Insights into Drying of Noncircular Sessile Nanofluid Droplets toward

Oct 4, 2016 - ... §Department of Mechanical Engineering, Indian Institute of Science, ... Lalit BansalApratim SanyalPrasenjit KabiBinita PathakSaptar...
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Insights into Drying of Noncircular Sessile Nanofluid Droplets toward Multiscale Surface Patterning Using a Wall-Less Confinement Architecture Prasenjit Kabi,† Swetaprovo Chaudhuri,†,‡ and Saptarshi Basu*,†,§ †

Interdisciplinary Centre for Energy Research, ‡Department of Aerospace Engineering, and §Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India S Supporting Information *

ABSTRACT: Surface patterning with functional colloids is an important research area because of its widespread applicability in domains such as nanoelectronics, pharmaceutics, semiconductors, and photovoltaics among others. In this endeavor, we propose a low-cost patterning technique that aspires to eliminate the more expensive methodologies that are presently in practice. Using a simple document stamp on which patterns of any geometry can be embossed, we are able to print 2D millimeter-scale “wall-less confinement” using an ink-based hydrophobic fence on any plasma-treated superhydrophilic surface. The confinement is subsequently filled with nanocolloidal liquid(s). Using confinement geometry, we are able to control the 3D shape of the droplet to exhibit multiple interfacial curvatures. The droplet in the “wallless confinements” evaporates naturally, exhibiting unique geometry (curvature)-induced flow structures that induce the nanoparticles to self-assemble into functional patterns. We have also shown that by modifying the geometry of the pattern, evaporation, flow, and particle deposition dynamics get altered, leading to precipitate topologies from macro- to microscales. We present two such geometrical designs that demonstrate the capability of modifying both macroscopic and microscopic features of the final precipitate. We have also provided a description of the physical mechanisms of the drying process by resolving the unique flow pattern using a combination of imaging and microparticle image velocimetry. These provide insights into the coupled dynamics of evaporation and flow responsible for the evolution of particle deposition pattern. Precipitate characterization using scanning electron microscopy and dark-field microscopy highlights the transformation in the deposit morphology.

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INTRODUCTION Surface patterning is indispensable to the rapidly progressing area of micro- and nanoelectronics, lab on a chip, biomedical engineering to name a few. For example, precise assembly of nano/micrometric devices upon semiconductor substrates requires various combinations of patterning techniques such as lithography,1 nano-imprinting,2 and scanning probe microscope writing method.3 Emerging lab-on-chip devices in medical technologies also require similar techniques to create patterns at various spatiotemporal scales. However, these methods are very time consuming and expensive. Templatebased patterning methods4 address this issue to a large extent. In this method, the structural topology as embossed in a template is transferred to the desired substrate ensuring the much required repeatable realizations of the desired pattern. Many of these patterning techniques use a droplet-based architecture, in which a functional droplet (containing nanoparticles or polymers or biofluids) is allowed to dry and self-assemble in a controlled fashion. In a multiwetting surface, the droplets can be made to undergo different types of evaporations at various spatial locations leading to striking © XXXX American Chemical Society

morphologies. An evaporating droplet exhibits distinct modes (such as constant contact radius or constant contact angle or mixed).5 In addition, the evaporation flux varies spatially along the droplet interface (from three-phase contact line to apex of the droplet). These two effects determine the nature and magnitude of the internal flow6−8 induced inside of the drop. This internal flow field controls the particle/species transport and hence the final deposit morphology. Thus, self-assembly in droplets provides an effective strategy for generating targeted surface patterns by simply changing the modes of evaporation. Particle-laden droplets on hydrophilic substrates develop a “coffee-ring”-like structure6 while drying. Subsequently, researchers9−13 have identified several means of avoiding such segregation of suspended matter to produce a more uniform deposit. The deposit patterns obtained from nanocolloidal droplets tend to form spatially varying circular deposits that develop cracks14 of various length scales determined by the Received: August 8, 2016 Revised: September 25, 2016

A

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Figure 1. Experimental methods. (a) Illustration of plasma treatment of the glass substrate using a handheld generator. (b) Printing hydrophobic lines on the substrate. (c) Snapshots showing the deployment sequence of droplets. (d) Dual curvatures in a single droplet. (e) Print templates for proof-of-concepts differing only in the aspect ratio (Wch/Wce). (f) Illustration of optical diagnostics used for monitoring evaporation dynamics and flow patterns. (Image courtesy for the μPIV setup: Lavision GMbh).

nature of particles, their concentration, and the substrate.15 If the substrate is changed from hydrophilic to hydrophobic, the mode of evaporation changes along with the deposit morphology. Nanocolloidal droplets on hydrophobic substrates form spherical shells instead of circular flat deposits. These shells undergo buckling16 under appropriate conditions17 forming hollow dome-shaped structures. When a colloidal droplet evaporates in the vicinity of other droplets (as applicable in droplet arrays19), the mode of evaporation is again modified18 leading to further modulation in the spatial deposit pattern. However, precipitates generated from hydrophilic droplets are invariably circular in shape. In a bid to replace the existing techniques, the methodology of droplet evaporation must evolve further. Exposing a surface to high energy plasma increases its wettability.20 Additionally, creating hydrophobic traps on hydrophilic substrates21 not only changes the evaporation pattern in the droplets deployed in those confinements but also allows control of the 3D shape of the droplet.22,23 Modulating the 3D shape of the droplet may offer possibilities of controlling the particle deposit patterns and thereby may lead to customized surface patterns.23 This paper presents a low-cost technique to obtain surface patterns by combining several of the strategies mentioned in the preceding paragraph. Initially, as shown in Figure 1a, we treat a surface to high energy plasma to make it highly wettable. Subsequently (Figure 1b), an ordinary self-inking document stamp with an embossed pattern on its polymeric face1 is brought in contact with the treated substrate to create a hydrophobic perimeter (of ink) upon the superhydrophilic surface. When two drops of nanocolloidal solution are introduced within this practically wall-less confinement, they spread rapidly and fill up the inner space, as shown in Figure 1c. The droplet segment occupying the confinement exhibits differential interfacial curvatures at multiple spatial locations without any ligament breakup (Figure 1d). Such a droplet undergoes curvature and evaporation-induced complicated flow dynamics that lead to preferential and spatially inhomogeneous nanoparticle deposit. The end result is the formation of spectacular nonuniform deposit patterns at hierarchical length scales. We also show that these surface patterns may be

controlled just by simply changing the aspect ratio of the wallless confinement (Figure 1e). It is worthwhile to mention that a similar strategy for regulating the 3D topography of the droplet using custom surface wettability (using various lithographic techniques) had been reported by Khademhosseini and coworkers.23 However, our work differs from theirs in many aspects. We have used commercially available low-cost selfinking document stamp for printing. We also offer detailed physical insights into the evolution of particle deposition and pattern formation using comprehensive analyses of the evaporation and flow dynamics of nanocolloidal droplets using low-speed imagery and microparticle image velocimetry (μPIV, Figure 1e,f). Finally, we demonstrate a detailed analysis and characterization of the final precipitate including the microstructural features, nanoparticle packing in the light of evaporation, and internal flow. Ideally, the methodology could be rapidly prototyped to generate a wide array of surface patterns with varying degrees of complexity on any given surface at a very low cost. Applications could be widely varying from printed circuit boards that would require a precise distribution of semiconductor materials to designing photoactive surfaces or even producing a multihued coat of paint.

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EXPERIMENTAL TECHNIQUES

Sample Preparation. Colloidal silica (CL-30, Sigma Aldrich, USA) was diluted to 0.5 wt % using deionized water and used in all reported experiments. The parent dispersion had a pH of 4.5, and the nominal particle diameter was reportedly 12 nm. The suspension was anionically stabilized against coagulation. The liquid dispersion was sonicated for five minutes before all experiments to ensure homogenous mixing and to eliminate any flocs that may have formed in the parent dispersion. Substrate Preparation. Microscope glass slides (Superfrost Plus, Fisher Scientific) were used for all experiments. Slides were precleaned with acetone before being subjected to plasma treatment for enhanced hydrophilicity. The plasma arc was generated at 10 kV and 4.5 MHz using a handheld plasma generator (BD 20 AC, Electro-Technic Products, USA) and was repeatedly scanned over the given glass substrate for 90 s. The static contact angle of deionized water on the plasma-treated glass surface reduced from 40° to less than 4°. B

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Figure 2. Stages of evaporation for the noncircular sessile droplet system for T1. (a) Top view of the droplet in the initial stage (t/T = 0.24), where t is the acquisition instant and T is the total drying time of the droplet. Dashed boxes denote the regions where magnified images were subsequently acquired (b) at t/T = 0.83 in the cell region, (c−e) between t/T = 0.86 and 0.88 in the cell region, and (f) at t/T = 0.83 in the channel region. Dashed box shows the region where fluorescent images were acquired (g) at t/T = 0.86 in the channel region; necking is initiated. (h) At t/T = 0.87, development of necking leads to pinch-off at (i) t/T = 0.88. See Video S1 (j) snippets of the side-profile showing decay in height difference. Designs to be printed on the glass surface were embossed on a strip of polymeric material like those found in any ordinary self-inking document stamp. The template was printed on the glass substrate by bringing it in contact with the stamp. The ink used was of commercial variety. The inked perimeter formed a hydrophobic fence creating a confinement boundary on the superhydrophilic substrate. The primary design of the template proposed for proof-of-concept experiments consists of two boxes (inner area is 2.8 × Wce mm2) connected via a thinner strip (5 × Wch). The boxlike region is denoted as the cell, whereas the strip is labeled as the channel (Figure 1d,e). Here, Wce and Wch are the respective widths of the cell and the channel, respectively. Two variants of the proposed design, as shown in Figure 1e, were employed: template 1 (T1) where Wch/Wce = 0.54 and template 2 (T2) where Wch/Wce = 0.72. Wce is maintained at 2.6 mm, whereas Wch is 1.4 mm for T1 and 1.88 mm for T2. Droplet Deployment and Imaging. Two syringes mounted on separate syringe pumps (New Era Pumpsystems Inc.) were used to simultaneously dispense two droplets of the same volume (3 ± 0.1 μL) and concentration (0.5 wt % nanoparticles) into the cell regions (Figure 1c). The glass slide was kept inside an enclosed chamber (to reduce convection effects) and left to dry naturally. The complete lifetime of the drying droplet system was recorded at 0.33 fps from top and side using CCD cameras (NR3S1 and Motionscope M5, IDT Vision, respectively) both of which were fitted with a Navitar zoom lens (4.5×) assembly (Figure 1f). The ambient relative humidity and temperature were maintained at 42% and 23 °C by using an air conditioner (Carrier Technologies) in conjunction with a dehumidifier (Origin, Novita). μPIV. The experimental technique is illustrated in Figure 1f. Numerous spatial locations (elaborated later) along the length of the confinement (y-direction; Figure 1e) were chosen for PIV measurements. Experiments were done with a rhodamine-coated microparticle (0.86 μm, R900, Thermofisher Inc.) dispersion of 1.775 × 10−5 wt %. Images were captured using an Imager Intense camera (Lavision) coupled to a 3-axis motorized microscope (Flowmaster Mitas, Lavision) (Figure 1f). A 5× objective lens with a depth-of-field of 28 μm and a field of view of 1.2 × 0.9 mm2 was fitted to the

microscope. The actual depth of focus of the system (lens and microscope) was 46 μm. The resulting lateral resolution was 3.5 μm. Volume illumination of the drying droplet was done using an Nd:Yag laser system (NanoPIV, Litron lasers) emitting at 532 nm. Single frame images were acquired at 0.25 fps (slower flow) to 1 fps (faster flow) to ensure a pixel shift of more than two between consecutive images. The measurement plane (z) was specified with respect to the droplet height (H) at any given location (Figure 1f). Three such planes were chosenz/H = 0.25, 0.5, and 0.75for measurements. Image preprocessing and vector field computation were done using Davis 7.2 software from Lavision. The preprocessing involved the removal of out-of-focus particles that contribute to background noise in μPIV experiments.24,25 The processed images were then subjected to time-series PIV that involved cross-correlation of consecutive pairs of images in the sequence. Interrogation window was maintained at 64 × 64 pixels in the first pass and 32 × 32 pixels in the second pass with 50% overlap. The instantaneous velocity vectors were temporally averaged (over 50 s) to obtain the average velocity field map. Characterization. Desiccated nanoparticle deposits were preserved for further characterization. Dark-field microscopy using a 5× objective lens (NA = 0.15) mounted on an upright microscope (Olympus BXFM) with a halogen light source was used to observe the global features of the preserved sample. A CCD camera (SC-30, Olympus) fitted to the microscope acquired static images of the sample. The samples were then subjected to scanning electron microscopy (SEM) characterization for microstructural detail. Before SEM, they were sputtered with 10 nm of gold particles (Quorom Technologies, UK) to ensure electron conductivity. Field emission SEM was performed using an Ultra 55 Mono-CL microscope (Zeiss, Germany). An accelerating voltage of 3−5 kV was used for excitation, and an SE2 lens was used to capture the emitted electrons. The working distance was maintained at 10 mm from the sample substrate. C

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DROPLET DRYING IN T1 (WCH/WCE = 0.57): GLOBAL OBSERVATIONS The T1 substrate is discussed first to examine the physical mechanisms that lead to the formation of the final nanocolloidal deposit. Discussion on T2 is deferred to a later section, where comparisons are drawn with T1 to reveal how Wch/Wce emerges as an important parameter. In the initial stages of postdeployment (Figure 2a), the droplet’s contact line is pinned while it assumes a static contact angle value of 28°. As evaporation progresses, solid precipitates are formed at the edge of the cell (Figure 2b) and the channel (Figure 2f). Evaporation in the cell region closely mimics an isolated spherical droplet with the exception that it is not axisymmetric. As shown in Figure 2b, the sharp corners at the cell region lead to higher flux of the solvent, and consequently, a more developed agglomeration front. At t/T = 0.86 (where T is the total time required for the deployed liquid volume to completely evaporate), the contact line begins to recede, detaching itself from the deposit. Figure 2d,e shows the later stages of recession. The channel region shows an interesting phenomenon. As shown in Figure 2g, the contact line appears to develop an inward kink (Video S1). The contact line detaches itself from the deposit (Figure 2h) and progressively necks till it pinches off (Figure 2i) at t/T = 0.88 (see Video S1). The constant contact radius (CCR) mode of evaporation (till t/T = 0.83) ensures that the curvature disparity between the cell and the channel (Figure 1d) slowly decays as shown in the image sequence of Figure 2j. The final morphology of the dried precipitate is shown in the later sections. Evolution of the Internal Flow. Normally if two liquid droplets come into contact with each other, they undergo spontaneous or delayed coalescence.26,27 However, when deployed in T1, as shown in Figure 1c, the droplets spread and merge at the channel center resulting in a shape that consists of two symmetrical side lobes interconnected by a thin strip, as shown in Figure 3a. It is quite intuitive to observe that

pressure in the channel is calculated as Pch =

γ C2

+ Patm , where

C2 is the curvature of the cylindrical segment in the channel. Indeed, the calculated pressure gradient and the presence of stagnation zone due to symmetry of the configuration would result in a flow field as illustrated in Figure 3b. In the absence of evaporation, the pressure-driven flow would be directed from the cell to the channel along the centerline while reversing along the edges (dashed arrows in red), such that the net mass flux across any cross section (EE′) perpendicular to the channel would be zero. However, sustained evaporation from the droplet’s free surface (evaporation flux is maximum at the three phase contact line) would induce an outward radial flow to compensate the solvent loss. This radial velocity component would result in the deflection of the velocity vectors, as shown in Figure 3b (solid arrows). So, the resultant internal flow is due to a combination of geometric curvature difference, symmetry of the pattern, and natural evaporation. To support our hypothesis regarding the internal flow pattern in such multilobed droplets, we perform μPIV at multiple spatial locations (y/L = 0.2 till 0.5) along the edge and the centerline of the droplet as illustrated in Figure 4a. Results from the measurement plane of z/H = 0.25 at three such axial locations (y/L) during various stages of drying are presented. Figure 4b shows the velocity vectors during the initial stage (t/ T = 0.24). In the cell region at y/L = 0.25, the flow is predominantly directed toward the channel as explained in the preceding section. At y/L = 0.34, the centerline flow is still toward the channel region, whereas the flow vectors nearer to the edge (x/W < 1) seem to be directed in the opposite direction. The flow pattern is similar at y/L = 0.44 as well. Before necking at t/T = 0.83, the flow pattern shown in Figure 4c remains similar to t/T = 0.24, but there is an increase in velocity magnitude at all aforementioned locations implying strong acceleration. Beyond t/T = 0.86, coincidence with the phenomenon of necking a complete reversal of flow from the channel to the cell is observed (Figure 4d). Figure 5a shows that the velocity component along the centerline (Vy,centerline) undergoes spatial acceleration (y/L = 0.2 − 0.42) as the curvature difference between the cell and the channel forces the solvent to flow through a tapering cross section (the straight part of the channel starts from y/L = 0.4). Beyond y/L = 0.42, the magnitude begins to decay and is nearly zero at y/L = 0.5 (which is the stagnation point for opposing streams from each of the two cells). Solvent loss at the edge is replenished by Vx, which in turn is aided by Vy,centerline. Because evaporation causes Vx to grow (explained before), mass conservation also requires Vy to grow proportionately (Figure 4b) to support Vx through a continuous thinning (in the zdirection only) of the liquid layer in the channel. These measurements prove that although the origin of Vy is due to the curvature difference between the cell and the channel, its spatiotemporal evolution is guided by the evaporation dynamics and the aspect ratio of the confinement. For the period beyond t/T = 0.86, the flow reversal is coincident with necking as explained here. Figure 2j shows the gradual reduction in the curvature disparity of the cell and the channel. Additionally, development of necking creates an additional curvature in the ⎡1 1 ⎤ channel region. Thus, Pch = γ ⎣⎢ C + C′ ⎥⎦ + Patm , where C′2 is 2 2 the curvature of the necking zone, as shown in Figure 2h. Because 1/C′2 increases with time after the onset of necking, Pch becomes strong enough to induce a complete reversal of

Figure 3. Evolution of the internal flow. (a) Side view illustrates how curvature difference induces pressure gradient to drive the flow from the cell to the channel. (b) A schematic top view illustrates centerline flow direction due to pressure gradient, whereas reversed flow is due to template symmetry. Dashed arrows in red indicate flow reversal in the absence of evaporation.

such a difference in curvature between the cell and the channel would result in an internal pressure gradient along the axial length of the droplet. Considering the liquid in the cell to assume spherical cap geometry, the internal pressure is 2γ calculated as Pce = C + Patm , where γ is the surface tension 1

of water, C1 is the mean curvature of the spherical cap in the cell, and Patm is the atmospheric pressure. Similarly, the internal D

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Figure 4. μPIV results. (a) Section of droplet for μPIV analysis. Magnified view of windows where μPIV was done along with the corresponding vector maps. The location is specified by y/L, where y is the location and L is the length of the printed pattern. (b) t/T = 0.24; initial stage. (c) t/T = 0.83; prenecking. (d) t/T = 0.86; onset of necking. For the vector maps, the scale bars in red denote 450 μm, whereas those in orange denote 425 μm.

Figure 5. (a) Vy,centerline plotted with respect to y/L for various times (t/T). t/T = 0.24 to 0.83 are plotted on the left axis, whereas t/T = 0.86 is plotted on the right axis. (b) Vy,centerline at x/W = 0 and y/L = 0.44 for various vertical planes (z/H = 0.25, 0.5, and 0.75) is plotted against time (t/T). (c) Vx,edge at x/W = 0.86 and y/L = 0.44 is plotted against time. (inset) Illustration of how the Vx component of the flow results in edgeward migration of suspended particles and deposit formation. See Video S2.

flow from the channel to the cell during the time period t/T = 0.86 − 1. We conducted the same PIV measurements at y/L = 0.44 for z/H = 0.5 and 0.75. When Vy,centerline from all three planes (z/H = 0.25, 0.5, and 0.75) were compared (Figure 5b), the maximum deviation among them was insignificant. The absence of gradient in axial velocity in the z-direction could be attributed to the thinness of the channel region. The outward component of flow (Vx) that contributes to agglomeration of particles at the edge is shown in Figure 5c (see Video S2). Vx was extracted at x/W = 0.86 and y/L = 0.44 while the plane of measurement was maintained at z/H = 0.25. The choice of x/W = 0.86 instead of x/W = 1 was made to avoid “lensing effects” observed in droplets.8 y/L = 0.5 was avoided by virtue of it being the symmetry point. Vx near the

edge shows a gradual increase (Figure 5a) with time to compensate for the solvent loss through a continuously thinning droplet height (Figure 2j) consistent with earlier findings.6 Video S2 also highlights the enhanced rate of deposition toward the end stage of drying. It is worth summarizing that the internal flow, the interfacial curvature, the evaporation rate, and the aspect ratio of the confinement are significantly coupled with one another. We have argued here that the aspect ratio leads to a multicurvature sessile droplet leading to a strong axial flow. Furthermore, this flow field and geometry of the droplet (contact angle and surface area) influences the natural evaporation rate, which in turn induces strong radial flow in the system. Hence, by finetuning the geometry of the confined perimeter, one can technically control the evaporation rate and the flow dynamics, E

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Figure 6. Evaporation dynamics. (a) Schematic illustration of how the proposed architecture modulates the flow and eventually the dynamics of evaporation. (b) Isometric view of the channel region illustrating the contact angle (θ2) and vnet. (c) Temporal variation of height, (inset) h1 − h2 vs t/T. (d) Contact angle change against normalized time (t/T). (e) Net rate of change of volume of the evaporation fluxes (theoretical vs experimental).

the channel region, and α is the central angle subtended by the circular segment EFE′, as illustrated in Figure 6b.

both of which are of paramount importance in particle transport. Evaporation Dynamics. The coupling effect is reemphasized in Figure 6a, where the cell seems to serve as source of replenishment for evaporative losses in the channel. We quantify droplet shrinkage by plotting its height and contact angle because the contact line remains pinned for majority of the droplet lifetime. Figure 6b illustrates the computational procedure of the channel’s contact angle because it cannot be observed directly. We have used its height (h2) and contact radius (x) to deduce the contact angle h2 x

The solvent loss from the cell components: evaporative

1

the channel (h2) are shown in Figure 6c, where h1 decays faster than h2. Contact angle variation, as shown in Figure 6d, is similar in both the channel and the cell and demonstrates the dominance of CCR mode of evaporation over the droplet’s lifetime (till t/T < 0.83). To further our analysis, we treat the cell and the channel as separate control volumes ABCDA and EFGHE. We assume ABCDA to be a spherical cap (neglecting the corners to simplify calculations) whose volume is given as

whose volume is expressed as Vch = πC2

(

( ) and outflow from the cell to dt

(1)

and e dV ch dV = ch + vnetA EFE′ dt dt

(2)

Figure 6e illustrates the rate of solvent loss due to evaporation. The rate of volume change in the cell

where r1 is the effective contact radius of the Vce = cell region. EFGHE is considered to be a cylindrical segment π α 180

consists of two

dV cee

dV cee dV = ce − vnetA EFE′ dt dt

πh1(3r12 + h12) , 6

2

dVce dt

( )

the channel (Vnet × AEFE′) (Figure 5a). AEFE′ is the cross section of the channel region (Figure 5b). The average velocity vector for the plane z/H = 0.25 is calculated as 1 x / W = 0.86 Vz / H = 0.25 = N ∑x / W = 0 (Vy), where N is the number of vector points. This is repeated for two more planes (z/H = 0.5 and 1 0.75) to get vnet = 3 ∑ (Vz / H = 0.25 + Vz / H = 0.5 + Vz / H = 0.75). Using vnet we get

( ). Height variations in both the cell (h ) and

θ2 = 2 × tan

( ddvt ) and its evaporative component. (f) Comparison

(

)

dVce dt

and

dV cee dt

) is 10 times higher than the corresponding

quantities of the channel region. dVce is higher than its dt evaporative component because it not only supports evaporation but also serves as a supply of solvent in the channel.

− sin α × l ,

where C2 is the radius of curvature of the circular cross section of the cylindrical cap, l is half the length of the cylindrical cap in F

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Langmuir Conversely, dVch is lower than its evaporative component dt because the loss of solvent is being compensated by flow from the cell. This is a profound result whose significance would be explained later. The above result was validated by comparison with the existing model for diffusion-based evaporation for single sessile droplets with circular contact area. Here, the evaporation flux from a given droplet with a contact angle θ and a contact radius r is given as Jtheory = −

2πDMrCs(1 − RH )f (θ ) ρA

(3) −5

where D is the diffusion constant (2.54 × 10 m /s), M is the molar mass of the solvent (18 g/mol), Cs is the saturated vapor concentration (1.278 mol/m3), RH is the relative humidity (0.4), ρ is the density of the solvent (1.0 g/mL), and A is the lateral surface area of the given droplet. The polynomial f(θ) = (0.00008957 + 0.633θ + 0.116θ2 − 0.887θ3 + 0.01033θ4),28 where θ is in radians. Jtheory was calculated using r = r1 in the cell region. Subsequently, the experimental values of the evaporation flux for the cell and the channel (Jcell and Jchannel) were calculated using 2

Figure 7. Illustration of necking in channel. (a) Schematic to show how the flow from the cell partially replenishes the evaporative loss in the channel. Here, vnet represents the net flow from the cell to the channel. (b) Progressive evaporation diminishes the cross section through which the channel receives replenishment. (c) Unsustained evaporation in the channel leads to necking which leads to pinch-off. (d) Liquid contact line (a/Wch) vs time (t/T). Blue region represents the pinned contact line. Orange region corresponds to the pinned contact line but concealed within agglomeration front. The necking stage is shown in red.

e

Jce =

1 dV ce Ace dt

(4)

where Ace = AABCDA − AEFE′, AABCDA is the surface area of the cell (assumed spherical cap of height h1 and contact radius r1). Similarly

liquid height in the channel becomes so thin that it is unable to maintain the solvent supply necessary for sustenance of evaporation flux (Jchannel) causing the contact line to slip (neck) radially inward (red shade; Figure 7d). This initiates “squeezing action” in the channel region that further drains the solvent (Figure 7d). At this stage, the channel loses the liquid via evaporation and by necking of the constricting liquid line. Effect of Geometry on Flow Field and Evaporation. Droplets drying in T1 undergo spontaneous necking (Figure 8a) because of the evaporation-driven flow dynamics, as discussed in the previous sections. It is imperative to see how the geometry of the template can be exploited to control the flow physics and evaporation so that the final deposit can be manipulated. The current section is devoted to comparison of the two templates: one which induces necking (T1) and another which eliminates the same (T2), as shown in Figure 8b. When the droplet is deployed in T2 (larger aspect ratio), the curvature difference between the cell and the channel represented by the ratio h1/h2 decreases from 2.6 to 1.6, as shown in Figure 8c,d. The static contact angle also decreases from 28° to 23°. μPIV results for the non-necking case are shown in Figure 8e. The Vx component in this case (Vx,nn) is lower than its necking counterpart Vx,n, indicating lower solvent depletion in the channel. The burden on the cell to sustain the channel evaporation flux is lowered. Furthermore, the lower height difference between the channel and the cell implies a lower value of the axial velocity Vy,nn. The higher aspect ratio also enables unrestrained Vy for a longer duration keeping the contact line pinned in the channel region while allowing considerable slippage in the cell (Figure 8b). Thus, necking is avoided in this configuration allowing the droplet to converge to the channel where it finally dries out. Geometry-Directed Deposit Patterns: Global and Microscale Characteristics. It is interesting to observe in Figure 9a (inset) that necking in the channel results in the

e

Jch =

1 dV ch Ach dt

(5)

where Ach is the surface area of the cylindrical segment EFGHE given by Vch/L. As shown in Figure 6e, Jce ≈ Jch, which implies that the evaporation flux remains nearly unchanged from the cell to the channel in the longitudinal direction. When compared to the theoretical results, experimental values deviate by ∼20%. This proves that even though the shape of the droplet presented here is drastically different from the perfect spherical cap geometry for which eq 3 is derived, it can still predict (within reasonable error limits) the evaporation rate. Particle Agglomeration and Necking. Schematic in Figure 7a shows the replenishing flow from the cell to the channel. This flow needs to be maintained through a continuously thinning channel, as shown in Figure 7b. When the channel cross section is too small to allow the influx required to sustain the evaporation in the channel, it leads to necking of the contact line. Progressive necking leads to pinchoff, as shown in Figure 7c, and thus creating twin daughter droplets (inset). Such a spontaneous pinch-off in droplets evaporating in a quiescent environment has never been observed before and can be exploited for a multitude of applications. The evolution of the contact line in the channel sheds light on the mechanism of necking. In the initial stages of evaporation till t/T = 0.5, the contact line appears pinned and is equal to the width of the channel (blue shade; Figure 7d). As the solute deposit grows at the edge (see deposition Video S1), the exact location of the contact line is concealed within the solid structure. To avoid ambiguity, we assume the extent of the contact line to be pinned to the inner edge of the deposit (orange shade; Figure 7d). Beyond t/T = 0.86, the G

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when compared to zone II (1−10 μm) that formed the edge deposit (Figure 9c). Zone III, which is shown in Figure 9d, consists of the central location in the channel and displays the finest of crack structures (40−200 nm). Rough estimate of the deposit’s average thickness via SEM is presented in Table 1. It Table 1. Comparison of Deposit Thickness in Necking vs No-Necking Condition deposit thickness (μm) zone edge (II) cell center (I) channel center (III)

necking conditions (template 1)

no-necking conditions (template 2)

18 ± 2 10 ± 2 4±2

26 ± 2 3±2 12 ± 2

is observed that the crack spacing is directly proportional to the deposit thickness, which is consistent with the previous work.29 The spatial variation in thickness is explained as follows. It is also well known that the free interface of a drying droplet is pinned at the edge resulting in particle transport and aggregation. Thus, longer pinning duration results in pronounced edge deposit. As shown in Figure 7d (blue-shaded region), the contact line resides at the edge for more than 80% of the droplet lifetime resulting in a very thick deposition of particles (∼18 μm) observed in zone II. Zone I consists of thinner deposit (∼10 μm) because majority of the particles had already aggregated at the edge. The channel center shows very fine thickness (∼4 μm) because the slipping contact line (due to necking) prevents any major particle deposition. For nonecking template depicted in Figure 9e, the entire liquid pool converges to the channel center forming a very different deposit morphology as compared to the necking case. Zone I in this case is very thin (∼3 μm) with smaller cracks (Figure 9f)

Figure 8. (a) Illustration of necking case where Wch/Wce = 0.54. (b) No necking case where Wch/Wce = 0.72. (c,d) The curvature disparity is lesser in no necking condition. (e) Comparison of Vx and Vy of no necking {nn} vs necking {n} conditions.

droplet pinch-off to form two daughter droplets both of which recede into the cell to create two separate centers of contact line convergence (Figure 9a). For discussion, we have divided the precipitate into three zones. Zone I represents the location where the daughter droplets converged. As shown in Figure 9b, this region is characterized by small crack spacing (0.2−1 μm)

Figure 9. Deposit characterization. (a) Final precipitate obtained from necking condition having three zones. (Inset) pinch-off in the channel creates two daughter droplets. (b) Zone I-droplet convergence. (c) Zone II-edge of precipitate. (d) Zone III-channel center. (e) Final precipitate obtained from no-necking condition. (Inset) absence of pinch-off results in the contact line converging within the channel. (f−h) Zones (I−III) in the same order as (b−d), with variation in different microstructures. H

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Figure 10. Flowchart of proposed technique: stage 1, functionalizing a drop; stage 2, substrate treatment; stage 3, template design and substrate printing; and stage 4, postdessicated surface pattern.

droplets. Low-speed imaging was used to observe the evaporation characteristics, whereas μPIV analysis was performed to understand the internal flow pattern. In addition to the outward capillary flow observed in the hydrophilic droplets, the curvature difference between the cell and the channel also created a longitudinal flow between the two regions. However, the symmetry of the pattern ensured a back flow as well. We discussed how this flow compensated solvent depletion in the channel. Our initial choice of geometrical constraints (Wch/Wce = 0.54) resulted in necking in the channel region because of Vy inability to maintain evaporation in the channel. By relaxing the constraint to Wch/Wce = 0.72, necking was eliminated. The nanoparticle deposits obtained from necking and non-necking droplets at the end of stage 4 were further subjected to microscopy analysis to reveal striking dissimilarities at both macroscopic and microscopic length scales. We have thus provided sufficient evidence that the initial choice of template geometry could be exploited to engineer the deposit morphology in drying colloidal dispersions. The simplicity and cost-effectiveness of the technique are amenable to designs far more complicated than the ones presented as proof-of-concept. A wide range of substrates other than glass could be patterned. In the current work, we have demonstrated how the crack structure of a nanosilica deposit could be tuned by simply changing a geometrical attribute of the template. Subtle changes in the template design may produce drastically different deposit morphologies using the same combination of substance and substrate. Thus, the combination of material, surface, and template design complexity gives rise to an endless possibility of surface patterns having precisely engineered spatial topology. There are other attributes of the template that must be exploited in a variety of applications. One possible avenue could be microfluidics where such a complex network of channels could be simply printed on a surface. Because the surface would be highly wettable, any liquid deployed at one end could spread to another without any active pumping source. Experiments to validate the portability of this technique to micro- or even nanoscale flows need to be performed. As μPIV results amply demonstrate, the flow magnitude is easily tuned based on the existing channel dimensions. A mixture of particles with drastically different Stokes numbers could be deployed in the cell from which we could draw channels of different width. Because each channel would have a

because the contact line receded away from the cell to the channel. The edge is still the thickest zone (∼26 μm) with the largest crack spacing (1−10 μm), as shown in Figure 9g. It is to be noted that the contact line never slips in the channel region resulting in this enhanced edge deposit compared to the necking counterpart. Zone III that formed the droplet convergence center in this case shows higher deposition thickness (∼12 μm) than zone I, which also results in slightly larger crack spacing (Figure 9h). In addition, radial cracks seem to originate from the cell for necking case. For no-necking scenario, the cracks seem to originate from the channel center and propagate along the length of the confinement. Thus, changes to the geometrical aspects of the template not only resulted in spatially varying deposit profiles but also effected dramatic variations in the crack pattern. For all cases, the nanoparticles seem to be in closed packing configuration with pore spacing equivalent to the particle size (Figure 9f). Experiments performed for lower concentration of nanoparticles (0.1 and 0.05 wt %) for Wch/Wce = 0.54 also show similar necking behavior, and they resulted in similar precipitates with the exception that the inner region appeared to be devoid of any residual patterns (due to the lower number of available nanoparticles). Because of their phenomenological similarity with the reported deposit patterns, they have been excluded from the present discussion. Experiments done with Wch/Wce = 1 also did not result in any necking, proving the existence of critical aspect ratio that determines the occurrence of necking.

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CONCLUSIONS The present work explores the fundamental dynamics of evaporation-driven flow in a sessile nanocolloidal deformed droplet. We have provided insights into how the shape of the droplet could be tuned using wall-less confinements to obtain different deposit patterns. The methodology is outlined into four stages, as shown in Figure 10. In stage 1, nanosilica dispersion was prepared for dispensing. In stage 2, the glass substrate was exposed to high energy atmospheric plasma making it superhydrophilic. Two design templates having different Wch/Wce ratios were used. In stage 3, the templates were transferred to the superhydrophilic glass substrate to create a wall-less confinement for the nanosilica deformed droplets to dry out. The resulting droplet assumed a unique dual curvature and a targeted contact line unlike sessile I

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different characteristic velocity, this may lead to particle segregation without the use of any external reagents or centrifuging devices. This could have immense impact in fields such as biosample analysis or healthcare diagnostics. Exhaustive experiments involving different parameters such as particle concentration, particle type, template design, and hydrophobicity of the template perimeter form a part of future studies.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b02962. Evaporation leading to necking in channel (AVI) Evaporation-induced capillary flow transports particles to three phase contact edge (AVI)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/acs.langmuir.6b02962 Langmuir XXXX, XXX, XXX−XXX