Nanoparticle motion and deposition near the triple line in evaporating sessile water droplet on a superhydrophilic substrate

Experimental Thermal and Fluid Science 76 (2016) 67–74

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Nanoparticle motion and deposition near the triple line in evaporating sessile water droplet on a superhydrophilic substrate Zhuo Sun, Leping Zhou ⇑, Congjie Xiao, Xiaoze Du, Yongping Yang Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China

a r t i c l e

i n f o

Article history: Received 8 December 2015 Received in revised form 1 March 2016 Accepted 8 March 2016 Available online 11 March 2016 Keywords: Sessile droplet Evaporation Nanoparticle movement Nano-PIV Deposition pattern

a b s t r a c t The evaporation of a sessile droplet with suspended nonvolatile materials has been extensively studied for its particular characteristics in heat and mass transfer. The deposition patterns of it were believed to be controlled by the contact line movement; however, the mechanisms of the deposition patterns are very complicated, especially due to the nanoparticle movement near the triple line. In this paper, the nanoparticle movement and deposition near the contact line of a drying droplet are experimentally investigated, using fluorescent nanoparticles as direct tracers. It shows that the nanoparticle velocity in the thin liquid film region, obtained by the evanescent wave based multilayer nano-particle image velocimetry (MnPIV) technique, can be much higher than that near the liquid–vapor interface at the later stage of evaporation process in water droplet on a superhydrophilic substrate. On the other hand, the deposition patterns, which exhibits scattered dots, radial spokes and multi-rings due to the constant contact radius (CCR) and constant contact angle (CCA) modes happened recurrently during the evaporation process, can also be altered substantially by the nanoparticle concentration, which is an important parameter influencing the energy barrier. The analysis on the energy barrier indicates that there exists the maximum energy barrier when the deposition transits from lambdoid pattern to multi-ring pattern. Ó 2016 Elsevier Inc. All rights reserved.

1. Introduction Droplet evaporation has been extensively studied for more than one hundred years due to its particular characteristics in heat and mass transfer. The evaporation of a sessile droplet of water or other volatile solvent, suspended with nonvolatile materials such as nanoparticles, normally leaves a ring stain on solid substrate and hence plays an important role in industrial applications such as inkjet printing, DNA microarrays, thin film coatings, and optoelectronic device manufacturing [1–4]. Besides ring-like patterns, the depositions can show many other forms including uniform film, central bulge, concentric rings, and branches-chevron patterns [1,5]. These deposition patterns were believed to be controlled by the fluid flow of droplet, especially the contact line movement which is pinning or depinning to the solid surface. For example, the contact line can advance at the initial stage of evaporation (corresponding to the CCR evaporation mode), then recede when the receding contact angle is reached (corresponding to the CCA evaporation mode), and finally diminish its contact angle and radius simultaneously [6]. The contact line can also move in a stick–slip

⇑ Corresponding author. http://dx.doi.org/10.1016/j.expthermflusci.2016.03.009 0894-1777/Ó 2016 Elsevier Inc. All rights reserved.

mode due to the chemical heterogeneity and physical roughness, and the potential energy barrier per unit length of the contact line was assumed to be attributed to the pinning effect [7]. The fluid flow of an evaporating droplet includes the capillary flow induced by the non-uniform evaporative flux and the Marangoni flow resulted from the temperature gradient or the solute concentration gradient along the free surface [8]. The main mechanisms which control the fluid flow of an evaporating droplet have been widely investigated as they determine the particle movement and the final deposition patterns to a great extent [9,10]. However, the fluid flow of the evaporating droplet and the final deposition patterns can be influenced by various factors. When a droplet is pinned on the solid surface, the capillary flow induced by surface tensions moves radially outward to replenish the liquid loss at the edge and thus the particles are driven outward and adsorbed at the triple line to form deposition pattern such as coffee-ring [8]. Meanwhile, the non-uniformities of evaporation rate along the droplet surface and heat transfer from the substrate determine the direction of the thermally induced Marangoni flow, and the distribution of solute determines the direction of the concentration gradient induced Marangoni flow which is usually moving toward the droplet center and therefore bringing the particles to the central region to ultimately form a relatively

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Nomenclature A F g G R t u U

proportional constant force (N) gravity (m/s2) Gibbs free energy (J) contact radius (m) time (s) velocity (m/s) energy barrier (J)

Greek symbols d deviation from equilibrium c surface tension (N/m)

uniform deposition pattern [8,11]. Factors that may influence the capillary flow and Marangoni flow include: solvent properties, surfactant concentration, droplet size, particle size and concentration for the liquid [12–15]; thermal conductivity, surface roughness, wettability and thickness for the solid substrate [14–18]; ambient temperature, relative humidity and atmospheric pressure for the vapor [19–21]; and external conditions such as substrate heating, magnetic or electric field, pH value and low frequency vibration [22–25]. The mechanisms of fluid flow and deposition patterns are therefore very complicated, especially due to the lack of understanding of the particle movement near the triple line during droplet evaporation. The method for obtaining the particle velocity is usually the fluorescent microscopy technique, by which high concentration of particles accumulated in the vicinity of the contact line at the early evaporation stage can be observed [26]. However, the movement of particles is not only passively driven by the capillary flow and Marangoni flow inside a droplet, but also depends on the forces such as drag, van der Waals, surface tension or the others [27]. Distinguished by the controlling van der Waals forces and the difference of transfer rate, the extended meniscus near the triple line where the droplet contacts with the substrate can be divided into regions of meniscus, thin film and adsorption layer [28]. Theoretical and experimental evidences have shown that liquid evaporates intensely in the thin film region [29], but direct observation of this region through the traditional methods is inherently difficult because of the optical limit. Although fluorescent microscopy has been used to study the evolution of the precursor film that precedes the macroscopic contact line, only a completely wetting fluid can be measured in these studies [30]. The total internal reflection fluorescence microscopy (TIRFM) technique, which uses the evanescent excitation field produced by total internal reflection of light, was recently proofed to be a very useful tool for near-wall measurements of the contact angle and film thickness of a partially wetting droplet with sufficient spatial resolution [31,32]. The TIRFM technique can actually be utilized for many other applications, including nano-particle image velocimetry (nano-PIV) for microflow visualization [33,34] and multilayer nano-particle image velocimetry (MnPIV) in the near wall region [35] at nanoscale level. In this work, we use fluorescent nanoparticles as tracers for particle movement near the contact line of an evaporating droplet to obtain experimentally the nearwall velocity profile near the contact line by the MnPIV technique. The tracer nanoparticles are then used directly for recording the deposition patterns after the droplet evaporation. The purpose of this paper is to analyze the influence of particle movement near the triple line in the near wall region, therefore an analysis of the energy barrier and its influence on the deposition patterns of the nanoparticles are presented in the end of this paper.

h

q

contact angle (°) liquid density (m3/s)

Subscripts 0 equilibrium state ave average f drying lg liquid–gas interface sg solid–gas interface sl solid–liquid interface

2. Experiments The nanoparticles used for direct observation of their motion and deposition are fluorescent polystyrene microspheres (Thermo Fisher, f-8803) with nominal diameter of 100 nm and coefficient of variation (CV) of about 5% [36]. The concentrations of the nanoparticles suspended in deionized water are 0%, 0.0005%, 0.001%, 0.002%, and 0.004% w/v, respectively. Before the test, each droplet with nanoparticle concentration of 4 mL is employed for calibrating the linearity between the fluorescence and the illumination. In the experiment, each droplet with volume of ca. 0.5 lL is carefully dripped on the substrate using a 10 lL micro syringe. The droplet radius is ca. 2.7 mm for deionized water and is smaller than the capillary length scale (c/qg)1/2, where c is the surface tension, q and g are the liquid density and the acceleration of gravity, respectively. Therefore, the gravity effect can be neglected and the spherical cap assumption holds for the droplet. The droplet evaporates under the natural conditions, in which the atmospheric temperature and relative humidity are 22 ± 0.5 °C and 40 ± 1%, respectively. Fig. 1 shows the schematic diagram of the experimental setup, the main body of which is an inverted microscope (Olympus IX71). For near-wall velocimetry using the nPIV and the MnPIV techniques, the droplet with fluorescent nanoparticles is illuminated by evanescent waves at 488 nm with a penetration depth zp of ca. 86 nm formed by a 60
total internal reflection fluorescence (TIRF) objective from the optical fiber coupled beam of a continuous wave solid laser (Coherent, FV5-LA-AR). The laser output power is less than 5 mW and the coupling efficiency of the optical fiber is about 65%. The polystyrene emissions are isolated by an epifluorescent bandpass filter cube (Chroma Tech hq550/40m + zq514rdc) that transmitted light at k = 512 nm and reflect the 488 nm illumination, then imaged at exposures of 15 ms by the TIRF objective onto the electron-multiplying charge-coupled device (EMCCD, Andor Ixon3 Ultra 897) at electronic gain of 10 times and framing rates of about 64 Hz and recorded as 16 bit 512
512 pixels images. The magnification of the imaging system is 60, corresponding to 0.267 lm/pixel and a 68.26
68.26 lm2 field of view. To minimize the effect of excitation light on evaporation, the tracer nanoparticles are illuminated only during image acquisition using a shutter. To check the effect of excitation light, the total drying time are compared for two cases with and without the excitation light, and it shows that there is unobvious difference between them under the same conditions of temperature and humidity. Under all conditions, the experiments are repeated 10
, showing consistent dynamics of the droplet evaporation. For deposition pattern recording after the droplet dries out, the laser beam and the 10
objective with the EMCCD are used directly for taking images of the deposition patterns.

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Droplet Deposition

Droplet Coverslip

Coverslip

Objective

Dichroic Mirror

Objective

λ = 488nm Solid Laser

Dichroic Mirror

λ = 488nm Solid Laser

Beam Splitter

Beam Splitter

Emission Filter

Emission Filter EMCCD camera

PC

EMCCD camera

PC

Fig. 1. Schematic diagram of the experimental setup. Left: TIRF observation; right: direct observation.

difficult to quantitatively analyze the impact of each factor on the accuracies of the measured velocity. It was generally suggested that the uncertainty for the velocity can be reduced to less than 4% by using the particle-tracking algorithm, carefully choosing the time interval and measuring window size, and averaging multiple results [41]. 3. Results and discussion 3.1. Near-wall nanoparticle motion near the triple line Fig. 2 shows the in-plane average velocity of the fluorescent nanoparticles near the triple line during the evaporation of deionized water on the superhydrophilic substrate, using eight groups of velocity data calculated with the image series by the nPIV method. The nonlinear fit of the average velocity with respective to the time is expressed as a reciprocal function uave = A/(tf–t), where A is a proportional constant, tf is the drying time, and t is the time. Taking the drying time as 425 s, one has the constant A = 2691 lm, then the fitting result can be shown as the dot line in Fig. 2. The R-square for this fitting, however, is 0.762. Taking A and tf as the fitting parameters, the result with A = 1387 lm and tf = 333 s shown as the dash line in Fig. 2 produces the R-square of 0.958. 25 nonlinear fit: u ave = A /( t f-t)

Average velocity (μm/s)

Coverslips (Thermo Fisher) with thickness of 0.13–0.17 mm is used as substrates. Before being used, the coverslips are cleansed manually and carefully by cleanser essence and deionized water, then they are put in a beaker of ethanol, sonicated for 30 min to remove all the organic matters on the surfaces, and rinsed repeatedly by deionized water. Then, they are put in a piranha solution (98% H2SO4 and 30% H2O2 with volume ratio of 3:1) at a water bath of 80 °C after sonicated for the purpose of hydrophilic treatment. These substrates are stored in deionized water to prevent the adsorption of airborne contaminants and are taken out for drying by hot air blower prior to each experiment. Observation of deionized water on the treated coverslips indicates that a typical value of contact angle of about 6° can be obtained for the water on the substrate. Since the contact angle is mainly influenced by the substrate wettability and we can only make the substrates as hydrophilic as possible during preparation of them, a range of 5–8° for the contact angle is observed. The treated superhydrophilic coverslips are used for the following experiment and analysis. The temperature and relative humidity change of ambient environment in this experiment are less than 1 °C and 2%, respectively, in order to reduce their impact on evaporation rates. The total drying time of a 0.5 lL deionized water droplet on a normal coverslip is about 784 s which is the average value of twenty measurements. When the droplet is placed on a superhydrophilic surface treated by the piranha solution, the droplet spreads to the major contact area of the surface and the total drying time is merely 425 s. Since the superhydrophilic coverslips are used as substrates, they will also be beneficial for observing the details of deposition patterns. The MnPIV technique utilizes the exponentially decaying nature of the evanescent-wave illumination for the tracer particles in a typical particle image velocimetry (PIV) image [35], which is further divided into sublayers based on the tracer intensity. By processing the sub-images using standard algorithm of particle tracking velocimetry, the particle position and the distance between the particle center and the wall can be correlated and thus the nanoparticle movement in the liquid film near the triple line can be directly quantified. The effectivity and accuracy of this method were first validated by prior researches including electro-osmotic flow, near-wall flow, microscale Poiseuille flow, and nanoscale near-wall contact line visualization [37–40]. However, due to the hindered Brownian diffusion, time interval within one image pair and non-uniform distribution of particles, it is

A =2691 μ m, t f=425 s

20

A =1387 μ m, t f=333 s 15

10

5

0

0

50

100

150

200

250

300

Time (s) Fig. 2. In-plane average velocity of nanoparticles near the triple line of a water droplet.

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Hence it is more reasonable to take tf = 333 s as the essential drying time rather than as the total drying time. Nevertheless, the nonlinear fit of the average velocity for the fluorescent nanoparticles is in good agreement with the analysis of ring stains from dried liquid droplets, in which the capillary flow is believed to be the major reason for nanoparticle deposition [42]. Droplet evaporation in ambient environment is usually considered as a diffusion-controlled process and is greater in the vicinity of the triple line. In this experiment, the velocity of the fluorescent nanoparticles in the extended meniscus of liquid film underneath the water droplet are measured by the evanescent wave based MnPIV technique, with which the near-wall region (about 500 nm away from the substrate surface) is illuminated by the evanescent wave. The results shown in Fig. 3(a) shows that the near-wall velocities with respective to the height from the substrate surface are complicated in the first 140 s. The general trend for the velocities are toward the droplet center at the lower sublayers and are toward the droplet edge at the upper sublayers, indicating that there are a counterclockwise and a clockwise circling motions in the droplet. In the next 90 s, as shown in Fig. 3(b), the circling motions may vanish, the diffusion process may be dominant, and the fluorescent nanoparticles uniformly move toward the droplet edge where the velocities increase with the time. In other words, due to the competition between the diffusion process and the macroscale circling motions in the droplet, the velocities of the nanoparticles in the thin liquid film region can be much higher than that near the liquid–vapor interface at the later stage of evaporation process in water droplet.

3.2. Nanoparticle deposition near the triple line The inclusion of nanoparticles can also influence the pinning of the contact line and thus the total drying time of the droplet by the deposition process. As shown in Fig. 4, the deposition for which the nanoparticle concentration is 0.002% w/v exhibits various patterns during the evaporation of the droplet. At the earlier stage of the evaporation, the contact line of the droplet keeps pinned on the substrate, with the contact radius remains constant (about 1.76 mm) while the contact angle decreases from the initial value of about 6.7° until it reaches a critical value (or the receding angle being about 4°) before the contact line starts shrinking slowly with a shrinking speed lower than 1 lm/s in about half of the total drying time. The critical contact angle at which the contact line starts to recede for pure water on the superhydrophilic substrate is about 4–5°. It notes that in some researches the critical value is about 2–4° on glass, about 10° on silicon surfaces (being 9.9° for the polished, 8.8° for the gold layered and 11.2° for the nano-structured),

350

(a)

(b)

Height (nm)

300 250 200 150 100 50 0

185s 210s 235s

0s 40s 90s 1 40s 0

2

4

6

8

5

275s

10 15 20 25 30

Velocity (μm/s) Fig. 3. Nanoparticle velocity for (a) the first 140 s and (b) the last 90 s of the evaporation in the extended meniscus near the triple line of a water droplet.

or 5–8° on an aluminum surface [43–45]. The difference of the critical contact angle between pure water and water with nanoparticle inclusions on the superhydrophilic substrate may result from the fact that nanoparticles near the contact line hinder the depinning process due to viscous adhesion. The capillary flow caused by non-uniform evaporative flux carries most of the nanoparticles inside the droplet toward the contact line and leaves a ring-like deposition. Subsequently, the contact radius begins to decrease during the depinning process while the contact angle remains constant in the CCA mode and uniformly dotted depositions form at the fringe near the outer ring stain when the shrinking speed is small. When the shrinking speed reaches a value of 20 lm/s and even higher, the droplet starts to dry out and forms patterned lambdoid depositions (radial spokes) next to the dotted deposition on the superhydrophilic substrate. The radial spokes, which are observed occasionally in many other studies [5,46–48], can be explained by the entrapment of some particles during the receding process of the contact line. The contact line, which is prevented from depinning at the trapping location of the particle clusters, could finally depin elsewhere and the receding process of it can cause a lateral flow near the immobile clusters, leading to further aggregation of the particles and the formation of rod-like conglomerates. When the shrinking speed reaches a certain value, e.g., 20 lm/s in this case, the contact line could no longer remain pinned at the clusters and will move inward, leaving behind the spoke-like depositions. The contact line retreats very fast at a critical position where it is reasonable to assume that the droplet volume remain unchanged while the contact angle increases, then the droplet evaporates at a novel equilibrium position and the CCR mode reoccurs. These processes cycle continuously, and hence the droplet evaporation undergoes the CCR mode and the CCA mode recurrently in the last tens of seconds and form multi-ring depositions near the droplet center. In Fig. 4, both the concentric pattern and the spoke-like depositions appear after the droplet dries out when the shrinking speed reaches a critical value. The critical shrinking speed, however, may depend on many factors including the wettability and thermal conductivity of the substrate. Hence, some evaporating water droplets leave a complete concentric pattern if the critical shrinking speed does not reach, while others show also a pattern with radial spokes, as shown in Fig. 5. Fig. 5 shows the deposition pattern changes for water droplets with nanoparticle concentrations of 0.0005, 0.001, 0.002 and 0.004% w/v, respectively, on the superhydrophilic substrate. For low nanoparticle concentration of 0.0005% w/v, the droplet evaporation behavior has no obvious difference from that of pure water, for which the depositions at the fringe are discontinuous, as shown in Fig. 5(a). When the nanoparticle concentration is high, at 0.004% w/v for example, the contact line pins on the substrate easier and tighter than the case of low nanoparticle concentration at 0.0005% w/v, and the depositions at the fringe are continuous, as shown in Fig. 5(b)–(d). The asymmetry of nanoparticle deposition shown in Fig. 5 should be influenced by many factors such as substrate inhomogeneity. Similar results can also be found in the literature, see for example the paragraph over Fig. 9 in [49]. However, the mechanisms of the asymmetrical deposition patterns require further investigation and are not discussed here. The depinning process of the contact line near the depositions at the fringe is observed prior to the formation of the next ring. In addition, more nanoparticles will deposit near the contact line due to the radial capillary flow and the increased adhesive force, the pinning time becomes longer and the thickness of the eventually formed rings become thicker. Therefore, the deposition pattern of the droplet on the superhydrophilic substrate can also be altered by the variation of nanoparticle concentration. It is clear that the number of

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Fig. 4. Deposition patterns for water droplet with nanoparticle concentration of 0.002% w/v. From the fringe to the center: (a) scattered dots, (b) radial spokes, and (c) multirings.

Fig. 5. Deposition patterns for water droplets at different nanoparticle concentrations: (a) 0.0005% w/v, (b) 0.001% w/v, (c) 0.002% w/v, and (d) 0.004% w/v. The images are spliced by sub-images.

concentric rings increases with increasing nanoparticle concentration, which is the most important single parameter influencing the formation for deposition. The formation of multi-ring patterns generally occurs at the final stage of droplet evaporation. Using fluorescent nanoparticle with concentration of 0.0005% w/v, the multi-ring patterns formed by the nanoparticle deposition can be directly visualized as given in Fig. 6, in which some of the nanoparticles on the right side that was near the triple line keep pinned to the surface and some other nanoparticles move toward the contact line driven by the radial capillary flow. The suspending nanoparticles stop moving toward the contact line and oscillate near the liquid–vapor interface which is horizontally about 15–25 lm away from the contact line. When the contact line begins to retreat, the suspending nanoparticles near the liquid–vapor interface stick to the substrate and the contact line stays at a new equilibrium position. These processes repeat until the droplet dries out.

The schematic diagram of the multi-ring pattern formation process is given in Fig. 6(f), in which the nanoparticles near the liquid– vapor interface retreat with the interface during the depinning process of the contact line and deposit on the substrate when the contact line moves to the next equilibrium position, by which the multi-ring pattern forms. In order to understand more clearly the formation process of deposition line, we use a 60
objective and record in 5 s the fluorescent intensity images taken at the position near the contact line with a gap of about 20 lm next to the contact line, which is pinned to the substrate during this short period of time. Merging 100 image series in the recording, a combined cloud image is obtained as shown in Fig. 7. It shows that the areas with deeper colors are where the nanoparticles appear more frequently and thus most of the nanoparticles concentrate at the region which is over 10 lm away from the contact line. These nanoparticles will possibly collide in the thin liquid film and deposit on the substrate. The

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Fig. 6. Formation of multi-ring pattern at the final stage of evaporation: (a) t = 684 s, (b) t = 686.6 s, (c) t = 690.9 s, (d) t = 694.8 s, (e) t = 697.3 s, and (f) schematic of multi-ring formation.


G ¼ clg pR2

Fig. 7. Cloud image for nanoparticle movement near the contact line with a central distance about 20 lm.

2  cos h0 1 þ cos h

 ð1Þ

where R is the contact radius of the droplet, h is the actual contact angle of the droplet, h0 is the equilibrium contact angle established at the atomically flat surface, A = 2pR2/(1 + cos h) is the liquid/vapor interfacial area of the spherical cap, and clg, csl and csg are the surface tensions at the liquid–gas, solid–liquid and solid–gas interface, respectively. When the droplet is out of equilibrium with contact radius R = R0 + dR, the excess free energy dG = G(R)  G(R0) can be approximated by dh(dG/dh)h=h0 + (dh)2(d2G/dh2)h=h0/2 for jump in CCR mode, or dR(dG/dR)R=R0 + (dR)2(d2G/dR2)R=R0/2 for jump in CCA mode. Here d denotes for the deviation from equilibrium which is usually small, R0 is the equilibrium contact radius for a given droplet volume V, and dR(dG/dR)R=R0 = 0 or dh(dG/dh)h=h0 = 0. Correspondingly, the excess free energy per unit length of the triple line due to the deviation of state from the equilibrium one for the same droplet volume can be derived in terms of change in contact angle or radius as [50]:

~¼ dG

! 2 clg RðdhÞ2 dG ðdhÞ2 d G ¼ ¼ 2 2pR 4pR dh 2ð2 þ cos h0 Þ h¼h

ð2Þ

0

collision, together with the nanoparticle movement induced by the shrinking of liquid–vapor interface near the contact line, will certainly cause very tiny vortex in the observation area, which is in good agreement with the formation of the latest ring that is somewhat blurred than the other deposited rings shown in Fig. 6. 3.3. Energy barrier on the movement of triple line The formation of the multi-ring pattern is also influenced by the energy barrier that prevents the movement of the triple line. During the evaporation, the capillary number and the Bond number of each droplet are sufficiently small and the surface tension dominates over gravity, thus the droplet in this experiment can be assumed to have the shape of a spherical cap. Then, using Young’s equation csl  csv = clgcos h0 for equilibrium state, the corresponding Gibbs free energy given by G = clgA + pR2(csl  csg) can be rewritten as

! 2 clg sin2 h0 ð2 þ cos h0 ÞðdRÞ2 dG ðdRÞ2 d G ~ ¼ ¼ dG ¼ 2 2pR 4pR dR 2R R¼R

ð3Þ

0

~ is the excess free energy of the droplet at the threshold Since dG of a jump, it is therefore simply equivalent to the energy barrier U. For the uniformly dotted deposition process with CCA mode at the earlier stage of droplet evaporation, it can be deduced from Eq. (3) that the jump step dR is a constant (or dR  R0) if U is assumed to be proportional to R1 (or oU/oR  R2) for a given nanoparticle concentration. This holds for the first several ring stains at the outer fringe, where there may have only limited nanoparticles precipitate, especially for water droplet at low nanoparticle concentration. When more nanoparticles deposit at around an equilibrium position, the energy barrier may increase substantially with decreasing R (or oU/oR  RM, where 0 < M < 2) compared with the uniformly dotted deposition process and correspondingly

Z. Sun et al. / Experimental Thermal and Fluid Science 76 (2016) 67–74

the jump step dR increases with decreasing R (or dR  RN, where 0 < N < 1) for patterned lambdoid deposition process with CCA mode at the next stage of droplet evaporation. For the multi-ring deposition process with recurrently happened CCR and CCA modes at the later stage of droplet evaporation, a relation between dh and dR can be obtained by equaling Eqs. (2) and (3) as dh = sin h0(2 + cos h0)(dR)/R. On the other hand, a slight deviation from the equilibrium contact angle h0 induces a force of magnitude dF = clgcos(h0  dh)  clgcos h0  clgsin h0dh acting toward the bulk liquid. This force attempts to cause the depinning behavior and is locally balanced by the opposing force created by the differential of energy barrier at the threshold of depinning. Integrating dh into dF yields a relation between the contact radius R and the slip distance dR between two pinning positions or deposition lines:

@U dR 2 ¼ dF ¼ clg sin h0 dh ¼ clg sin h0 ð2 þ cos h0 Þ @R R

ð4Þ

From Eq. (4), it is clear that the relative jump step (dR)/R is a constant (or dR  R1) if oU/oR is assumed to be a constant (or oU/o R  R0) for a given nanoparticle concentration. This assumption is satisfied by a constant dh which is valid for a given volume of droplet with a specific value of clg and h0. The constant value of (dR)/R indicates that the slip distance decreases with the decreasing contact radius in the pinning/depinning process, which is consistent with our experimental observation that the space between two neighbor deposition lines decreases with decreasing deposition radius. Also, from Eqs. (2) and (3), it is clear that the energy barrier increases with the increasing nanoparticle concentration, since the equilibrium contact angle h0 is an increasing function of the nanoparticle concentration. According to the above-mentioned discussion, the schematic variation of U⁄0 (=oU⁄/oR⁄), U⁄ and oR⁄ with respective to R⁄ can be summarized in Fig. 8, where U0 = oU/oR, and U⁄ and R⁄ are the normalized U and R over their maximum values, respectively. The variation of U⁄ indicates that there exists the maximum energy barrier when the deposition transits from lambdoid pattern to multi-ring pattern. The maximum energy barrier may be produced at the position where the deposition line is the thickest. This can be caused by the depositions in radial lambdoid pattern and concentric multi-ring pattern at the same position. Once the transition happens, the energy barrier decreases linearly with the ongoing of the fast evaporation process. Meanwhile, the variation of oR⁄ indicates that the jump step or the slip distance decreases monotonically during almost the entire evaporation process. The nearly constant jump step during the earlier stage of evaporation process makes it possible to be utilized for the beneficial characteristics

1.0

δ R*

0.8

73

that the nanoparticles deposit uniformly on the hydrophilic substrate. It notes, however, that the jump step may not approach to zero before the droplet dries out, since the duration of the later stage of evaporation process is relatively short as compared with other stages.

4. Conclusions In this paper, the nanoparticle movement and deposition near the contact line of a drying droplet are experimentally investigated. It shows that the near-wall velocities with respective to the height from the substrate surface, obtained by the MnPIV technique, are complicated at the initial stage of evaporation process in water droplet on a superhydrophilic substrate and it exhibits a counterclockwise and a clockwise circling motions in the droplet. At the later stage of evaporation, the circling motions may vanish and the nanoparticle velocity in the thin film region can be much higher than that near the liquid–vapor interface. The influence of nanoparticles on the pinning time of the contact line is also given, which inversely indicates that the motion of contact line has obvious impact on the deposition patterns. The deposition patterns, which exhibits scattered dots, radial spokes and multi-rings due to the CCR and CCA modes happened recurrently during the evaporation process, can also be altered substantially by the nanoparticle concentration, which is an important parameter influencing the energy barrier. A combined cloud image is obtained by merging 100 fluorescent intensity images and it shows that most of the nanoparticles concentrate at the region which is over 10 lm away from the contact line and will certainly cause very tiny vortex in the observation area. The corresponding theoretical analysis on the energy barrier indicates that there exists the maximum energy barrier when the deposition transits from lambdoid pattern to multi-ring pattern. This work thereby reveals an alternative way of obtaining the uniform deposition pattern using superhydrophilic substrate other than those include surfactant, and it will be helpful for better understanding the mechanisms of the coupled heat and mass transfer in the critical thin film region of a sessile evaporating droplet. Acknowledgments The programming for near-wall velocity is based on the MnPIV codes developed in Prof. M. Yoda’s group at Georgia Tech, USA. The authors are grateful to their support. We acknowledge the financial supports from the Program for New Century Excellent Talents in University (No. NCET-12-0845), the Fundamental Research Funds for the Central Universities (Nos. 2014ZD10 and JB2015RCJ03), and the National Key Basic Research Program of China (No. 2015CB251505). References

0.6

0.4

U*

0.2

U*'

0.0 0.0

0.2

0.4

0.6

0.8

1.0

R* Fig. 8. Schematic variation of U0 , U, and oR with respective to R in normalized coordinates.

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