/10.1016/j.colsurfa.2013.04.064. [140] R. Espinosa, L. Franke, G. Deckelmann, Predicting efflorescence and subflorescences of salts, MRS Proc. 1047 (2007) 1047–Y04–03, http: //dx.doi.org/10.1557/PROC-1047-Y04-03. [141] M. Dutta Choudhury, T. Dutta, S. Tarafdar, Growth kinetics of NaCl crystals in a drying drop of gelatin: transition from faceted to dendritic growth, Soft Matter 11 (2015) 6938–6947, http://dx.doi.org/10.1039/C5SM00742A. [142] D. Kaya, V.A. Belyi, M. Muthukumar, Pattern formation in drying droplets of polyelectrolyte and salt, J. Chem. Phys. 133 (11) (2010) 114905, http://dx.doi.org/10.1063/1.3493687. [143] X. Zhong, J. Ren, F. Duan, Wettability effect on evaporation dynamics and crystalline patterns of sessile saline droplets, J. Phys. Chem. B 121 (33) (2017) 7924–7933, http://dx.doi.org/10.1021/acs.jpcb.7b03690. [144] S.A. McBride, S. Dash, K.K. Varanasi, Evaporative crystallization in drops on superhydrophobic and liquid-impregnated surfaces, Langmuir 34 (41) (2018) 12350–12358, http://dx.doi.org/10.1021/acs.langmuir.8b00049. [145] J. Zhang, M.K. Borg, K. Ritos, J.M. Reese, Electrowetting controls the deposit patterns of evaporated salt water nanodroplets, Langmuir 32 (6) (2016) 1542–1549, http://dx.doi.org/10.1021/acs.langmuir.5b04424. [146] G. Xu, W. Hong, W. Sun, T. Wang, Z. Tong, Effect of salt concentration on the motion of particles near the substrate in drying sessile colloidal droplets, Langmuir 33 (3) (2017) 685–695, http://dx.doi.org/10.1021/acs.langmuir.6b03899. [147] Y. Msambwa, A.S.D. Shackleford, F.F. Ouali, D.J. Fairhurst, Controlling and characterising the deposits from polymer droplets containing microparticles and salt, Eur. Phys. J. E 39 (2) (2016) 21, http://dx.doi.org/10.1140/epje/i2016-16021-x.

50

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

[148] B. Roy, M. Dutta Choudhuri, T. Dutta, S. Tarafdar, Multi-scale patterns formed by sodium sulphate in a drying droplet of gelatin, Appl. Surf. Sci. 357 (Part A) (2015) 1000–1006, http://dx.doi.org/10.1016/j.apsusc.2015.09.085. [149] M.E. Buzoverya, Y.P. Shcherbak, I.V. Shishpor, Y.P. Potekhina, Microstructural analysis of biological fluids, Tech. Phys. 57 (7) (2012) 1019–1024, http://dx.doi.org/10.1134/S1063784212070079. [150] M.E. Buzoverya, Y.P. Shcherbak, I.V. Shishpor, Experimental investigation of the serum albumin fascia microstructure, Tech. Phys. 57 (9) (2012) 1270–1276, http://dx.doi.org/10.1134/S1063784212090071. [151] T.A. Yakhno, V.G. Yakhno, A.G. Sanin, O.A. Sanina, A.S. Pelyushenko, Protein and salt: Spatiotemporal dynamics of events in a drying drop, Tech. Phys. 49 (8) (2004) 1055–1063, http://dx.doi.org/10.1134/1.1787668. [152] T.A. Yakhno, Sodium chloride crystallization from drying drops of albumin–salt solutions with different albumin concentrations, Tech. Phys. 60 (11) (2015) 1601–1608, http://dx.doi.org/10.1134/S1063784215110262. [153] M.E. Buzoverya, Y.P. Shcherbak, I.V. Shishpor, Quantitative estimation of the microstructural inhomogeneity of biological fluid facies, Tech. Phys. 59 (10) (2014) 1550–1555, http://dx.doi.org/10.1134/S1063784214100119. [154] G. Chen, G.J. Mohamed, Complex protein patterns formation via salt-induced self-assembly and droplet evaporation, Eur. Phys. J. E 33 (1) (2010) 19–26, http://dx.doi.org/10.1140/epje/i2010-10649-4. [155] C.C. Annarelli, L. Reyes, J. Fornazero, J. Bert, R. Cohen, A.W. Coleman, Ion and molecular recognition effects on the crystallisation of bovine serum albumin-salt mixtures, Cryst. Eng. 3 (3) (2000) 173–194, http://dx.doi.org/10.1016/S1463-0184(00)00038-1. [156] T.A. Yakhno, V.G. Yakhno, A.V. Sokolov, Shaping processes in drying drops of serum in norm and pathology, Biophysics 50 (4) (2005) 638–645. [157] S. Rafaï, D. Sarker, V. Bergeron, J. Meunier, D. Bonn, Superspreading: Aqueous surfactant drops spreading on hydrophobic surfaces, Langmuir 18 (26) (2002) 10486–10488, http://dx.doi.org/10.1021/la020271i. [158] A.R. Harikrishnan, P. Dhar, P.K. Agnihotri, S. Gedupudi, S.K. Das, Wettability of complex fluids and surfactant capped nanoparticle-induced quasi-universal wetting behavior, J. Phys. Chem. B 121 (24) (2017) 6081–6095, http://dx.doi.org/10.1021/acs.jpcb.7b02723. [159] B. Roy, S. Karmakar, S. Tarafdar, Self assembled transparent conducting network of multi-walled carbon nanotubes formed by evaporation, Mater. Lett. 207 (2017) 86–88, http://dx.doi.org/10.1016/j.matlet.2017.07.032. [160] L. Yan, Y. Li, Z.-X. Deng, J. Zhuang, X. Sun, Surfactant-assisted hydrothermal synthesis of hydroxyapatite nanorods, Int. J. Inorg. Mater. 3 (7) (2001) 633–637, http://dx.doi.org/10.1016/S1466-6049(01)00164-7. [161] P.K. Kilpatrick, W.G. Miller, Y. Talmon, Staining and drying-induced artifacts in electron microscopy of surfactant dispersions. II. Change in phase behavior produced by variation in pH modifiers, stain, and concentration, J. Colloid Interface Sci. 107 (1) (1985) 146–158, http://dx.doi.org/10.1016/0021-9797(85)90158-4. [162] V.X. Nguyen, K.J. Stebe, Patterning of small particles by a surfactant-enhanced Marangoni—Bénard instability, Phys. Rev. Lett. 88 (2002) 164501, http://dx.doi.org/10.1103/PhysRevLett.88.164501. [163] V.N. Truskett, K.J. Stebe, Influence of surfactants on an evaporating drop: Fluorescence images and particle deposition patterns, Langmuir 19 (20) (2003) 8271–8279, http://dx.doi.org/10.1021/la030049t. [164] M. Singh, H.M. Haverinen, P. Dhagat, G.E. Jabbour, Inkjet printing — process and its applications, Adv. Mater. 22 (6) (2010) 673–685, http://dx.doi.org/10.1002/adma.200901141. [165] A. Kamyshny, M. Ben-Moshe, S. Aviezer, S. Magdassi, Ink-jet printing of metallic nanoparticles and microemulsions, Macromolecular Rapid Commun. 26 (4) (2005) 281–288, http://dx.doi.org/10.1002/marc.200400522. [166] W.R. Small, C.D. Walton, J. Loos, M. in het Panhuis, CaRbon nanotube network formation from evaporating sessile drops, J. Phys. Chem. B 110 (26) (2006) 13029–13036, http://dx.doi.org/10.1021/jp062365x. [167] A. Crivoi, F. Duan, Effect of surfactant on the drying patterns of graphite nanofluid droplets, J. Phys. Chem. B 117 (19) (2013) 5932–5938, http://dx.doi.org/10.1021/jp401751z. [168] T. Still, P.J. Yunker, A.G. Yodh, Surfactant-induced marangoni eddies alter the coffee-rings of evaporating colloidal drops, Langmuir 28 (11) (2012) 4984–4988, http://dx.doi.org/10.1021/la204928m. [169] T. Kajiya, W. Kobayashi, T. Okuzono, M. Doi, Controlling the drying and film formation processes of polymer solution droplets with addition of small amount of surfactants, J. Phys. Chem. B 113 (47) (2009) 15460–15466, http://dx.doi.org/10.1021/jp9077757. [170] A. Osman, N. Shahidzadeh, H. Stitt, N. Shokri, Morphological transformations during drying of surfactant-nanofluid droplets, J. Ind. Eng. Chem. (2018) http://dx.doi.org/10.1016/j.jiec.2018.06.019. [171] W. Sempels, R. De Dier, H. Mizuno, J. Hofkens, J. Vermant, Auto-production of biosurfactants reverses the coffee ring effect in a bacterial system, Nature Commun. 4 (2013) 1757, http://dx.doi.org/10.1038/ncomms2746. [172] R. De Dier, W. Sempels, J. Hofkens, J. Vermant, Thermocapillary fingering in surfactant-laden water droplets, Langmuir 30 (44) (2014) 13338–13344, http://dx.doi.org/10.1021/la503655j. [173] N. Jung, H.W. Seo, P.H. Leo, J. Kim, P. Kim, C.S. Yoo, Surfactant effects on droplet dynamics and deposition patterns: a lattice gas model, Soft Matter 13 (2017) 6529–6541, http://dx.doi.org/10.1039/C7SM01224A. [174] J. Fukai, H. Ishizuka, Y. Sakai, M. Kaneda, M. Morita, A. Takahara, Effects of droplet size and solute concentration on drying process of polymer solution droplets deposited on homogeneous surfaces, Int. J. Heat Mass Transfer 49 (19) (2006) 3561–3567, http://dx.doi.org/10. 1016/j.ijheatmasstransfer.2006.02.049. [175] B.-J. de Gans, U.S. Schubert, Inkjet printing of well-defined polymer dots and arrays, Langmuir 20 (18) (2004) 7789–7793, http://dx.doi.org/ 10.1021/la049469o. [176] L. Pauchard, C. Allain, Stable and unstable surface evolution during the drying of a polymer solution drop, Phys. Rev. E 68 (5) (2003) 052801, http://dx.doi.org/10.1103/PhysRevE.68.052801. [177] D. Willmer, K.A. Baldwin, C. Kwartnik, D.J. Fairhurst, Growth of solid conical structures during multistage drying of sessile poly(ethylene oxide) droplets, Phys. Chem. Chem. Phys. 12 (2010) 3998–4004, http://dx.doi.org/10.1039/B922727J. [178] K.A. Baldwin, D.J. Fairhurst, The effects of molecular weight, evaporation rate and polymer concentration on pillar formation in drying poly (ethylene oxide) droplets, Colloids Surf. A 441 (2014) 867–871, http://dx.doi.org/10.1016/j.colsurfa.2012.10.049. [179] K.A. Baldwin, D.J. Fairhurst, Classifying dynamic contact line modes in drying drops, Soft Matter 11 (2015) 1628–1633, http://dx.doi.org/10. 1039/C4SM02642J. [180] K.A. Baldwin, M. Granjard, D.I. Willmer, K. Sefiane, D.J. Fairhurst, Drying and deposition of poly(ethylene oxide) droplets determined by Péclet number, Soft Matter 7 (2011) 7819–7826, http://dx.doi.org/10.1039/C1SM05220A. [181] L. Pauchard, C. Allain, Buckling instability induced by polymer solution drying, Europhys. Lett. 62 (6) (2003) 897–903, http://dx.doi.org/10. 1209/epl/i2003-00457-7. [182] T. Dutta, A. Giri, M. Dutta Choudhury, S. Tarafdar, Experiment and simulation of multifractal growth of crystalline NaCl aggregates in aqueous gelatin medium, Colloids Surf. A 432 (2013) 127–131, http://dx.doi.org/10.1016/j.colsurfa.2013.04.040, Wetting and evaporation: Droplets of pure and complex fluids. [183] T.A. Yakhno, V.G. Yakhno, A.G. Sanin, O.A. Sanina, A.S. Pelyushenko, N.A. Egorova, I.G. Terentiev, S.V. Smetanina, O.V. Korochkina, E.V. Yashukova, The informative-capacity phenomenon of drying drops, IEEE Eng. Med. Biol. Mag. 24 (2) (2005) 96–104, http://dx.doi.org/10.1109/memb.2005. 1411354.

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

51

[184] E. Rapis, Protein and Life (Self-Assembling and Symmetry of Protein Nanostructures), Philobiblion and Milta-PKPGIT, Jerusalem and Moscow, 2003 (in Russian). [185] T.A. Yakhno, O.A. Sedova, A.G. Sanin, A.S. Pelyushenko, On the existence of regular structures in liquid human blood serum (plasma) and phase transitions in the course of its drying, Tech. Phys. 48 (4) (2003) 399–403, http://dx.doi.org/10.1134/1.1568479. [186] T. Yakhno, Salt-induced protein phase transitions in drying drops, J. Colloid Interface Sci. 318 (2) (2008) 225–230, http://dx.doi.org/10.1016/ j.jcis.2007.10.020. [187] H.M. Gorr, J.M. Zueger, J.A. Barnard, Lysozyme pattern formation in evaporating drops, Langmuir 28 (9) (2012) 4039–4042, http://dx.doi.org/ 10.1021/la300125y. [188] H.M. Gorr, Z. Xiong, J.A. Barnard, Pattern recognition for identification of lysozyme droplet solution chemistry, Colloids Surf. B 115 (2014) 170–175, http://dx.doi.org/10.1016/j.colsurfb.2013.11.005. [189] Y.J.P. Carreón, J. González-Gutiérrez, M.I. Pérez-Camacho, H. Mercado-Uribe, Patterns produced by dried droplets of protein binary mixtures suspended in water, Colloids Surf. B 161 (Suppl. C) (2018) 103–110, http://dx.doi.org/10.1016/j.colsurfb.2017.10.028. [190] A.L. Fink, Protein aggregation: folding aggregates, inclusion bodies and amyloid, Fold. Des. 3 (1) (1998) R9–R23, http://dx.doi.org/10.1016/ S1359-0278(98)00002-9. [191] J. Filik, N. Stone, Drop coating deposition Raman spectroscopy of protein mixtures, Analyst 132 (2007) 544–550, http://dx.doi.org/10.1039/ B701541K. [192] Y. Liu, Y.F. Li, C.Z. Huang, Fluorimetric determination of fluorescein at the femtomole level with a self-ordered ring of a sessile droplet on glass slide support, J. Analyt. Chem. 61 (7) (2006) 647–653, http://dx.doi.org/10.1134/S1061934806070082. [193] S. Devineau, M. Anyfantakis, L. Marichal, L. Kiger, M. Morel, S. Rudiuk, D. Baigl, Protein adsorption and reorganization on nanoparticles probed by the coffee-ring effect: Application to single point mutation detection, J. Am. Chem. Soc. 138 (36) (2016) 11623–11632, http: //dx.doi.org/10.1021/jacs.6b04833. [194] Y.J.P. Carreón, M. Ríos-Ramírez, R.E. Moctezuma, J. González-Gutiérrez, Texture analysis of protein deposits produced by droplet evaporation, Sci. Rep. 8 (2018) 9580, http://dx.doi.org/10.1038/s41598-018-27959-0. [195] J. Sun, W.W. Gerberich, L.F. Francis, Electrical and optical properties of ceramic–polymer nanocomposite coatings, J. Polym. Sci. B 41 (14) (2003) 1744–1761, http://dx.doi.org/10.1002/polb.10532. [196] C.J. Martinez, J.A. Lewis, Shape evolution and stress development during latex–silica film formation, Langmuir 18 (12) (2002) 4689–4698, http://dx.doi.org/10.1021/la0114833. [197] Y. Masuda, T. Koumura, T. Okawa, K. Koumoto, Micropatterning of Ni particles on a BaTiO3 green sheet using a self-assembled monolayer, J. Colloid Interface Sci. 263 (1) (2003) 190–195, http://dx.doi.org/10.1016/S0021-9797(03)00217-0. [198] J. Jing, J. Reed, J. Huang, X. Hu, V. Clarke, J. Edington, D. Housman, T.S. Anantharaman, E.J. Huff, B. Mishra, B. Porter, A. Shenker, E. Wolfson, C. Hiort, R. Kantor, C. Aston, D.C. Schwartz, Automated high resolution optical mapping using arrayed, fluid-fixed DNA molecules, Proc. Natl. Acad. Sci. USA 95 (14) (1998) 8046–8051, http://dx.doi.org/10.1073/pnas.95.14.8046. [199] J. Aizenberg, P.V. Braun, P. Wiltzius, Patterned colloidal deposition controlled by electrostatic and capillary forces, Phys. Rev. Lett. 84 (2000) 2997–3000, http://dx.doi.org/10.1103/PhysRevLett.84.2997. [200] H. Zheng, I. Lee, M.F. Rubner, P.T. Hammond, Two component particle arrays on patterned polyelectrolyte multilayer templates, Adv. Mater. 14 (8) (2002) 569–572, http://dx.doi.org/10.1002/1521-4095(20020418)14:8<569::AID-ADMA569>3.0.CO;2-O. [201] I. Lee, H. Zheng, M.F. Rubner, P.T. Hammond, Controlled cluster size in patterned particle arrays via directed adsorption on confined surfaces, Adv. Mater. 14 (8) (2002) 572–577, http://dx.doi.org/10.1002/1521-4095(20020418)14:8<572::AID-ADMA572>3.0.CO;2-B. [202] W. Lee, A. Chan, M.A. Bevan, J.A. Lewis, P.V. Braun, Nanoparticle-mediated epitaxial assembly of colloidal crystals on patterned substrates, Langmuir 20 (13) (2004) 5262–5270, http://dx.doi.org/10.1021/la035694e. [203] A. van Blaaderen, R. Ruel, P. Wiltzius, Template-directed colloidal crystallization, Nature 385 (6614) (1997) 321–324, http://dx.doi.org/10.1038/ 385321a0. [204] K.-h. Lin, J.C. Crocker, V. Prasad, A. Schofield, D.A. Weitz, T.C. Lubensky, A.G. Yodh, Entropically driven colloidal crystallization on patterned surfaces, Phys. Rev. Lett. 85 (2000) 1770–1773, http://dx.doi.org/10.1103/PhysRevLett.85.1770. [205] W.D. Ristenpart, I.A. Aksay, D.A. Saville, Assembly of colloidal aggregates by electrohydrodynamic flow: Kinetic experiments and scaling analysis, Phys. Rev. E 69 (2004) 021405, http://dx.doi.org/10.1103/PhysRevE.69.021405. [206] K.H. Bhatt, S. Grego, O.D. Velev, An AC electrokinetic technique for collection and concentration of particles and cells on patterned electrodes, Langmuir 21 (14) (2005) 6603–6612, http://dx.doi.org/10.1021/la050658w. [207] O.D. Velev, K.H. Bhatt, On-chip micromanipulation and assembly of colloidal particles by electric fields, Soft Matter 2 (2006) 738–750, http://dx.doi.org/10.1039/B605052B. [208] A. Georgiadis, F.N. Muhamad, A. Utgenannt, J.L. Keddie, Aesthetically textured hard latex coatings by fast IR-assisted evaporative lithography, Prog. Org. Coat. 76 (12) (2013) 1786–1791, coatings Science International 2012, http://dx.doi.org/10.1016/j.porgcoat.2013.05.017. [209] H.M.J.M. Wedershoven, K.R.M. Deuss, C. Fantin, J.C.H. Zeegers, A.A. Darhuber, Active control of evaporative solution deposition by means of modulated gas phase convection, Int. J. Heat Mass Transfer 117 (Suppl. C) (2018) 303–312, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017. 09.123. [210] K.S. Kolegov, Simulation of patterned glass film formation in the evaporating colloidal liquid under IR heating, Microgravity Sci. Technol. 30 (1) (2018) 113–120, http://dx.doi.org/10.1007/s12217-017-9587-0. [211] D.J. Harris, J.A. Lewis, Marangoni effects on evaporative lithographic patterning of colloidal films, Langmuir 24 (8) (2008) 3681–3685, http://dx.doi.org/10.1021/la8000637. [212] D.J. Harris, J.C. Conrad, J.A. Lewis, Evaporative lithographic patterning of binary colloidal films, Phil. Trans. R. Soc. A 367 (1909) (2009) 5157–5165, http://dx.doi.org/10.1098/rsta.2009.0157. [213] Y.Y. Tarasevich, I.V. Vodolazskaya, L.V. Sakharova, Mathematical modeling of pattern formation caused by drying of colloidal film under a mask, Eur. Phys. J. E 39 (2) (2016) 26, http://dx.doi.org/10.1140/epje/i2016-16026-5. [214] Y.Y. Tarasevich, I.V. Vodolazskaya, Mass transfer during drying of colloidal film beneath a patterned mask that contains a hexagonal array of holes, J. Phys. Conf. Ser. 681 (1) (2016) 012033, http://dx.doi.org/10.1088/1742-6596/681/1/012033. [215] Y. Lin, Y. Chen, F. Tseng, D. Yao, Monolayer uniformity of the nanosphere mask: Two-dimensional ordered gold nanoparticle arrays with nanosphere lithography, IEEE Nanotechnol. Mag. 8 (3) (2014) 20–28, http://dx.doi.org/10.1109/MNANO.2014.2327671. [216] N. Eshtiaghi, K.P. Hapgood, A quantitative framework for the formation of liquid marbles and hollow granules from hydrophobic powders, Powder Technol. 223 (2012) 65–76, invited papers from delegates of Chemeca 2010: The 40th Annual Australasian Chemical Engineering Conference, http://dx.doi.org/10.1016/j.powtec.2011.05.007. [217] B.P. Binks, R. Murakami, Phase inversion of particle-stabilized materials from foams to dry water, Nature Mater. 5 (11) (2006) 865–869, http://dx.doi.org/10.1038/nmat1757. [218] D. Dupin, S.P. Armes, S. Fujii, Stimulus-responsive liquid marbles, J. Am. Chem. Soc. 131 (15) (2009) 5386–5387, http://dx.doi.org/10.1021/ ja901641v. [219] G. McHale, M.I. Newton, Liquid marbles: principles and applications, Soft Matter 7 (2011) 5473–5481, http://dx.doi.org/10.1039/C1SM05066D.

52

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

[220] C.P. Whitby, X. Bian, R. Sedev, Spontaneous liquid marble formation on packed porous beds, Soft Matter 8 (2012) 11336–11342, http: //dx.doi.org/10.1039/C2SM26529J. [221] B. Laborie, F. Lachaussée, E. Lorenceau, F. Rouyer, How coatings with hydrophobic particles may change the drying of water droplets: incompressible surface versus porous media effects, Soft Matter 9 (2013) 4822–4830, http://dx.doi.org/10.1039/C3SM50164G. [222] P.S. Bhosale, M.V. Panchagnula, H.A. Stretz, Mechanically robust nanoparticle stabilized transparent liquid marbles, Appl. Phys. Lett. 93 (3) (2008) 034109, http://dx.doi.org/10.1063/1.2959853. [223] R.J. Hopkins, J.P. Reid, A comparative study of the mass and heat transfer dynamics of evaporating ethanol/water, methanol/water, and 1-propanol/water aerosol droplets, J. Phys. Chem. B 110 (7) (2006) 3239–3249, http://dx.doi.org/10.1021/jp056523g. [224] K. Sefiane, S. David, M.E.R. Shanahan, Wetting and evaporation of binary mixture drops, J. Phys. Chem. B 112 (36) (2008) 11317–11323, http://dx.doi.org/10.1021/jp8030418. [225] A.K.H. Cheng, D.M. Soolaman, H.-Z. Yu, Evaporation of microdroplets of ethanol—water mixtures on gold surfaces modified with self-assembled monolayers, J. Phys. Chem. B 110 (23) (2006) 11267–11271, http://dx.doi.org/10.1021/jp0572885. [226] L. Shi, P. Shen, D. Zhang, Q. Lin, Q. Jiang, Wetting and evaporation behaviors of water—ethanol sessile drops on PTFE surfaces, Surf. Interface Anal. 41 (12–13) (2009) 95–955, http://dx.doi.org/10.1002/sia.3123. [227] Y. Hamamoto, J.R.E. Christy, K. Sefiane, Order-of-magnitude increase in flow velocity driven by mass conservation during the evaporation of sessile drops, Phys. Rev. E 83 (2011) 051602, http://dx.doi.org/10.1103/PhysRevE.83.051602. [228] J.R.E. Christy, Y. Hamamoto, K. Sefiane, Flow transition within an evaporating binary mixture sessile drop, Phys. Rev. Lett. 106 (2011) 205701, http://dx.doi.org/10.1103/PhysRevLett.106.205701. [229] R. Bennacer, K. Sefiane, Vortices, dissipation and flow transition in volatile binary drops, J. Fluid Mech. 749 (2014) 649–665, http://dx.doi.org/ 10.1017/jfm.2014.220. [230] P.G. de Gennes, Polymers at an interface; a simplified view, Adv. Colloid Interface Sci. 27 (3) (1987) 189–209, http://dx.doi.org/10.1016/00018686(87)85003-0. [231] G.J.C. Braithwaite, P.F. Luckham, Effect of molecular weight on the interactions between poly(ethylene oxide) layers adsorbed to glass surfaces, J. Chem. Soc. Faraday Trans. 93 (1997) 1409–1415, http://dx.doi.org/10.1039/A606976B. [232] J. Park, J. Moon, Control of colloidal particle deposit patterns within picoliter droplets ejected by ink-jet printing, Langmuir 22 (8) (2006) 3506–3513, http://dx.doi.org/10.1021/la053450j. [233] E.L. Talbot, A. Berson, C.D. Bain, Drying and deposition of picolitre droplets of colloidal suspensions in binary solvent mixtures, in: NIP & Digital Fabrication Conference, 2012 International Conference on Digital Printing Technologies. Pages 277–570, Society for Imaging Science and Technology, 2012, pp. 420–423. [234] K.N. Al-Milaji, R.R. Secondo, T.N. Ng, N. Kinsey, H. Zhao, Interfacial self-assembly of colloidal nanoparticles in dual-droplet inkjet printing, Adv. Mater. Interfaces 5 (10) (2018) 1701561, http://dx.doi.org/10.1002/admi.201701561. [235] J.C. Loudet, A.G. Yodh, B. Pouligny, Wetting and contact lines of micrometer-sized ellipsoids, Phys. Rev. Lett. 97 (2006) 018304, http: //dx.doi.org/10.1103/PhysRevLett.97.018304. [236] M. Parsa, R. Boubaker, S. Harmand, K. Sefiane, M. Bigerelle, R. Deltombe, Patterns from dried water-butanol binary-based nanofluid drops, J. Nanoparticle Res. 19 (8) (2017) 268, http://dx.doi.org/10.1007/s11051-017-3951-2. [237] G. Petre, M.A. Azouni, Experimental evidence for the minimum of surface tension with temperature at aqueous alcohol solution/air interfaces, J. Colloid Interface Sci. 98 (1) (1984) 261–263, http://dx.doi.org/10.1016/0021-9797(84)90503-4. [238] D. Orejon, K. Sefiane, M.E.R. Shanahan, Stick–slip of evaporating droplets: Substrate hydrophobicity and nanoparticle concentration, Langmuir 27 (21) (2011) 12834–12843, http://dx.doi.org/10.1021/la2026736. [239] A. Askounis, K. Sefiane, V. Koutsos, M.E.R. Shanahan, The effect of evaporation kinetics on nanoparticle structuring within contact line deposits of volatile drops, Colloids Surf. A 441 (2014) 855–866, http://dx.doi.org/10.1016/j.colsurfa.2012.10.017. [240] M. Parsa, S. Harmand, K. Sefiane, M. Bigerelle, R. Deltombe, Effect of substrate temperature on pattern formation of nanoparticles from volatile drops, Langmuir 31 (11) (2015) 3354–3367, http://dx.doi.org/10.1021/acs.langmuir.5b00362. [241] A.L. Yarin, G. Brenn, D. Rensink, Evaporation of acoustically levitated droplets of binary liquid mixtures, Int. J. Heat Fluid Flow 23 (4) (2002) 471–486, http://dx.doi.org/10.1016/s0142-727x(02)00142-x. [242] E. Wulsten, F. Kiekens, F. van Dycke, J. Voorspoels, G. Lee, Levitated single-droplet drying: Case study with itraconazole dried in binary organic solvent mixtures, Int. J. Pharm. 378 (1–2) (2009) 116–121, http://dx.doi.org/10.1016/j.ijpharm.2009.05.060. [243] L. Pauchard, Chapter 22 — droplets of polymers, in: D. Brutin (Ed.), Droplet Wetting and Evaporation, Academic Press, Oxford, 2015, pp. 339–350, http://dx.doi.org/10.1016/B978-0-12-800722-8.00022-9. [244] L. Pauchard, C. Allain, Mechanical instability induced by complex liquid desiccation, C. R. Phys. 4 (2) (2003) 231–239, http://dx.doi.org/10. 1016/S1631-0705(03)00027-6. [245] Y. Gorand, L. Pauchard, G. Calligari, J.P. Hulin, C. Allain, Mechanical instability induced by the desiccation of sessile drops, Langmuir 20 (12) (2004) 5138–5140, http://dx.doi.org/10.1021/la0301947. [246] A.F. Routh, Drying of thin colloidal films, Rep. Progr. Phys. 76 (4) (2013) 046603, http://dx.doi.org/10.1088/0034-4885/76/4/046603. [247] A.F. Routh, W.B. Zimmerman, Distribution of particles during solvent evaporation from films, Chem. Eng. Sci. 59 (14) (2004) 2961–2968, http://dx.doi.org/10.1016/j.ces.2004.04.027. [248] T. Okuzono, K. Ozawa, M. Doi, Simple model of skin formation caused by solvent evaporation in polymer solutions, Phys. Rev. Lett. 97 (2006) 136103, http://dx.doi.org/10.1103/PhysRevLett.97.136103. [249] Y. Li, Q. Yang, M. Li, Y. Song, Rate-dependent interface capture beyond the coffee-ring effect, Sci. Rep. 6 (1) (2016) 24628, http://dx.doi.org/ 10.1038/srep24628. [250] M.G. Hennessy, G.L. Ferretti, J.T. Cabral, O.K. Matar, A minimal model for solvent evaporation and absorption in thin films, J. Colloid Interface Sci. 488 (Suppl. C) (2017) 61–71, http://dx.doi.org/10.1016/j.jcis.2016.10.074. [251] J. Zhou, X. Man, Y. Jiang, M. Doi, Structure formation in soft-matter solutions induced by solvent evaporation, Adv. Mater. 29 (45) (2017) 1703769, http://dx.doi.org/10.1002/adma.201703769. [252] D. Sen, S. Mazumder, J.S. Melo, A. Khan, S. Bhattyacharya, S.F. D’Souza, Evaporation driven self-assembly of a colloidal dispersion during spray drying: Volume fraction dependent morphological transition, Langmuir 25 (12) (2009) 6690–6695, http://dx.doi.org/10.1021/la900160z. [253] N. Tsapis, E.R. Dufresne, S.S. Sinha, C.S. Riera, J.W. Hutchinson, L. Mahadevan, D.A. Weitz, Onset of buckling in drying droplets of colloidal suspensions, Phys. Rev. Lett. 94 (2005) 018302, http://dx.doi.org/10.1103/PhysRevLett.94.018302. [254] E. Tijerino, S. Basu, R. Kumar, Nanoparticle agglomeration in an evaporating levitated droplet for different acoustic amplitudes, J. Appl. Phys. 113 (3) (2013) 034307, http://dx.doi.org/10.1063/1.4775791. [255] Y. Zhang, Y. Qian, Z. Liu, Z. Li, D. Zang, Surface wrinkling and cracking dynamics in the drying of colloidal droplets, Eur. Phys. J. E 37 (9) (2014) 84, http://dx.doi.org/10.1140/epje/i2014-14084-3. [256] J.-L. Liu, X.-Q. Feng, On elastocapillarity: A review, Acta Mech. Sinica 28 (4) (2012) 928–940, http://dx.doi.org/10.1007/s10409-012-0131-6. [257] B. Li, F. Jia, Y.-P. Cao, X.-Q. Feng, H. Gao, Surface wrinkling patterns on a core–shell soft sphere, Phys. Rev. Lett. 106 (2011) 234301, http://dx.doi.org/10.1103/PhysRevLett.106.234301.

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

53

[258] B. Li, Y.-P. Cao, X.-Q. Feng, H. Gao, Mechanics of morphological instabilities and surface wrinkling in soft materials: a review, Soft Matter 8 (2012) 5728–5745, http://dx.doi.org/10.1039/C2SM00011C. [259] C. Zhang, Y.-K. Hao, B. Li, X.-Q. Feng, H. Gao, Wrinkling patterns in soft shells, Soft Matter 14 (2018) 1681–1688, http://dx.doi.org/10.1039/ C7SM02261A. [260] J.-C. Lin, J.W. Gentry, Spray drying drop morphology: Experimental study, Aerosol Sci. Technol. 37 (1) (2003) 15–32, http://dx.doi.org/10.1080/ 02786820300888. [261] W.S. Cheow, S. Li, K. Hadinoto, Spray drying formulation of hollow spherical aggregates of silica nanoparticles by experimental design, Chem. Eng. Res. Des. 88 (5) (2010) 673–685, http://dx.doi.org/10.1016/j.cherd.2009.11.012. [262] J. Elversson, A. Millqvist-Fureby, G. Alderborn, U. Elofsson, Droplet and particle size relationship and shell thickness of inhalable lactose particles during spray drying, J. Pharm. Sci. 92 (4) (2003) 900–910, http://dx.doi.org/10.1002/jps.10352. [263] R. Vehring, Pharmaceutical particle engineering via spray drying, Pharmaceut. Res. 25 (5) (2008) 999–1022, http://dx.doi.org/10.1007/s11095007-9475-1. [264] F. Iskandar, L. Gradon, K. Okuyama, Control of the morphology of nanostructured particles prepared by the spray drying of a nanoparticle sol, J. Colloid Interface Sci. 265 (2) (2003) 296–303, http://dx.doi.org/10.1016/S0021-9797(03)00519-8. [265] A.G. Marín, H. Gelderblom, D. Lohse, J.H. Snoeijer, Rush-hour in evaporating coffee drops, Phys. Fluids 23 (9) (2011) 091111, http://dx.doi.org/ 10.1063/1.3640018. [266] G. Huber, Rush hour in a drop of coffee, Physics 4 (2011) 65, http://dx.doi.org/10.1103/Physics.4.65. [267] N. Tsapis, D. Bennett, B. Jackson, D.A. Weitz, D.A. Edwards, Trojan particles: Large porous carriers of nanoparticles for drug delivery, Proc. Natl. Acad. Sci. 99 (19) (2002) 12001–12005, http://dx.doi.org/10.1073/pnas.182233999. [268] R.E. Trueman, E. Lago Domingues, S.N. Emmett, M.W. Murray, J.L. Keddie, A.F. Routh, Autostratification in drying colloidal dispersions: Experimental investigations, Langmuir 28 (7) (2012) 3420–3428, http://dx.doi.org/10.1021/la203975b. [269] A. Osman, L. Goehring, A. Patti, H. Stitt, N. Shokri, Fundamental investigation of the drying of solid suspensions, Ind. Eng. Chem. Res. 56 (37) (2017) 10506–10513, http://dx.doi.org/10.1021/acs.iecr.7b02334. [270] R. Kumar, E. Tijerino, A. Saha, S. Basu, Structural morphology of acoustically levitated and heated nanosilica droplet, Appl. Phys. Lett. 97 (12) (2010) 123106, http://dx.doi.org/10.1063/1.3493178. [271] L. Bansal, A. Miglani, S. Basu, Universal buckling kinetics in drying nanoparticle-laden droplets on a hydrophobic substrate, Phys. Rev. E 92 (2015) 042304, http://dx.doi.org/10.1103/PhysRevE.92.042304. [272] L. Chen, J.R.G. Evans, Arched structures created by colloidal droplets as they dry, Langmuir 25 (19) (2009) 11299–11301, http://dx.doi.org/10. 1021/la902918m. [273] N. Fu, M. Yu, X.D. Chen, A differential shrinkage approach for evaluating particle formation behavior during drying of sucrose, lactose, mannitol, skim milk, and other solid-containing droplets, Dry. Technol. (2018) http://dx.doi.org/10.1080/07373937.2018.1480028. [274] N. Fu, M.W. Woo, C. Selomulya, X.D. Chen, Shrinkage behaviour of skim milk droplets during air drying, J. Food Eng. 116 (1) (2013) 37–44, http://dx.doi.org/10.1016/j.jfoodeng.2012.11.005. [275] S.X.Q. Lin, X.D. Chen, Changes in milk droplet diameter during drying under constant drying conditions investigated using the glass-filament method, Food Bioprod. Process. 82 (3) (2004) 213–218, http://dx.doi.org/10.1205/fbio.82.3.213.44178. [276] C.S. Handscomb, M. Kraft, Simulating the structural evolution of droplets following shell formation, Chem. Eng. Sci. 65 (2) (2010) 713–725, http://dx.doi.org/10.1016/j.ces.2009.09.025. [277] N. Grasmeijer, H.W. Frijlink, W.L.J. Hinrichs, Model to predict inhomogeneous protein—sugar distribution in powders prepared by spray drying, J. Aerosol Sci. 101 (2016) 22–33, http://dx.doi.org/10.1016/j.jaerosci.2016.07.012. [278] L. Pauchard, F. Giorgiutti-Dauphiné, Mechanical instabilities induced by the drying of complex liquids, in: C. Duprat, H. Stone (Eds.), FluidStructure Interactions in Low-Reynolds-Number Flows, in: Soft Matter Series, The Royal Society of Chemistry, 2016, pp. 247–279 (Chapter 7), http://dx.doi.org/10.1039/9781782628491-00247. [279] S. Basu, L. Bansal, A. Miglani, Towards universal buckling dynamics in nanocolloidal sessile droplets: the effect of hydrophilic to superhydrophobic substrates and evaporation modes, Soft Matter 12 (2016) 4896–4902, http://dx.doi.org/10.1039/C6SM00837B. [280] L. Pauchard, Y. Couder, Invagination during the collapse of an inhomogeneous spheroidal shell, Europhys. Lett. 66 (5) (2004) 667, http: //dx.doi.org/10.1209/epl/i2003-10242-8. [281] M.S. Tirumkudulu, Buckling of a drying colloidal drop, Soft Matter 14 (2018) 7455–7461, http://dx.doi.org/10.1039/C8SM01324A. [282] F. Meng, M. Doi, Z. Ouyang, Cavitation in drying droplets of soft matter solutions, Phys. Rev. Lett. 113 (2014) 098301, http://dx.doi.org/10. 1103/PhysRevLett.113.098301. [283] L. Luo, F. Meng, J. Zhang, M. Doi, Skin formation in drying a film of soft matter solutions: Application of solute based Lagrangian scheme, Chin. Phys. B 25 (7) (2016) 076801, http://dx.doi.org/10.1088/1674-1056/25/7/076801. [284] F. Meng, L. Luo, M. Doi, Z. Ouyang, Solute based Lagrangian scheme in modeling the drying process of soft matter solutions, Eur. Phys. J. E 39 (2) (2016) 22, http://dx.doi.org/10.1140/epje/i2016-16022-9. [285] C. Sadek, H. Tabuteau, P. Schuck, Y. Fallourd, N. Pradeau, C. Le Floch-Fouéré, R. Jeantet, Shape, shell, and vacuole formation during the drying of a single concentrated whey protein droplet, Langmuir 29 (50) (2013) 15606–15613, http://dx.doi.org/10.1021/la404108v. [286] S. Arai, M. Doi, Skin formation and bubble growth during drying process of polymer solution, Eur. Phys. J. E 35 (7) (2012) 57, http: //dx.doi.org/10.1140/epje/i2012-12057-2. [287] L. Goehring, A. Nakahara, T. Dutta, S. Kitsunezaki, S. Tarafdar, Desiccation, Wiley-Blackwell, 2015, pp. 117–143 (Chapter 6), http://dx.doi.org/ 10.1002/9783527671922.ch6. [288] B. Barkia, J.L. Courouau, E. Perrin, V. Lorentz, M. Rivollier, R. Robin, L. Nicolas, C. Cabet, T. Auger, Investigation of crack propagation resistance of 304l, 316l and 316l(n) austenitic steels in liquid sodium, J. Nucl. Mater. 507 (2018) 15–23, http://dx.doi.org/10.1016/j.jnucmat.2018.04.036. [289] H. Lama, M.G. Basavaraj, D.K. Satapathy, Tailoring crack morphology in coffee-ring deposits via substrate heating, Soft Matter 13 (32) (2017) 5445–5452, http://dx.doi.org/10.1039/c7sm00567a. [290] R. Chen, L. Zhang, D. Zang, W. Shen, Understanding desiccation patterns of blood sessile drops, J. Mater. Chem. B 5 (2017) 8991–8998, http://dx.doi.org/10.1039/C7TB02290E. [291] M.S. Tirumkudulu, W.B. Russel, Cracking in drying latex films, Langmuir 21 (11) (2005) 4938–4948, http://dx.doi.org/10.1021/la048298k. [292] T. Khatun, T. Dutta, S. Tarafdar, Crack formation under an electric field in droplets of Laponite gel: Memory effect and scaling relations, Langmuir 29 (50) (2013) 15535–15542, http://dx.doi.org/10.1021/la404297k. R [293] S. Hazra, S. Sircar, T. Khatun, M.D. Choudhury, A. Giri, S. Karmakar, T. Dutta, S. Das, S. Tarafdar, Unstable crack propagation in laponite⃝ gels: selection of a sinusoidal mode in an electric field, RSC Adv. 6 (2016) 64297–64305, http://dx.doi.org/10.1039/C6RA12116K. [294] S. Tarafdar, T. Dutta, Formation of desiccation crack patterns in electric fields: a review, Phil. Trans. R. Soc. A 377 (2136) (2019) 20170398, http://dx.doi.org/10.1098/rsta.2017.0398. [295] H. Lama, R. Mondal, M.G. Basavaraj, D.K. Satapathy, Cracks in dried deposits of hematite ellipsoids: Interplay between magnetic and hydrodynamic torques, J. Colloid Interface Sci. 510 (2018) 172–180, http://dx.doi.org/10.1016/j.jcis.2017.09.022.

54

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

[296] L. Pauchard, F. Elias, P. Boltenhagen, A. Cebers, J.C. Bacri, When a crack is oriented by a magnetic field, Phys. Rev. E 77 (2008) 021402, http://dx.doi.org/10.1103/PhysRevE.77.021402. [297] L. Pauchard, F. Parisse, C. Allain, Influence of salt content on crack patterns formed through colloidal suspension desiccation, Phys. Rev. E 59 (3) (1999) 3737–3740, http://dx.doi.org/10.1103/PhysRevE.59.3737. [298] J. McQuade, L.T. Vuong, Solvent retention and crack evolution in dropcast pedot:pss and dependence on surface wetting, ACS Omega 3 (4) (2018) 3868–3873, http://dx.doi.org/10.1021/acsomega.8b00085. [299] Y. Li, C. Lv, Z. Li, D. Quéré, Q. Zheng, From coffee rings to coffee eyes, Soft Matter 11 (2015) 4669–4673, http://dx.doi.org/10.1039/C5SM00654F. [300] L. Goehring, W.J. Clegg, A.F. Routh, Wavy cracks in drying colloidal films, Soft Matter 7 (2011) 7984–7987, http://dx.doi.org/10.1039/ C1SM05979C. [301] M. Gao, X. Huang, Y. Zhao, Formation of wavy-ring crack in drying droplet of protein solutions, Sci. China Technol. Sci. 61 (7) (2018) 949–958, http://dx.doi.org/10.1007/s11431-017-9202-y. [302] M. Hirata, Kirin No Madara - Dapples in Giraffes, Chuokoron Inc., 1975 (in Japanese). [303] B. Lawn, Fracture of Brittle Solids, second ed., in: Cambridge Solid State Science Series, Cambridge University Press, Cambridge, 1993, http://dx.doi.org/10.1017/CBO9780511623127. [304] E. Bouchbinder, T. Goldman, J. Fineberg, The dynamics of rapid fracture: instabilities, nonlinearities and length scales, Rep. Progr. Phys. 77 (4) (2014) 046501, http://dx.doi.org/10.1088/0034-4885/77/4/046501. [305] Y. Xu, W.C. Engl, E.R. Jerison, K.J. Wallenstein, C. Hyland, L.A. Wilen, E.R. Dufresne, Imaging in-plane and normal stresses near an interface crack using traction force microscopy, Proc. Natl. Acad. Sci. (2010) http://dx.doi.org/10.1073/pnas.1005537107. [306] J.Y. Kim, K. Cho, S.-a. Ryu, S.Y. Kim, B.M. Weon, Crack formation and prevention in colloidal drops, Sci. Rep. 5 (2015) 13166, http: //dx.doi.org/10.1038/srep13166. [307] S. Nag, S. Sinha, S. Sadhukhan, T. Dutta, S. Tarafdar, Crack patterns in desiccating clay-polymer mixtures with varying composition, J. Phys.: Condens. Matter 22 (1) (2010) 015402, http://dx.doi.org/10.1088/0953-8984/22/1/015402. [308] S.S. Sazhin, O. Rybdylova, A.S. Pannala, S. Somavarapu, S.K. Zaripov, A new model for a drying droplet, Int. J. Heat Mass Transfer 122 (2018) 451–458, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2018.01.094. [309] B.J. Fischer, Particle convection in an evaporating colloidal droplet, Langmuir 18 (1) (2002) 60–67, http://dx.doi.org/10.1021/la015518a. [310] H. Hu, R.G. Larson, Evaporation of a sessile droplet on a substrate, J. Phys. Chem. B 106 (6) (2002) 1334–1344, http://dx.doi.org/10.1021/ jp0118322. [311] Y.O. Popov, Evaporative deposition patterns: Spatial dimensions of the deposit, Phys. Rev. E 71 (3) (2005) 036313, http://dx.doi.org/10.1103/ PhysRevE.71.036313. [312] M. Cachile, O. Bénichou, C. Poulard, A.M. Cazabat, Evaporating droplets, Langmuir 18 (21) (2002) 8070–8078, http://dx.doi.org/10.1021/ la0204646. [313] M. Cachile, O. Bénichou, A.M. Cazabat, Evaporating droplets of completely wetting liquids, Langmuir 18 (21) (2002) 7985–7990, http: //dx.doi.org/10.1021/la020231e. [314] S.F. Chini, A. Amirfazli, Resolving an ostensible inconsistency in calculating the evaporation rate of sessile drops, Adv. Colloid Interface Sci. 243 (2017) 121–128, http://dx.doi.org/10.1016/j.cis.2016.05.015. [315] Y. Tsoumpas, S. Dehaeck, A. Rednikov, P. Colinet, Effect of Marangoni flows on the shape of thin sessile droplets evaporating into air, Langmuir 31 (49) (2015) 13334–13340, http://dx.doi.org/10.1021/acs.langmuir.5b02673. [316] H.V. Tran, T.A.H. Nguyen, S.R. Biggs, A.V. Nguyen, On the predictions for diffusion-driven evaporation of sessile droplets with interface cooling, Chem. Eng. Sci. 177 (2018) 417–421, http://dx.doi.org/10.1016/j.ces.2017.12.003. [317] T.A.H. Nguyen, S.R. Biggs, A.V. Nguyen, Analytical model for diffusive evaporation of sessile droplets coupled with interfacial cooling effect, Langmuir 34 (23) (2018) 6955–6962, http://dx.doi.org/10.1021/acs.langmuir.7b03862. [318] C. Xie, G. Liu, M. Wang, Evaporation flux distribution of drops on a hydrophilic or hydrophobic flat surface by molecular simulations, Langmuir 32 (32) (2016) 8255–8264, http://dx.doi.org/10.1021/acs.langmuir.6b01986. [319] N. Jung, C.S. Yoo, P.H. Leo, Instability deposit patterns in an evaporating droplet, J. Phys. Chem. B 118 (9) (2014) 2535–2543, http: //dx.doi.org/10.1021/jp4111844. [320] H. Zhang, Y.G. Shan, L. Li, M. Lu, R. Li, Modeling the self-assembly of nanoparticles into branched aggregates from a sessile nanofluid droplet, Appl. Therm. Eng. 94 (2016) 650–656, http://dx.doi.org/10.1016/j.applthermaleng.2015.10.160. [321] E. Rabani, D.R. Reichman, P.L. Geissler, L.E. Brus, Drying-mediated self-assembly of nanoparticles, Nature 426 (6964) (2003) 271–274, http://dx.doi.org/10.1038/nature02087. [322] Y.Y. Tarasevich, D.M. Pravoslavnova, Segregation in desiccated sessile drops of biological fluids, Eur. Phys. J. E 22 (4) (2007) 311–314, http://dx.doi.org/10.1140/epje/e2007-00037-6. [323] K. Ozawa, E. Nishitani, M. Doi, Modeling of the drying process of liquid droplet to form thin film, Japan. J. Appl. Phys. 44 (2005) 4229–4234, http://dx.doi.org/10.1143/JJAP.44.4229. [324] M. Kobayashi, M. Makino, T. Okuzono, M. Doi, Interference effects in the drying of polymer droplets on substrate, J. Phys. Soc. Japan 79 (4) (2010) 044802, http://dx.doi.org/10.1143/JPSJ.79.044802. [325] Y. Tarasevich, I. Vodolazskaya, O. Isakova, Desiccating colloidal sessile drop: dynamics of shape and concentration, Colloid Polym. Sci. 289 (2011) 1015–1023, http://dx.doi.org/10.1007/s00396-011-2418-8. [326] Y.Y. Tarasevich, I.V. Vodolazskaya, O.P. Bondarenko, Modeling of spatial–temporal distribution of the components in the drying sessile droplet of biological fluid, Colloids Surf. A 432 (2013) 99–103, Wetting and evaporation: Droplets of pure and complex fluids, http: //dx.doi.org/10.1016/j.colsurfa.2013.04.069. [327] N.I. Lebovka, V.A. Gigiberiya, O.S. Lytvyn, Y.Y. Tarasevich, I.V. Vodolazskaya, O.P. Bondarenko, Drying of sessile droplets of laponite-based aqueous nanofluids, Colloids Surf. A 462 (2014) 52–63, http://dx.doi.org/10.1016/j.colsurfa.2014.08.014. [328] W.J. Gerken, M.A. Oehlschlaeger, Modeling nanofluid sessile drop evaporation, Heat Mass Transf. 53 (7) (2017) 2341–2349, http://dx.doi.org/ 10.1007/s00231-017-1986-7. [329] A.D. Eales, A.F. Routh, N. Dartnell, G. Simon, Evaporation of pinned droplets containing polymer — an examination of the important groups controlling final shape, AIChE J. 61 (5) (2015) 1759–1767, http://dx.doi.org/10.1002/aic.14777. [330] A. Zigelman, O. Manor, A model for pattern deposition from an evaporating solution subject to contact angle hysteresis and finite solubility, Soft Matter 12 (26) (2016) 5693–5707, http://dx.doi.org/10.1039/c6sm00579a. [331] A. Zigelman, O. Manor, The deposition of colloidal particles from a sessile drop of a volatile suspension subject to particle adsorption and coagulation, J. Colloid Interface Sci. 509 (2018) 195–208, http://dx.doi.org/10.1016/j.jcis.2017.08.088. [332] A. Zigelman, O. Manor, Simulations of the dynamic deposition of colloidal particles from a volatile sessile drop, J. Colloid Interface Sci. 525 (2018) 282–290, http://dx.doi.org/10.1016/j.jcis.2018.04.054. [333] K.L. Maki, S. Kumar, Fast evaporation of spreading droplets of colloidal suspensions, Langmuir 27 (18) (2011) 11347–11363, http://dx.doi.org/ 10.1021/la202088s.

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

55

[334] Y.Y. Tarasevich, Simple analytical model of capillary flow in an evaporating sessile drop, Phys. Rev. E 71 (2) (2005) 027301, http://dx.doi.org/ 10.1103/PhysRevE.71.027301. [335] H. Masoud, J.D. Felske, Analytical solution for inviscid flow inside an evaporating sessile drop, Phys. Rev. E 79 (1) (2009) 016301, http: //dx.doi.org/10.1103/PhysRevE.79.016301. [336] H. Masoud, J.D. Felske, Analytical solution for stokes flow inside an evaporating sessile drop: Spherical and cylindrical cap shapes, Phys. Fluids 21 (4) (2009) 042102, http://dx.doi.org/10.1063/1.3112002. [337] M.R. Barmi, C.D. Meinhart, Convective flows in evaporating sessile droplets, J. Phys. Chem. B 118 (9) (2014) 2414–2421, http://dx.doi.org/10. 1021/jp408241f. [338] C. Bouchenna, M.A. Saada, S. Chikh, L. Tadrist, Generalized formulation for evaporation rate and flow pattern prediction inside an evaporating pinned sessile drop, Int. J. Heat Mass Transfer 109 (2017) 482–500, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.114. [339] L.Y. Barash, T.P. Bigioni, V.M. Vinokur, L.N. Shchur, Evaporation and fluid dynamics of a sessile drop of capillary size, Phys. Rev. E 79 (4) (2009) 046301, http://dx.doi.org/10.1103/PhysRevE.79.046301. [340] L.Y. Barash, Dependence of fluid flows in an evaporating sessile droplet on the characteristics of the substrate, Int. J. Heat Mass Transfer 84 (Suppl. C) (2015) 419–426, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.01.014. [341] L.Y. Barash, Marangoni convection in an evaporating droplet: Analytical and numerical descriptions, Int. J. Heat Mass Transfer 102 (Suppl. C) (2016) 445–454, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.06.042. [342] C. Diddens, Detailed finite element method modeling of evaporating multi-component droplets, J. Comput. Phys. 340 (Suppl. C) (2017) 670–687, http://dx.doi.org/10.1016/j.jcp.2017.03.049. [343] C. Diddens, J.G.M. Kuerten, C.W.M. van der Geld, H.M.A. Wijshoff, Modeling the evaporation of sessile multi-component droplets, J. Colloid Interface Sci. 487 (Suppl. C) (2017) 426–436, http://dx.doi.org/10.1016/j.jcis.2016.10.030. [344] R. Bhardwaj, X. Fang, D. Attinger, Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study, New J. Phys. 11 (7) (2009) 075020, http://dx.doi.org/10.1088/1367-2630/11/7/075020. [345] E. Widjaja, M. Harris, Particle deposition study during sessile drop evaporation, AIChE J. 54 (9) (2008) 2250–2260, http://dx.doi.org/10.1002/ aic.11558. [346] T. Breinlinger, T. Kraft, A simple method for simulating the coffee stain effect, Powder Technol. 256 (2014) 279–284, http://dx.doi.org/10.1016/ j.powtec.2014.02.024. [347] T.A.H. Nguyen, S.R. Biggs, A.V. Nguyen, Manipulating colloidal residue deposit from drying droplets: Air/liquid interface capture competes with coffee-ring effect, Chem. Eng. Sci. 167 (Suppl. C) (2017) 78–87, http://dx.doi.org/10.1016/j.ces.2017.04.001. [348] N.R. Devlin, K. Loehr, M.T. Harris, The importance of gravity in droplet evaporation: A comparison of pendant and sessile drop evaporation with particles, AIChE J. 62 (3) (2015) 947–955, http://dx.doi.org/10.1002/aic.15120. [349] G. Son, Numerical simulation of particle-laden droplet evaporation with the Marangoni effect, Eur. Phys. J. Spec. Top. 224 (2) (2015) 401–413, http://dx.doi.org/10.1140/epjst/e2015-02369-y. [350] J. Lee, G. Son, A level-set method for analysis of particle motion in an evaporating microdroplet, Numer. Heat Transfer B 67 (1) (2015) 25–46, http://dx.doi.org/10.1080/10407790.2014.949556. [351] H. Hwang, G. Son, A level-set method for the direct numerical simulation of particle motion in droplet evaporation, Numer. Heat Transfer B 68 (6) (2015) 479–494, http://dx.doi.org/10.1080/10407790.2015.1052309. [352] S. Jafari Kang, V. Vandadi, J.D. Felske, H. Masoud, Alternative mechanism for coffee-ring deposition based on active role of free surface, Phys. Rev. E 94 (2016) 063104, http://dx.doi.org/10.1103/PhysRevE.94.063104. [353] M. Zhao, X. Yong, Modeling evaporation and particle assembly in colloidal droplets, Langmuir 33 (23) (2017) 5734–5744, http://dx.doi.org/10. 1021/acs.langmuir.7b00284. [354] B. Shi, E.B. Webb III, Self-pinning of a nanosuspension droplet: Molecular dynamics simulations, Phys. Rev. E 94 (2016) 012614, http: //dx.doi.org/10.1103/PhysRevE.94.012614. [355] A. Crivoi, F. Duan, Three-dimensional Monte Carlo model of the coffee-ring effect in evaporating colloidal droplets, Sci. Rep. 4 (1) (2014) 4310, http://dx.doi.org/10.1038/srep04310. [356] H.-S. Kim, S.S. Park, F. Hagelberg, Computational approach to drying a nanoparticle-suspended liquid droplet, J. Nanopart. Res. 13 (1) (2011) 59–68, http://dx.doi.org/10.1007/s11051-010-0062-8. [357] J.A. Warren, W.J. Boettinger, Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method, Acta Metall. Mater. 43 (2) (1995) 689–703, http://dx.doi.org/10.1016/0956-7151(94)00285-P. [358] A.C. Levi, M. Kotrla, Theory and simulation of crystal growth, J. Phys. Condens. Matter 9 (2) (1997) 299–344, http://dx.doi.org/10.1088/09538984/9/2/001. [359] A. Crivoi, F. Duan, Evaporation-induced formation of fractal-like structures from nanofluids, Phys. Chem. Chem. Phys. 14 (2012) 1449–1454, http://dx.doi.org/10.1039/C1CP22989C. [360] Y.Y. Tarasevich, Computer simulation of crystal growth from solution, Tech. Phys. 46 (5) (2001) 627–629, http://dx.doi.org/10.1134/1.1372959. [361] D. Mampallil, J. Reboud, R. Wilson, D. Wylie, D.R. Klug, J.M. Cooper, Acoustic suppression of the coffee-ring effect, Soft Matter 11 (2015) 7207–7213, http://dx.doi.org/10.1039/C5SM01196E. [362] L. Bansal, P. Seth, B. Murugappan, S. Basu, Suppression of coffee ring: (particle) size matters, Appl. Phys. Lett. 112 (21) (2018) 211605, http://dx.doi.org/10.1063/1.5034119. [363] M. Layani, M. Gruchko, O. Milo, I. Balberg, D. Azulay, S. Magdassi, Transparent conductive coatings by printing coffee ring arrays obtained at room temperature, ACS Nano 3 (11) (2009) 3537–3542, http://dx.doi.org/10.1021/nn901239z. [364] A. Shimoni, S. Azoubel, S. Magdassi, Inkjet printing of flexible high-performance carbon nanotube transparent conductive films by ‘‘coffee ring effect’’, Nanoscale 6 (19) (2014) 11084–11089, http://dx.doi.org/10.1039/c4nr02133a. [365] T.-S. Wong, T.-H. Chen, X. Shen, C.-M. Ho, Nanochromatography driven by the coffee ring effect, Anal. Chem. 83 (6) (2011) 1871–1873, http://dx.doi.org/10.1021/ac102963x. [366] Y. Cai, B.-m. Zhang Newby, Marangoni flow-induced self-assembly of hexagonal and stripelike nanoparticle patterns, J. Am. Chem. Soc. 130 (19) (2008) 6076–6077, http://dx.doi.org/10.1021/ja801438u. [367] T. Vicsek, Fractal Growth Phenomena, second ed., World Scientific, 1992, http://dx.doi.org/10.1142/1407. [368] E. Josten, E. Wetterskog, A. Glavic, P. Boesecke, A. Feoktystov, E. Brauweiler-Reuters, U. Rücker, G. Salazar-Alvarez, T. Brückel, L. Bergström, Superlattice growth and rearrangement during evaporation-induced nanoparticle self-assembly, Sci. Rep. 7 (1) (2017) 2802, http://dx.doi.org/ 10.1038/s41598-017-02121-4. [369] T. Sekido, S. Wooh, R. Fuchs, M. Kappl, Y. Nakamura, H.-J. Butt, S. Fujii, Controlling the structure of supraballs by pH-responsive particle assembly, Langmuir 33 (8) (2017) 1995–2002, http://dx.doi.org/10.1021/acs.langmuir.6b04648. [370] S.-H. Kim, S.Y. Lee, S.-M. Yang, G.-R. Yi, Self-assembled colloidal structures for photonics, NPG Asia Mater. 3 (1) (2011) 25–33, http: //dx.doi.org/10.1038/asiamat.2010.192. [371] E. Alonso-Redondo, M. Schmitt, Z. Urbach, C.M. Hui, R. Sainidou, P. Rembert, K. Matyjaszewski, M.R. Bockstaller, G. Fytas, A new class of tunable hypersonic phononic crystals based on polymer-tethered colloids, Nature Commun. 6 (1) (2015) http://dx.doi.org/10.1038/ncomms9309.

56

D. Zang, S. Tarafdar, Y.Y. Tarasevich et al. / Physics Reports 804 (2019) 1–56

[372] S. Ryu, J.Y. Kim, S.Y. Kim, B.M. Weon, Drying-mediated patterns in colloid-polymer suspensions, Sci. Rep. 7 (1) (2017) 1079, http://dx.doi.org/ 10.1038/s41598-017-00932-z. [373] H. Ahmed, L. Lee, C. Darmanin, L.Y. Yeo, Crystallization: A novel acoustomicrofluidic nebulization technique yielding new crystallization morphologies, Adv. Mater. 30 (3) (2018) 1870018, http://dx.doi.org/10.1002/adma.201870018. [374] M. Goto, Y. Oaki, H. Imai, Dendritic growth of NaCl crystals in a gel matrix: Variation of branching and control of bending, Cryst. Growth Des. 16 (8) (2016) 4278–4284, http://dx.doi.org/10.1021/acs.cgd.6b00323. [375] H.K. Henisch, Crystal Growth in Gels and Liesegang Rings, Cambridge University Press, Cambridge, 1988, http://dx.doi.org/10.1017/ CBO9780511525223. [376] A. Nemcsics, Quantum dots prepared by droplet epitaxial method, in: V.N. Stavrou (Ed.), Quantum Dots, IntechOpen, Rijeka, 2015 (Chapter 5). http://dx.doi.org/10.5772/60823. [377] J. Chen, W.-S. Liao, X. Chen, T. Yang, S.E. Wark, D.H. Son, J.D. Batteas, P.S. Cremer, Evaporation-induced assembly of quantum dots into nanorings, ACS Nano 3 (1) (2009) 173–180, http://dx.doi.org/10.1021/nn800568t. [378] C.-H. Yang, K.-S. Huang, Y.-S. Lin, K. Lu, C.-C. Tzeng, E.-C. Wang, C.-H. Lin, W.-Y. Hsu, J.-Y. Chang, Microfluidic assisted synthesis of multifunctional polycaprolactone microcapsules: incorporation of CdTe quantum dots, Fe3 O4 superparamagnetic nanoparticles and tamoxifen anticancer drugs, Lab Chip 9 (2009) 961–965, http://dx.doi.org/10.1039/B814952F. [379] H.-J. Jian, R.-S. Wu, T.-Y. Lin, Y.-J. Li, H.-J. Lin, S.G. Harroun, J.-Y. Lai, C.-C. Huang, Super-cationic carbon quantum dots synthesized from spermidine as an eye drop formulation for topical treatment of bacterial keratitis, ACS Nano 11 (7) (2017) 6703–6716, http://dx.doi.org/10. 1021/acsnano.7b01023. [380] K. Sefiane, On the formation of regular patterns from drying droplets and their potential use for bio-medical applications, J. Bionic Eng. 7 (Suppl.) (2010) S82–S93, http://dx.doi.org/10.1016/S1672-6529(09)60221-3. [381] W. Bou Zeid, J. Vicente, D. Brutin, Influence of evaporation rate on cracks’ formation of a drying drop of whole blood, Colloids Surf. A 432 (2013) 139–146, http://dx.doi.org/10.1016/j.colsurfa.2013.04.044. [382] B. Sobac, D. Brutin, Desiccation of a sessile drop of blood: Cracks, folds formation and delamination, Colloids Surf. A 448 (2014) 34–44, http://dx.doi.org/10.1016/j.colsurfa.2014.01.076. [383] C. Hurth, T. Contente-Cuomo, M. Murtaza, F. Zenhausern, Influence of a single nucleotide polymorphism (SNP) and DNA hybridization on the drying patterns of microdroplets, J. Nanomed. 2 (2018) 1010. [384] P. Lebedev-Stepanov, M. Buzoverya, Y. Potekhina, K. Vlasov, Morphological analysis of images of dried droplets of saliva for determination the degree of endogenous intoxication, J. Bioinform. Genomics 4 (9) (2018) 2, http://dx.doi.org/10.18454/jbg.2018.4.9.2. [385] R.L. Rosemond, S.J. Lombardi, F.H. Boehm, Ferning of amniotic fluid contaminated with blood, Obstet. Gynecol. 75 (3 Pt 1) (1990) 338–340, http://europepmc.org/abstract/MED/2304705. [386] E. Alberts, C. Warner, E. Barnes, K. Pilkiewicz, E. Perkins, A. Poda, Genetically tunable M13 phage films utilizing evaporating droplets, Colloid. Surface. B 161 (2018) 210–218, http://dx.doi.org/10.1016/j.colsurfb.2017.10.039. [387] T.V. Kasyap, D.L. Koch, M. Wu, Bacterial collective motion near the contact line of an evaporating sessile drop, Phys. Fluids 26 (11) (2014) 111703, http://dx.doi.org/10.1063/1.4901958. [388] A.K. Thokchom, R. Swaminathan, A. Singh, Fluid flow and particle dynamics inside an evaporating droplet containing live bacteria displaying chemotaxis, Langmuir 30 (41) (2014) 12144–12153, http://dx.doi.org/10.1021/la502491e. [389] D.M. Glibitskiy, O.A. Gorobchenko, O.T. Nikolov, A.V. Shestopalova, M.A. Semenov, Characterization of zigzag patterns on the surface of bovine serum albumin films, Biophys. Bull. 1 (37) (2017) 16–29. [390] I.I. Smalyukh, J. Butler, J.D. Shrout, M.R. Parsek, G.C.L. Wong, Elasticity-mediated nematiclike bacterial organization in model extracellular DNA matrix, Phys. Rev. E 78 (2008) 030701, http://dx.doi.org/10.1103/PhysRevE.78.030701. [391] B. Roy, S. Karmakar, A. Giri, S. Tarafdar, Pattern formation of drying lyotropic liquid crystalline droplet, RSC Adv. 6 (2016) 112695–112703, http://dx.doi.org/10.1039/C6RA22579A. [392] M.O. Kokornaczyk, G. Dinelli, I. Marotti, S. Benedettelli, D. Nani, L. Betti, Self-organized crystallization patterns from evaporating droplets of common wheat grain leakages as a potential tool for quality analysis, Sci. World J. 11 (2011) 1712–1725, http://dx.doi.org/10.1100/2011/937149. [393] J.-O. Andersen, C.B. Henriksen, A.A. Laursen, J. and. Nielsen, Computerised image analysis of biocrystallograms originating from agricultural products, Comput. Electron. Agric. 22 (1) (1999) 51–69, http://dx.doi.org/10.1016/S0168-1699(98)00043-X. [394] N. Busscher, J. Kahl, J.-O. Andersen, M. Huber, G. Mergardt, P. Doesburg, M. Paulsen, A. Ploeger, Standardization of the biocrystallization method for carrot samples, Biol. Agric. Hortic. 27 (1) (2010) 1–23, http://dx.doi.org/10.1080/01448765.2010.10510427. [395] J. González-Gutiérrez, R. Pérez-Isidoro, J.C. Ruiz-Suárez, A technique based on droplet evaporation to recognize alcoholic drinks, Rev. Sci. Instrum. 88 (7) (2017) 074101, http://dx.doi.org/10.1063/1.4991818. [396] N. Laan, F. Smith, C. Nicloux, D. Brutin, Morphology of drying blood pools, Forensic Sci. Int. 267 (2016) 104–109, http://dx.doi.org/10.1016/j. forsciint.2016.08.005. [397] F.R. Smith, D. Brutin, Wetting and spreading of human blood: Recent advances and applications, Curr. Opin. Colloid Interface Sci. 36 (2018) 78–83, http://dx.doi.org/10.1016/j.cocis.2018.01.013. [398] F.R. Smith, C. Nicloux, D. Brutin, Influence of the impact energy on the pattern of blood drip stains, Phys. Rev. Fluids 3 (2018) 013601, http://dx.doi.org/10.1103/PhysRevFluids.3.013601. [399] F.R. Smith, N.C. Buntsma, D. Brutin, Roughness influence on human blood drop spreading and splashing, Langmuir 34 (3) (2018) 1143–1150, http://dx.doi.org/10.1021/acs.langmuir.7b02718. [400] M. Wu, X. Man, M. Doi, Multi-ring deposition pattern of drying droplets, Langmuir 34 (32) (2018) 9572–9578, http://dx.doi.org/10.1021/acs. langmuir.8b01655. [401] Q. Shi, W. Di, D. Dong, L.W. Yap, L. Li, D. Zang, W. Cheng, A general approach to free-standing nanoassemblies via acoustic levitation self-assembly, ACS Nano (2019) under revision. [402] G. Ahmed, O. Arjmandi Tash, J. Cook, A. Trybala, V. Starov, Biological applications of kinetics of wetting and spreading, Adv. Colloid Interface Sci. 249 (2017) 17–36, Recent nanotechnology and colloid science development for biomedical applications, http://dx.doi.org/10.1016/j.cis. 2017.08.004. [403] R. Gebhardt, J.-M. Teulon, J.-L. Pellequer, M. Burghammer, J.-P. Colletierde, C. Riekel, Virus particle assembly into crystalline domains enabled by the coffee ring effect, Soft Matter 10 (2014) 5458, http://dx.doi.org/10.1039/c4sm00414k.