Temporal and spatial evolution of the thin film near triple line during droplet evaporation

International Journal of Heat and Mass Transfer 117 (2018) 1147–1157

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Temporal and spatial evolution of the thin film near triple line during droplet evaporation Leping Zhou ⇑, Yang Yang, Shengsheng Yin, 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 9 January 2017 Received in revised form 10 October 2017 Accepted 18 October 2017 Available online 5 November 2017 Keywords: Droplet Evaporation Thin film Thickness Triple line

a b s t r a c t The evaporation process of the thin film region near the triple line for a liquid suspended with nanoparticles involves important interfacial phenomena such as contact line movement, deposition, and evaporation. In this paper, droplets that are seeded with fluorescent nanoparticles of different diameters and of the same particle numbers were investigated for their evaporation rates, deposition patterns, and inplane average velocities within the field-of-view. The results present different modes of deposition patterns for the fluorescent nanoparticles, and stronger evaporation can be obtained using nanoparticles of small diameter. The temporal and spatial evolution of velocities and thicknesses in the thin films near the triple lines during the droplet evaporation were obtained by using a proposed sub-region method, which is developed from an evanescent wave based nanoparticle image velocimetry technique. It shows that, depending on the nanoparticle size, the spatial variation of the local thin film thickness can be linear or nonlinear. The fluorescent nanoparticles can affect the evaporation modes, the internal flow, and the temporal and spatial evolution of the thin film during the droplet evaporation through the interaction between the particles and the interface near the contact line and their influence on the change of the microscopic contact angle during the pinning process of the contact line. This work can help capture insights on how nanosized particles affect the droplet evaporation near the triple line. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Drop evaporation is important in many industrial applications such as dropwise cooling, spray cooling, and fuel injection. The evaporation of a sessile droplet suspended with nanoparticles plays a crucial role in engineering including inkjet printing, thin film coatings, and optoelectronic device manufacturing. The movement and deposition of the nanoparticles were believed to be controlled by the fluid flow in the droplet, especially the contact line pinning or depinning motion on the solid surface [1]. However, the fluid flow of an evaporating droplet and its final deposition pattern may be influenced by various factors, including the capillary flow induced by surface tensions and the Marangoni flow resulted from the temperature gradient or the solute concentration gradient along the liquid-vapor interface [2]. It is therefore necessary to explore the mechanisms of fluid flow and deposition patterns of an evaporating droplet. These are inherently related to the temporal and spatial evolution of the thin liquid film near the triple line during the evaporation [3]. ⇑ Corresponding author. E-mail address: [email protected] (L. Zhou). https://doi.org/10.1016/j.ijheatmasstransfer.2017.10.077 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

The extended meniscus can be divided into three regions once a drop spreading over a substrate surface shown in Fig. 1: the adsorption layer region, where liquid is adsorbed on the wall; the thin-film region, where the attractive force of the solid surface is weaker than the long-range molecular forces; and the intrinsic meniscus region, where the capillary forces dominate. Enormous researches have proved that a strong evaporating process happens in the evaporating thin film region and the internal flows in this region are crucial for revealing the mechanism of drop evaporation [4,5]. The thin liquid film is part of a contact line, and the liquidvapor interface has measurable curvature [6,7]. It was shown that the mass flux (m00 in Fig. 1) in this region increases along the interfacial direction towards the contact line [8]. The long-range molecular forces were proved to be crucial for the liquid supply (the mass flow rate m0 along the wall surface shown in Fig. 1) into the thin film region [9] and were found to be dependent on the thin film profile [10]. This requires theoretical prediction and numerical simulation for the thin film region. However, direct observation of this region through traditional methods is difficult due to the inherent optical limit. Atomic Force Microscopy (AFM) in a tapping-mode was successfully used for characterization of thin film profile at about 1 nm away from the contact line [11], and

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Nomenclature a Ca d D G h H I L m0 m00 Ma n r t T u V x y z

radius of the fluorescent particles (m) capillary number (–) diameter (m) diffusion coefficient (m2s1) gray scale (–) distance from the wall (m) local thin film thickness (m) intensity (candela; lumen) distance (m) mass flow rate along the wall surface (kgm1s1) mass flux at the interface (kgm2s1) Marangoni number (–) refractive index (–) contact radius of droplets (m) time (s) temperature (°C) velocity (m/s) thinning velocity (m/s) x-axis (m) y-axis (m) penetration depth of evanescent wave (m)

interferometry technique worked quite well to study the flow pattern in completely wetting fluid [12,13], while these are insufficient to further investigate how the thin film profile varies with the time. In fact, the evolution of the thin film profile is critical for understanding the mechanisms of the thin film dynamics [14,15]. The fluorescence microscopy was extensively used to study the evolution of precursor film that precedes the macroscopic contact line, while only a completely wetting fluid can be measured [16]. For the velocimetry based on evanescent wave illumination, some subtleties which contribute to the measurement inaccuracy and bias errors may exist, e.g., hindered Brownian motion [17], shearinduced reduction in particle mobility [18], long-range electrostatic and van der Waals force interactions [18], imaging exposure time [19], and particle variations [20]. The evanescent wave-based velocimetry has still been shown to be a valuable tool in nanofluidics. High resolution measurement of flow pattern in the thin film region was realized by using the unique characteristics of evanescent wave illumination, which intensity decays exponentially with the distance normal to the wall, to the instantaneous and nonintrusive approach of nanoparticle image velocimetry [21]. This technique is based on the nanoparticle image velocimetry with multilayers, which as a particle image velocimetry assumes that the particle motion represents the fluid motion and hence the particle velocities represent the fluid velocities, and the images recorded by this velocimetry technique were divided into several sublayers by classifying each tracer image into different layers using the fluorescent nanoparticle intensity that correlates to the

Greek symbols a thermal diffusivity (m2s1) u contact angle (o) l dynamic viscosity (kgm1s1) h incident angle (o) r surface tension (N/m) s normalized time (–) f micrometer scale of the microscope (m) Subscripts 0 at the wall surface 1 medium 1 2 medium 2 1 unconfined Brownian motion c critical f drying p penetration o origin

distance from the wall [22]. In our recent work, the local thin film thickness was approximated by searching the maximum distance between the nanoparticles and the wall using the developed sublayers, and it was found that the thin film thickness decreases just before the droplet shrinks [21]. However, since the fluid velocities are diverging towards the contact line [23], the buoyancy effects of the particles with different diameters might have an impact on the measurement bias. Meanwhile, high resolution measurement of thickness variation requires characterization of the temporal and spatial evolution of the thin film near the triple line during the droplet evaporation. In this work, droplets that are seeded with fluorescent nanoparticles of different diameters and of the same particle numbers are investigated for their evaporation rates, deposition patterns, and in-plane average velocities within the field-of-view. Then the temporal and spatial evolution of the thin film near the triple line during the droplet evaporation is obtained using a proposed subregion method, which divides the field-of-view into multiple sub-regions along the direction of capillary flow. The evolution of the local thin film thickness in droplets seeded with fluorescent nanoparticles of different diameters are compared. Finally, the local thin film thickness, together with the evaporation rates, the deposition patterns, and the in-plane average velocities, are analyzed to understand their relation to the evolution of the thin film near the triple line in different droplets.

2. Experiment 2.1. Experimental method

Adsorption layer region

Thin-film region

Intrinsic meniscus region

m"

δ

1 m

Fig. 1. Schematic diagram for an evaporating thin film.

m'

The intensity of an evanescent wave, which is totally reflected at the interface of a medium exposed to another transparent medium with a lower refractive index, decays exponentially with the distance normal to the wall. This characteristic was used in multilayer nanoparticle image velocimetry, in which the images were divided into several sublayers based on the nanoparticle intensity correlating to the distance from the wall [22]. The multilayer nanoparticle image velocimetry method was validated for its accuracy by prior studies [24–26]. This technique can be extended to

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explore the evolution of liquid-vapor interface during thin film evaporation. The experimental setup used in this investigation is schematically shown in Fig. 2. The main body of it is an inverted, evanescent wave based Total Internal Reflection Fluorescence (TIRF) microscope (Olympus IX71). As described in our previous work [21], the variation of the local thin film thickness can be approximated by searching the maximum distance between the nanoparticles and the coverslip, using the developed sublayers which are based on the evanescent wave technique. This can be briefly summarized as follows. The droplet height during the evaporation decreases until less sublayers are illuminated, and thus the thin film thickness at the illumination field may decrease with the time. The velocities in higher sublayers will not be obtained since less tracer nanoparticles exist, and it is insufficient to track for velocimetry even if there does have any

nanoparticle. Notes that the nanoparticle center in each sublayer is available only if the tracking algorithm is valid, thus the sublayers with valid velocities were used for approximately determining the thin film thickness. Consequently, the velocity profile near the triple line and the variation of the thin film thickness were obtained. In this work, this approach is extended by dividing the field-ofview into multiple sub-regions along the direction of capillary flow, as schematically shown in Fig. 3. In each of the sub-regions, the extended particle image velocimetry technique can be used to identify the position of the highest nanoparticle, which approximately stands for the local thin film thickness of the interface. The local thin film thicknesses are then used for data fitting to achieve the thin film profile. The temporal variation of thin film profile is then obtained when repeating the data fitting at different time steps. Thus the temporal and spatial evolution of the thin film near the triple line during the droplet evaporation is visualized. 2.2. Experimental procedure

droplet

immersion oil

coverslip back focal plane

PC

solid laser dichroic mirror

emission filter EMCCD camera

Fig. 2. Schematic of experimental setup for interface visualization near the triple line.

direction perpendicular to the interface

y

liquid Film

o

highest ighest Particle Par

fluorescent Particles

a) the observation area is divided into several segments

x

b) the highest particle is selected in each segment

intercept

y

reverse direction of the capillary flow

ill i i D illumination Depth

λ = 488 nm

microscope objective

excitation filter

A series of 16-bit images are recorded by the inverted microscope and an Electron-Multiplying Charge-Coupled Device (EMCCD, Andor Ixon3 Ultra 897) in one measurement with 50 sets of intensity data, which are in-plane averaged to minimize the random errors. The electronic gain is set as 8. The resolution is set as 256  256 pixels, with an area of 0.267  0.267 lm2 per pixel. The exposure time for each measurement is set as 10 ms, and the frame rate for taking the photos is 64 fps. The environment temperature is 15 °C and the humidity is 32% during the experiment. In the experiment, the incident angle is directly calibrated by fitting of the relationship between the micrometer scale f of the microscope and the incident angle h of the laser beam. The incident laser beam transmits a prism (Daheng Optics, K9) put on the microscope stage (see Fig. 4(a)) and its path (see Fig. 4(b)) is recorded using a digital camera at different micrometer scales. The recorded images are processed using ImageJ to obtain the incident

o

c) the fitting liquid film is obtained

Fig. 3. Sub-region method for detecting the evolution of the thin film near the triple line.

x

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Incident light

b) path of the incident light

prism

θ a) experimental set up

c) determination of θ using ImageJ

Fig. 4. Calibration of the incident angle.

angle of the laser beam (see Fig. 4(c)), and then its relation to the micrometer scale is fitted as h = arcsin(0.39f + 0.63) (see Fig. 5). The immersion oil is also used between the microscope objective and the prism base to diminish the influence of the air. Here the incident angle of the excitation light is determined to be 66°, and the accuracy of the incident angle is estimated to be about 0.05°. The addition of fluorescent particles more or less affects the transmission direction of the incident wave. Considering all the types of scattering, reflection at the particle-fluid and wall-fluid interfaces should be quite small given the modest refractive index mismatch for these three media (1.57 for polystyrene, 1.33 for water, and 1.52 for glass); in both cases, the Fresnel equations at normal incidence predict that less than 0.1% of the light will be reflected [25]. Thus, fluorescent particles have a minor impact on the refractive index of the solutions. The refractive index of the borosilicate coverslip is n1 = 1.52, and the refractive index of the water droplets is n2 = 1.33. Therefore, light will be totally reflected at the glass-water interface at a critical incident angle of hc = 61.4°. Using the incident angle of the excitation light, the depth of the illumination field is then determined to be about 450 nm, which is divided into four sublayers with thickness of 110 nm for each layer. Furthermore, fluorescent polystyrene nanoparticles are used as tracers, with each tracer nanoparticle being assigned into one layer based on their distance to the coverslip. Then the thin film velocity

1.0 Measurement Linear fitting

sinθ

0.9

0.8

0.7

0.6

0.0

0.2

0.4

0.6

ζ (mm) Fig. 5. Calibration result of the incident angle.

0.8

profile near the triple line is obtained by averaging all the particle velocities in each layer. The coverslip (Fisherbrand FIS12-545F) is first washed repeatedly by deionized water, and immersed in a piranha solution (98% H2SO4 and 30% H2O2 with volume ratio of 3:1) heated by thermostatic water bath at temperature of 80 °C for one hour. Then it is washed by deionized water again and stored in a beaker filled with deionized water. Before each test, the coverslip is immersed in deionized water to sonicate for ten minutes. Thus the coverslip is processed to be more hydrophilic due to the hydroxylation of the surface. The fluorescent solution with polystyrene tracer nanoparticles is employed in the evanescent wave based TIRF velocimetry. Liquids that are seeded with fluorescent nanoparticles of different diameters and of the same particle numbers are prepared in order to understand how the particle size influence the droplet evaporation near the triple line. The fluorescent nanoparticles are 100 nm (ThermoFisher/Invitrogen FluoSphere f-8803) and 40 nm (ThermoFisher/Invitrogen FluoSphere f-8795) in diameter, respectively. The particle number is the number of nanoparticles contained in the solution of the same volume and is calculated by using the parametric data of the fluorescent particles provided at its official website. The actual sizes for these two particle tracers are 0.045 ± 0.008 and 0.1 ± 0.012 lm. According to the product handbook of FluoSpheres [27], the statistical standard deviation of the particle size are 17.8% and 12% for the 100 and 40 nm particle tracers, respectively. Consequently, from the criteria of measurement bias in evanescent wave-based velocimetry due to tracer size variations [28], the ratios of the measured velocities to its real values are estimated to be 1.075 and 1.060 for the TIRF velocimetry using the 100 and 40 nm particle tracers, respectively. Using a pipette (MettlerToledo Rainin SL-2XLS+), a drop of 1.50 ll solution seeded with 2 mM, 100 nm nanoparticles are added into 25 ml deionized water, and a drop of 0.21 ll solution seeded with 5 mM, 40 nm nanoparticles are added into 100 ml deionized water. The particle number density of the solutions is 21,672,353 P/ll. The concentrations of these solutions are 12.0  104 w/v% and 10.6  105 w/v%, respectively. The solutions, which are labelled as the S1 and S2 samples correspondingly, are sonicated for 30 minutes to ensure the nanoparticles are uniformly distributed. The evaporation rates of the droplets are measured by using an electronic balance (Mettler Toledo AB135-S) with a precision of 0.01 mg. At the beginning of the measurement, the internal air flow

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3. Results and discussion The initial contact angles u before the evaporation of the S1 and S2 droplets, which have the same volume of 0.5 ll, are measured to be 4.873° and 4.374°, respectively. Therefore, the contact angle is affected by nanoparticle interaction with the surface and the liquid [28]. The evaporation patterns are generally in good agreement with the results from literature (see, e.g., the transport and deposition patterns in drying sessile droplets [29]. Details of the evaporation patterns of the sessile droplets containing fluorescent nanoparticles can be referred to our previous investigation on the particle motion and deposition near the triple line for evaporating sessile water droplet on a superhydrophilic substrate [30]. Fig. 6 shows that the evaporation rates are constant and the drop masses decreases linearly with the time [31]. The evaporation rates for S1 and S2 droplets are determined as 0.00315 and 0.00352 mg/s, respectively. These are in good agreement with available literature data (e.g. [32,33]), in which the evaporation rates range between 0.00310 and 0.00335 mg/s. It indicates that the evaporation rate of the droplet is affected by the volume fraction of the nanoparticles contained. However, since the volume fraction of nanoparticles for the S2 droplet is rather smaller than that of the S1 droplet, the larger evaporation rate might be attributed to other factors such as longer pinning time for the S2 droplet seeded with smaller particles and having a smaller contact angle when compared with the S1 droplet which has the same volume [34].

1.6

Droplet mass (mg)

will temporarily affect the results of the experiment after the windshield of the electronic balance was closed. At the end of evaporation, the measurement uncertainty in the evaporation rates is largely dependent on the small droplet mass. The uncertainty is small due to the high precision of the electronic balance. The droplet masses are weighted for every 10 s in order to obtain their evaporation rates, which are the slopes of the linear fits of the measured masses versus the time. The cleaned coverslip is first put on the electronic balance, then a 0.5 ll testing fluid is taken by using the pipette and dripped onto the coverslip. The droplet mass is measured every 10 s during the entire evaporation process, until it dries out. The static contact angles of the droplets are first measured using a contact angle meter (Powereach JC2000D4M). For the small contact angles, a microscope objective with magnification of 1.2 (Powereach, 85 pixel/mm) is used to take the images. The measurement repeats 10 times for each droplet sample to diminish the measurement error. Then the coverslip is first put on the object stage of the microscope. A 60 microscope objective (Olympus APON 60) is adjusted to contact with the coverslip bottom through an immersion oil (Olympus Type-F, refractive index: 1.518). A 0.5 ll droplet is dripped carefully onto the coverslip to keep its shape of spherical cap. The microscope objective is adjusted to focus on the contacted surface of the droplet and the coverslip. The incident angle of the laser beam is adjusted to create total internal reflection at the liquid-solid interface. The evanescent wave generated is used for illuminating the tracer nanoparticles near the solid wall of the triple line. After moving the field-of-view into the area in the vicinity of triple line, the static, spread droplet is pictured every 10 s for in-plane average velocity measurement. When the droplet dries out, a 4 objective is used to record the deposition pattern of the fluorescent nanoparticles. The procedure of the experimental preparation for the near wall velocimetry using the multiple-layer nano-PIV technique is the same as the in-plane average velocity measurement. A series of 100 images are recorded by the EMCCD camera and are in-plane averaged to minimize the random errors. These image pairs are then post-processed by using MATLAB toolkits to obtain the near wall velocity profile.

S1 S2 Linear fit of S1 Linear fit of S2

1.2

0.8

ΔD/Δt= -0.00315 mg/s

0.4

ΔD/Δt= -0.00352 mg/s 0.0

0

100

200

300

400

500

Evaporation time (s) Fig. 6. Evaporation rates of the S1 and S2 droplets.

Meanwhile, since the number of particles are the same for the two droplets and hence their volume fractions are different, the larger evaporation rate for the S2 droplet may also be attributed to the mass effect from the nanoparticles. The deposition patterns of the fluorescent nanoparticles are then recorded using a 4 objective after the droplets dry out. As shown in Fig. 7, the zoom in at the fringe clearly shows that obvious ring stains are formed with S1 droplet, while scattered dots are formed with S2 droplet. The reason behind the deposition pattern is inherently related to the nanoparticle motion near the triple line during the droplet evaporation. The nanoparticle motion near the triple line is visualized using a 60 objective illuminated by evanescent wave, and near wall velocities for the droplets are compared in order to understand how the motion affect the contact line and the deposition pattern. When the 0.5 ll droplets spreads onto the coverslip, the nanoparticle depositions after the contact line motion are recorded every 10 s. Fig. 8 shows the evolution of contact line indicated by the motion of fluorescent nanoparticles. The capillary flow caused by the non-uniform evaporative flux at the liquid-vapor interface carries most of the nanoparticles seeded in the droplet towards the contact line and leaves a ring-like deposition. For S1 droplet, the contact line advances at the initial stage of evaporation with a Constant Contact Radius (CCR) mode. The waiting time between two ring stains are about 100 s. During the waiting time, the contact line keeps pinned on the coverslip, with contact radius remains constant at about 1.96 mm while the contact angle decreases from the initial value of 4.873° until it reaches a critical value (about 4°) before the contact line starts shrinking slowly with a shrinking speed lower than 1 lm/s. The critical contact angle for the sessile water droplet on the superhydrophilic substrate is related to the depinning process of the seeded nanoparticles, which is hindered by the viscous adhesion yielded from the nanoparticles near the triple line [21]. For the S2 droplet, the contact line advances with a Constant Contact Angle (CCA) mode. The contact radius decreases during the depinning process while the contact angle remains constant in the CCA mode and dotted depositions form at the fringe near the outer ring when the shrinking speed is small. In this mode, the moving front is clear, but it is not easy to form ring stains due to the smaller size of nanoparticles as compared to those seeded in the S1 droplet. Therefore, the final deposition pattern is generally dotted lines with trend of forming radial spokes. The in-plane average velocities in the field-of-view are measured during the droplet evaporation, in order to understand the effect of fluorescent nanoparticles with different sizes on the evaporation. Using the illumination from evanescent wave, the particle image velocimetry technique is extended to the measurement of

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(a) full view

(b) close up Fig. 7. Deposition patterns of fluorescent nanoparticles: (a) full view; (b) close up.

the average velocities 50 s after the droplets are dripped onto the coverslip. The fluorescent intensity images for the average velocity measurement are taken at the position with the field-of-view being about 40 lm next to the contact line observed in this experiment. The influence of the time interval Dt between two images on the measurement accuracy are investigated. The result shows that the calculation error is related to the distance between the particles and the wall, and the largest errors are in layer I, the thinnest layer and the one next the wall, where only about 20% of particle images are ‘‘matched” within an image pair over this 30 nm thick layer [25]. In this experiment, the time interval Dt is set as 15 ms which is normalized by a Brownian diffusion timescale:

s¼

Dt a2 =D1

ð1Þ

where a is the radius of the fluorescent particles and D1 is the unconfined Brownian diffusion coefficient. For the S1 and S2 droplets, s is 0.85 and 4.95 respectively. According to the abovementioned method [25], the maximum errors of the velocity calculation of the S1 and S2 droplets are about 8% and 20%, respectively. As shown in Fig. 9, the measured velocities fit well with an increasing function of (tf  t)1, where tf is the drying time and t is the time. This is also consistent with the analysis of ring stains from evaporating droplets [35], therefore the capillary flow should be the main contributor to the fluid flow near the triple line. Meanwhile, the

drying time tf for the S2 droplet is much smaller than that of the S1 droplet. This indicates a stronger evaporation which increases with decreasing nanoparticle diameter, and the reason can be identical with the analysis on the evaporation rate given in Fig. 6. The decrease of the average velocity around 20 s for both the S1 and S2 droplets might be related to the contact line movement when the droplet is initially spreading on the surface. The coefficients of determination R2 (or the fit accuracies) for the S1 and S2 droplets are 0.82055 and 0.79156, respectively. Utilizing the characteristics of evanescent wave illumination, which intensity decays exponentially with the distance normal to the wall, the evolution of velocities in the thin films near the triple lines can be further distinguished [21]. After the depth of illumination field (about 450 nm as mentioned above) is divided into multiple sub-fields according to the intensity, the average velocity in each of the sub-field can be obtained using the extended particle image velocimetry technique. As shown in Fig. 10, the velocity profiles in the same field-of-view as discussed in Fig. 9 are obtained for four sub-layers. For the S1 droplet, the velocities at the upper sublayer are small and those at the central sublayers are large. This means a Marangoni flow exists near the upper part of the droplet interface, and the flow direction is opposite to the capillary flow which is believed to taking the nanoparticles towards the contact line. In order to study how the particles inside the droplets move, the trajectories of particles at some typical positions inside the

L. Zhou et al. / International Journal of Heat and Mass Transfer 117 (2018) 1147–1157

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(a) S1 droplet

(b) S2 droplet Fig. 8. Evolution of contact line indicated by motion of fluorescent nanoparticles.

with the S2 droplet. It can be verified through the discussion on the evolution of the thin film thickness (see Fig. 12): for the S2 droplet, the thin film thickness is generally smaller than that of the S1 droplet and hence the Marangoni flow could be negligible; therefore, the capillary flow dominated velocities at the upper sublayers in the S2 droplet increase faster than that in the S1 droplet. To further understand the internal motion of droplets, the dimensionless Marangoni number and capillary number are calculated. The Marangoni number is defined as [37,38]:

Average velocity (μm/s)

8 Measured velocity (S1) Fitting line (S1) Measured velocity (S2) Fitting line (S2)

6 4 2

Ma ¼

0 0

20

40

60

80

100

120

Evaporation time (s) Fig. 9. In-plane average velocity near the triple line.

field-of-view are obtained for the S1 droplet, and the time interval between the two images is 15 ms. As shown in Fig. 11, the lower particles move towards the contact line, while the upper particles remain almost immobile and even tend to move away from the contact line. The results show that there is a motion in the droplet directing from the top region of the S1 droplet to its three-phase contact line, then it turns inside to the droplet. This flow is consistent with the literature [36] and indicates that Marangoni convection exists in the droplet which may be induced by the temperature difference along the liquid-vapor interface since the thin film thickness should be larger for the S1 droplet as compared

r DT @ r la @T

ð2Þ

where the partial derivative of the surface tension with respective to the temperature is or/oT = 1.081  104 N/(mK), l is the dynamic viscosity at the given liquid temperature, a is the thermal diffusion coefficient of water, r is the contact radius of droplets, and DT is the temperature difference between the micro region and the macro region which is about 0.08 K [39]. Thus, the Marangoni number is approximately 117.73 for the S1 droplet. The liquid film thickness of the S2 droplet is less than that of the S1 droplet, and the temperature difference between the two regions (the thin liquid film region and the top center region of the droplet surface) of the S2 droplet is smaller than that of the S1 droplet [40], so Ma for the S2 droplet is relatively smaller than that for the S1 droplet. The dimensionless number of capillary number is defined as [37]:

Ca ¼

lV r

ð3Þ

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450 400

0s 10s 20s

30s 40s 50s

60s 70s 80s

90s 100s

Height (nm)

350 300 250 200 150

the imaging system is 60, which corresponds to 0.267 lm/pixel, thus a 65.42  65.42 lm2 field-of-view is taken. Here seven subregions, with a width of about 9.35 lm for each sub-region, are used for the calculation. Because of the non-uniformity of the intensity of incident light and the particle diameter, the maximum difference DG between the reference gray scale and the actual gray scale of the 100 nm particles on the wall surface is about 100. According to the characteristic of the evanescent wave, the distance between the particles and the height of the wall can be expressed as:

100 50 -3 0 3 6 9 -3 0 3 6 9 -3 0 3 6 9 -3 0 3 6 9 12 450 400

0s 10s

20s

30s

40s

Height (nm)

350

h ¼ z ln

G0 G

ð4Þ

where z is the intensity-based e1 penetration depth of evanescent wave, or the distance into the less dense medium from the interface where the wave intensity is reduced by a factor of 1/e, G is the gray scale of fluorescent particles, and G0 is the gray scale of the particles at the wall surface (y = 0). The height error of the particles is expressed as:

300

Dh ¼ zp ln

250 200 150 100 50

-2 0 2 4 6 -2 0 2 4 6 -2 0 2 4 6 0 2 4 6

Fig. 10. Velocity profiles in the thin films near the triple lines for the (a) S1 and (b) S2 droplets.

where r (=69.55 mN/m) is the surface tension of pure water, V is the characteristic velocity which is taken as the average velocity of the liquid-vapor interface. The average velocity at the later stage of evaporation for upper fluid (about 1.30 and 3.15 lm/s for the S1 and S2 droplets, respectively) is selected as the characteristic velocity V, and correspondingly the Ca numbers are calculated to be 1.88  106 and 4.55  106 for them. The calculated capillary numbers indicate that the surface tension forces play more important role than the viscous forces on the liquid-vapor interface. Using the recorded 16-bit images of 256  256 pixels, an effective calculation region of 245  245 pixels field-of-view are available to detect the evolution of the thin film. The magnification of

G0 þ DG G0

ð5Þ

In the experiment, the incident angle of the excitation light is 66° and zp is about 112 nm. The reference gray scale of the 100 nm particles on the wall surface in the experiment is 811.57. The maximum difference Dh between the calculated value and the actual value of h for the 100 nm particles is about 13.0 nm which can affect the accuracy of the fitted liquid film. Similarly, the reference gray scale of the 40 nm particles on the wall surface in the experiment is 493.80, the maximum difference DG between the reference gray scale and the actual gray scale of the 40 nm particles on the wall surface is about 150, and the maximum difference Dh between the calculated value and the actual value of h for the 40 nm particles is about 29.7 nm. As the evaporation proceeds, the error will decrease gradually. We denote o as the origin which lies on the closest side of the field-of-view to the contact line, D as the distance from the origin in the field-of-view, and H as the local thin film thickness. The accuracy of this method is influenced by many factors including the non-uniform distribution of particles, which can be improved such that an error less than 4% can be obtained by using the particle-tracking algorithm, carefully choosing the time interval and measuring window size, and averaging multiple results [41]. As shown in Fig. 12, the evolutions of local thin film thickness for the droplets are different. For the S1 droplet, the spatial

(a) Motion of upper particles

Δt = 15ms (b) Motion of lower particles

Fig. 11. Motion of the upper and lower particles.

t

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H=385.99+0.99L

440

440 H=392.93+0.69L

400 H=385.60+1.06L

440

H (nm)

440 H=396.43+0.72L 400

20s H=405.25+0.64L

H=395.20+0.72L

30

80s

400

40s 20

70s

440 H=397.79+0.59L

400 10

400

400

30s

0

440 H=388.83+0.83L

440 H=400.29+0.41L

400 440

60s

400

10s

440

50s

440 H=415.79+0.27L

400

H (nm)

400

0s

40

50

L

60

70

90s 0

10

20

30

L

(a)

40

50

60

70

(b)

420 H=360.87-0.98L+0.024L2 360

0s

300 420 H=362.56-0.99L+0.023L2

H (nm)

360

10s

300 420 H=354.05+0.26L+0.0038L2 360 300 420 H=350.11+0.13L+0.0045L2

20s

360 30s

300 420

H=373.22-1.72L+0.032L2

360 300

40s 0

10

20

30 L

40

50

60

70

(c)

Fig. 12. Evolution of the local thin film thickness for the (a) and (b) S1 and (c) S2 droplets.

variation of the local thin film thickness is basically linear and the temporal variation of local thin film thickness seems to be complicated. For the S2 droplet, the spatial profile of the thin film appears to change in a nonlinear way instead of a linear one, and hence the thickness can be well fitted as a quadratic polynomial about the distance L. The experimental results indicate that the seeded fluorescent nanoparticles with smaller diameter tends to change the thin film thickness in a nonlinear way due to the solutophoresis interaction with the interface. However, although the second order polynomial seems to be better fitting than a linear one, the wavy behavior of the thin film may be a result of the curve fitting and needs for further experimental evidence which is hardly observed in an experiment due to the inherent optical limit of direct observation of this region through traditional methods. Therefore, a wavy variation of film thickness simply means that a second order polynomial fitting is better than a linear one. In order to better understand the relationship between the liquid film thickness and the evaporation time, the intercept of the y-axis and the slope of the linear fitting of the thin film are taken into account, as shown in Fig. 13. It indicates that the local thin film

thickness at D = 0 remains almost unchanged at a mean value of about 396 nm, and the slope of the liquid-vapor interface seems to decline linearly with respective to the time. The evolution of the thin film is closely related to its microscopic contact angle. In fact, the result shows that the microscopic contact angle is as small as 0.567° during the thinning process of the thin film for the S1 droplet, with a thinning speed of the microscopic contact angle at about 0.000051° per second. This corresponds to a thinning velocity of thin film at about 2.04 nm/s in this observation region, while for the thinning velocity of a free thin film of water it is estimated to be 0.02 nm/s using the Reynolds equation [42]. Therefore, it verifies that the gravity and inertia forces may be taken into account as compared to the viscous forces when concerning the thin film evolution or the thinning process, in which the capillary and disjoining pressures are responsible for the thin film evaporation [21]. The evolution of the thin film in the S2 droplet is also closely related to its microscopic contact angle. The spatial profile of the thin film for the S2 droplet appears to change in a nonlinear way, and this means that, even the macroscopic contact angle of the

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500

Intercept (nm)

400

1.4

References

1.2

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1.0 300

0.8

200

0.6 0.4

100 0

Intercept Slope

0

20

0.2 40

60

80

0.0 100

Evaporation time (s) Fig. 13. Evolution of the thin film profile for the S1 droplet with CCR mode.

droplet undergoes a process of CCA mode, the transient profile of the liquid-vapor interface near the triple line varies nonlinearly and reciprocally due to the change of the microscopic contact angle near the interfacial place predicted by the CCA theory. Compared to those with larger particles (i.e., in the S1 droplet), the solutophoresis interaction with the interface and the change of the microscopic contact angle induced by the pinning process of the contact line can be much more easily produced, therefore the nonlinear variation of the thin film interface near the triple line may be often found in droplet seeded with small nanoparticles. 4. Conclusions For droplets seeded with fluorescent nanoparticles of different diameters and of the same particle numbers, the evaporation rates of the droplets and the deposition patterns of the fluorescent nanoparticles were first obtained. The evolution of contact line indicated by the motion of the fluorescent nanoparticles, which exhibit respectively the CCR and CCA modes, were then visualized. The in-plane average velocities in the field-of-view were measured during the droplet evaporation. The results indicate that the evaporation rate can be enhanced by smaller nanoparticles. The evolution of velocities in the thin films near the triple lines was distinguished by utilizing the characteristics of evanescent wave illumination. Finally, using the sub-region method, the temporal and spatial evolution of the thin film near the triple line during the droplet evaporation was obtained. For droplet seeded with larger fluorescent nanoparticles, the spatial variation of local thin film thickness is basically linear; while for droplet seeded with smaller fluorescent nanoparticles, the spatial profile of thin film tends to change in a nonlinear way. The analysis shows that these behaviors are closely related to the interaction between the nanoparticles and the interface near the contact line and the change of the microscopic contact angle induced by the pinning process of the contact line that are also influenced by the nanoparticle. Conflict of interest None declared. Acknowledgments The authors are grateful to the financial support from the National Natural Science Foundation of China (No. 91634115). The authors acknowledge the support of Prof. M. Yoda’s group at Georgia Tech, USA for developing the multiple-layer nano-PIV code used for near-wall velocity calculation. The authors also acknowledge the helpful suggestion from the reviewers.

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