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Insights into Vapor-Mediated Interactions in a Nanocolloidal Droplet System: Evaporation Dynamics and Affects on Self-Assembly Topologies on Macro- to Microscales Angkur Shaikeea, Saptarshi Basu,* Sandeep Hatte, and Lalit Bansal Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India S Supporting Information *

ABSTRACT: Particle-laden droplet-based systems ranging from micro- to nanoscale have become increasingly popular in applications such as inkjet printing, pharmaceutics, nanoelectronics, and surface patterning. All such applications involve multidroplet arrays in which vapor-mediated interactions can significantly affect the evaporation dynamics and morphological topology of precipitates. A fundamental study was conducted on nanocolloidal paired droplets (droplets kept adjacent to each other as in an array) to understand the physics related to the evaporation dynamics, internal flow pattern, particle transport, and nanoparticle self-assembly, primarily using optical diagnostic techniques [such as micro-particle image velocimetry (μPIV)]. Paired droplets exhibit contact angle asymmetry, inhomogeneous contact line slip, and unique single-toroid microscale flow, which are unobserved in single droplets. Furthermore, nanoparticles self-assemble (at the nanoscale) to form a unique variable-thickness (microscale) tilted dome-shaped structure that eventually ruptures at an angle because of evaporation at a nanopore scale to form cavities (miniscale). The geometry and morphology of the dome can be further fine-tuned at a macro- to microscale by varying the initial particle concentration and substrate properties. This concept has been extended to a linear array of droplets to showcase how to custom design two-dimensional drop arrangements to create controlled surface patterns at multiple length scales.

1. INTRODUCTION Sessile functional droplets form the backbone of many applications across multiple length scales. The working fluid for the droplets usually ranges from a pure solvent to complex groups such as biofluids, colloids, polymers, surfactants, and even human blood.1−6 All these additives impart functional capabilities to the drop for applications such as targeted drug delivery, inkjet printing, surface patterning, and digital microfluidics.7−13 In most of these applications, the sessile droplets undergo natural or forced evaporation, and their vaporization dynamics (even when diffusion driven) are not straightforward like those of contact-free droplets. In fact, the evaporation flux varies significantly across the droplet surface. The variation in the contact angle and the contact radius normally determines the evaporation mode of a sessile droplet [constant contact radius (CCR) or constant contact angle (CCA) or mixed], which in turn tunes the vaporization flux. These dynamics invariably induce microscale internal flow patterns, which in turn aid in the preferential transport of functional groups (colloidal particles and polymers) in different regions of the droplet. Such a spatiotemporally nonuniform but controlled transport offers tremendous potential in processes such as cell separation and topologically graded surface patterning, to name a few. The droplet architecture is particularly attractive for electronic systems such as patterning microscale structures on semiconductor substrates.14,15 It is therefore important to © 2016 American Chemical Society

understand the evaporation dynamics of such sessile droplets. Efforts have ranged from modelling the drop as a capacitor to visualizing the internal flow patterns using modern optical diagnostic techniques.16−18 Most of the applications, however, involve vapor-mediated interactions19 where arrays of functional droplets are arranged in a certain sequence (certain droplet-todroplet distance or pitch) rather than a single drop.20−24 Hence, it is imperative to understand the behavior of functional drops in an arrangement where the evaporation dynamics can be altered significantly by the presence of a neighboring drop. In this context, a fundamental study was conducted by Shaikeea and Basu25 for vapor-mediated interactions in paired droplets (two droplets in the vicinity of each other; Figure 1) with pure water as the working fluid. The study found that the evaporation rate in such paired droplets is completely different from that of single droplets. The vapor mediation between the droplet pair also leads to significant variation in the evaporation modes and consequently the internal flow pattern. Although this study was valuable, the role of such alterations in both flow and evaporation-driven transport of colloidal particles or similar functional groups in the interacting droplets is scarcely available. Previously, Pradhan and Panigrahi26 had reported asymmetric Received: August 13, 2016 Revised: September 16, 2016 Published: September 16, 2016 10334

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Figure 1. Single droplet vs paired droplets (deionized water) on a hydrophobic substrate. (a) Evaporation dynamics of a single sessile droplet; uniform contact line recede and contact angle variations. (b) Paired droplets initially separated by L0/D0 ≈ 1.2 undergoing inhomogeneous contact line slip and contact angle asymmetry because of the suppressed evaporation flux in the shadowed region 1. With progressive evaporation, the droplets separate out from region 1 (L0/D → 2) and undergo free evaporation (k → 1). (c) Typical behavior of paired droplets asymptotic to a single droplet with increasing separation L0/D. Here, L0 is the center-to-center distance between the droplets, D0 is the initial droplet diameter, and k is the evaporation rate correction factor.25

deposition patterns (qualitatively and quantitatively) for paired droplets on hydrophilic substrates. However, in the present work, we extend this study to elucidate the behavior of nanoparticle (NP)-laden or nanocolloidal paired droplets on hydrophobic substrates. Unlike pure water, nanocolloidal droplets demonstrate additional phenomena such as particle agglomeration, spherical shell formation, buckling, and cavity formation, leading to striking morphologies at different length scales. However, the morphologies of the precipitate for the paired droplets and an isolated droplet (Figure 2c,d) can be significantly different, as outlined in the current work. Herein, we conducted a comprehensive methodical study on paired nanofluid droplets (see Experimental Section) to understand the physical mechanisms that determine the dynamics of the system leading to modulation of the final precipitate. Our system comprises two 3 μL droplets separated by a fixed initial distance deployed on two different kinds of hydrophobic substratespolydimethylsiloxane (PDMS) and a gas diffusion layer (GDL), referred to as S1 and S2, respectively. S1 has a low average surface roughness (Ra ≈ 40 nm) compared with S2 (Ra ≈ 12 μm). The deployed droplets are strongly pinned on S2 and weakly pinned on S1 because of these roughness variations. In addition, nanoparticle concentrations or the particle loading rate (PLR) is varied up to 30 wt %. These variables help us to decipher the sensitivity of the dynamics of the system and the final precipitate toward PLR and droplet pinning. Paired droplets interact through their vapor fields and suppress the evaporation dynamics of one another. Although the drops are dynamically separate from one another with continued solvent loss leading to increase in the evaporation flux, there are hysteresis effects for NP-laden droplets. We have shown that paired nanofluid droplets exhibit asymmetric evaporation suppression and differential/inhomogeneous slip in the left and right contact edges (Figure 2b), leading to a single-toroid flow. This flow structure was previously reported by Shaikeea and Basu27 for pure water, but the report lacked quantitative estimation. These features are not seen in a single isolated droplet (Figure 2a). The paired droplets also show a sideways tilt. All these factors in combination result in a buckled precipitate with a sideways cavity and a deformed structure (Figure 2d). Therefore, we investigated the internal flow,

Figure 2. Evaporation dynamics of nanocolloidal droplets (single vs paired). (a) For a single droplet, buckling and subsequent cavity propagation occurring from the top zone (buckling angle, ψb ≈ 0°). (b) For paired droplets (L0/D0 ≈ 1.2), emergence of asymmetry, inhomogeneous slip, dynamics separation (L0/D0 > 2), and sideways buckling (ψb > 0°) observed across a wide range of hydrophobic substrates (contact angle between 115° and 135°). SEM images of final precipitates(c) a single droplet and (d) paired droplets (Movie S1). The scale bar shown in (a) applies to all other images unless otherwise specified.

qualitatively and quantitatively, using high-fidelity micro-particle image velocimetry (μPIV) techniques. We also examined the evolution in the geometrical parameters of the droplet such as 10335

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droplets separate (L0/D > 2) to a sufficiently large distance. To characterize this separation scale for single and paired (interacting) droplets, a parameter k is defined as given by eq 125

the contact radius and the contact angle. We precisely demarcated the variations from an isolated identical nanofluid droplet, using parameters such as the contact angle asymmetry and the contact line slip (local mode of evaporation). This work hence can open up a new understanding and insights into multidroplet systems, leading to a better design and efficient control.

k=

dV dV / dt paired droplets dt single droplet

(1)

where V is the instantaneous droplet volume and t is the time elapsed. As the droplets vaporize, their separation increases and k asymptotes to 1 (L0/D → 2; Figure 1c). Thereafter, the droplets evaporate as independent entities. These observations are universal to droplets on all hydrophobic substrates. However, relative variations in the degree of asymmetry and the contact line slip were noted for two different classes of hydrophobic substrates: strongly pinned and weakly pinned droplets.27 2.2. Dynamics of a Single Nanocolloidal Droplet. For the current study, we disperse silica NPs stably into the solvent (water). During evaporation, the contact line and the contact angle recede uniformly and the NPs begin to deposit first at the contact line and subsequently form a shell around the air−drop interface (Figure 2a). Thereafter, the drop undergoes a morphological transition in a two-phase process: first, buckling from a weak spot of minimum shell thickness, forming a primary cavity (PC), and secondly, rupturing of the PC to form a daughter cavity (DC) and its growth inside of the droplet (sequence of events shown in Figure 2a). Preferential solvent evaporation from the droplet results in an accumulation of the NPs on the droplet periphery. This preferential evaporation is due to the suppression of the evaporation flux from the bottom sector of the droplet.32 As the particles agglomerate, the droplet undergoes sol−gel transformation to form a thin viscoelastic shell around the droplet periphery. The capillary pressure developed in the pores of the viscoelastic shell because of the solvent evaporation is given by the following equation

2. RESULTS AND DISCUSSION Evaporation of sessile droplets from hydrophobic substrates is characterized by physical transformations in the contact radius and the contact angle. However, a single sessile droplet satisfies the spherical cap assumption unless the diameter is greater than the capillary length scale, γ ≈ 2.73 cm , where γ is the surface ρg

tension, ρ is the fluid density, and g is the acceleration due to gravity. A single droplet evaporates in a symmetric fashion as shown in Figure 1a. If the droplet is placed on a hydrophobic substrate, the evaporation is locally suppressed near the threephase contact line because of the vapor wedge formed by the droplet (Figure 1b). The evaporation, however, still shows symmetry in the azimuthal direction. Placing a neighboring second droplet deforms the droplet geometry along with alterations in evaporation characteristics, such as the contact line slip, contact angle asymmetry, and flow transitions (to be addressed in section 2.1). Furthermore, when laden with NPs, droplets exhibit the phenomenon of spherical shell formation that eventually buckles (Figure 2). Such buckling morphologies have been extensively studied and characterized by many researchers.28−31 However, paired nanocolloidal droplets exhibit even more interesting dynamics that combine the effects of paired pure water droplets and the particle agglomeration (shell formation) dynamics of NPs, which leads to the formation of spectacular final precipitates. In this paper, we report the internal flow, particle deposition rate and pattern, agglomeration kinetics, and the evolution of buckling front in such paired droplets in detail (section 2.3). In addition, we provide a detailed analysis of the effects of NP concentration and the types of substrates (strongly pinned versus weakly pinned) on the drying of paired droplets (section 3). 2.1. Evaporation of Single and Paired Water Droplets. Isolated sessile droplets (deionized water) on hydrophobic substrates vaporize symmetrically either by uniformly receding its CCA or CCR or sometimes both (mixed mode) (Figure 1a). In contrast to this, when a second identical droplet is brought in its vicinity (L0/D0 ≈ 1.2, where L0 is the initial center-to-center distance between the droplets and D0 is the initial droplet diameter), the evaporation dynamics is significantly altered. For instance, the paired droplets show significant asymmetry in the contact angle (δθ = θR − θL > 8°), resulting in deformed shape, and suffer an inhomogeneous contact line slip. For droplet separation (L0/D0) between ∼1.2 and ∼2, the water vapor in region 1 tends to accumulate and raise the ambient partial pressure (Figure 1a). As a result, the evaporation flux, J ∝ (CS − C∞) (where CS is the saturated vapor concentration and C∞ is the ambient vapor concentration), is drastically lowered as C∞ → CS. However, the free side of the droplet (left side of the left droplet in the pair; Figure 1b) is not subjected to any geometric constraints and consequently exhibit a normal evaporation flux as in a single droplet. The evaporation therefore is asymmetrically suppressed in one sector of the droplet compared with that in the other parts. This suppression is sustained until the

Pcap =

μJδ k

(2)

where μ is the fluid viscosity, J is the evaporation flux, δ is the shell thickness, and k is the permeability of the porous shell. According to thin-shell theory, the shell buckles when Pcap

( R 2 α ≈ 10( δ )

exceeds the critical buckling pressure Pcr ≈ the Young’s modulus and

b

10Y α

),

33

where Y is

is the Foppl−von

Karman number (Rb is the droplet radius at the onset of buckling). The shell is stretched because of the growth of the buckling-induced PC, ultimately leading to rupture. Rupturing of the shell results in the formation of a DC as air invades into the ruptured hole as per the invasion−percolation theory.34 Buckling in a single droplet is observed the most from the apex region of the droplet [scanning electron microscopy (SEM) image; Figure 2c] as explained previously by Bansal et al.28 However, it is to be noted that an NP-laden droplet buckles only if φi < φm, where φi and φm are the initial and minimum threshold PLRs, respectively, as explained by Basu et al.35 Upon understanding the evaporation dynamics of paired pure water droplets and a single nanocolloidal droplet, it is imperative to conduct a study that combines the effect of both, as stated earlier. The experimental details including measurement methodology can be found in the Experimental Section. 2.3. Global Dynamics of Paired Nanocolloidal Droplets. We adopt the framework of paired droplets in which NPs are dispersed. It is observed that the effect of the second drop is 10336

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Figure 3. Droplet flow field vectors (from μPIV results) and shell growth. (a) Single droplets: nonuniform but symmetric evaporation flux (J) leads to the double-toroidal flow pattern. Average flow velocity gradually decreases because of the increasing viscosity caused by solvent evaporation. The shell grows from the base to the apex where the weak spot is developed. (b) Paired droplets: nonuniform and asymmetrical evaporation flux leads to the single-toroid flow and henceforth the weak spot is shifted toward the suppressed evaporation region where the shell growth is delayed. The flow velocities decrease similar to a single droplet. (c) Formation of an inclined base before shell growth: inclination is due to the preferential particle transport away from the suppressed evaporation region. (d) SEM image of the meridional cut section of the final residue, with shell thicknesses shown along AA′ (a single droplet). (e) SEM image of the horizontal cut section BB′ taken toward the base, showing the differential shell thickness and the weak spot susceptible to buckling. Here, the left drop from the paired droplets in Figure 1b is taken into consideration (Movies S2 and S3). Flow fields correspond to two-thirds of the droplet height from the bottom.

toroidal patterns from side-view imaging (Figure 3a and Movie S2). However, for paired droplets, locally suppressed evaporation results in a nonuniform and asymmetric evaporation flux as shown in Figure 3b. This results in a flow that is predominantly unidirectional (directed toward the region of higher evaporation flux; Movie S2), similar to that reported by Pradhan and Panigrahi.37 In essence, the double-toroidal flow decays rapidly, resulting in a single-toroid flow field as illustrated in Figure 3b. To measure this flow field quantitatively, the μPIV technique (see Experimental Section) was used (Movie S3). The time sequence images were processed to obtain the corresponding velocity vector fields. Velocity vector maps at different time instances are shown in Figure 3. For a single droplet, the average velocity is ∼8 μm s−1 (t/te ≈ 0), which is in agreement with the previous findings, with an accuracy of ∼±15%.36 For paired droplets, the average velocity scales to ∼15 μm s−1. With evolution of time, the solvent evaporates and the droplet shrinks in volume. As vapors around the droplet are relaxed, evaporation resumes from the suppressed zone (Figure 1b). This results in a change in the internal flow from being unidirectional to symmetrically divergent (similar to a single droplet). However, by this time, the particles have begun to agglomerate and there is an increase in the instantaneous PLR, thereby increasing the nanofluid viscosity. Hence, the flow velocity reduces to ∼1−3 μm s−1 for both single and paired droplets at t/te ≈ 0.75. For paired droplets, the double-toroidal flow is reinitiated (at t/te ≈ 0.75) with relaxation of the suppressed evaporation region 1 (Figure 1b; k approaches 1).

more pronounced for the NP-laden droplets. Degree of asymmetry, contact line dynamics, and buckling morphologies are distinctly altered. For weakly pinned paired droplets on substrate S1, the contact angle asymmetry (δθ = θR − θL; Figure 2b) increases to ∼15° as compared with ∼8° for pure water. Similarly, for strongly pinned droplets on S2, the asymmetry is as high as ∼20° (which is ∼14° for pure water). However, the extent of pinning is different at different locations on the drop. Near the second drop (where evaporation is suppressed), the contact edge is loosely held because of the relative absence of particles (because of the directional flow as will be explained later), leading to a distinct inhomogeneous slip (Figure 2b). In the course of evaporation, the particles form a shell about the drop periphery. Here, unlike its single-droplet counterpart wherein buckling of the shell is preferentially from the apex, a paired droplet buckles facing each other (Figure 2c and Movie S1). To represent this angular shift in buckling location, the buckling angle ψb is defined as shown in Figure 2c. For paired droplets, ψb is always found to be greater than 0°. Following buckling, the DC propagates along the same angular direction, as seen in Figure 2b and from the SEM image of the final residue (Figure 2d). Because there exists a minimum PLR at which buckling occurs (varies with the substrate; section 3.3), the present study is limited to minimum concentrations of 5 wt % (on S1) and 10 wt % (on S2). 2.3.1. Internal Flow and NP Deposition. The flow inside of a sessile droplet is governed by the evaporation behavior around the drop periphery. On a hydrophobic substrate, a spatially nonuniform but symmetric evaporation flux results in a symmetrical buoyancy-driven flow,36 observed as double10337

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Figure 4. Particle transport (left droplet from Figure 1b is considered) as a result of the suppressed evaporation generates a concentration gradient across the periphery. Continuous single-toroid flow field causes particle agglomeration and shell formation, whereas concentration gradient causes diffusion of NPs. Left inset shows the SEM micrograph of particle packing in the final precipitate. Right inset depicts evaporation through the nanomenisci of the viscoelastic shell.

The flow pattern and its magnitude greatly affect the particle deposition and further agglomeration occurring at the nanoscale [as particle size ∼O (10−9) m]. Unlike in a single NP-laden droplet, the development of the shell in paired droplets is spatially asymmetric as illustrated in Figure 3b. Because of the single-toroid flow (from 0 < t/te < 0.6) with a relatively higher flow velocity (vavg ≈ 15 μm s−1), preferential particle transport and subsequent deposition occur at the base toward the free edge of the drop where the evaporation is relatively higher. As seen in Figure 3c, this leads to the formation of an inclined deposit near the base. In the aftermath of base formation, the shell begins to form around the droplet periphery. However, the paired droplets have not undergone sufficient relaxation in the vapor wedge enclosed by the two drops (t/te < 0.5). As a result, the shell is first initiated from the free evaporation region of the drop and continues to grow toward the apex. The shell formation near the suppressed edge (near the second drop) is delayed till the relaxation of the entrapped vapor zone (region 1; Figure 1b; L0/D → 2, and k approaches 1). This differential shell growth results in spatially inhomogeneous shell thickness. The weakest spot (of minimum shell thickness) favorable for buckling is displaced from the apex (as in the single nanocolloidal droplet) to an angular zone (ψb > 0), that is, toward the suppressed edge. This is verified from the SEM images shown in Figure 3d. AA′ and BB′ in the SEM images correspond to the sections on single and paired droplets, respectively. The shell thickness varies in the micrometer range, δ but the average relative shell thicknesses are δ11 ≈ 1 (at AA′; a

(Figure 4). The difference (NH − NL) is the rate of particle deposition per flow cycle that ultimately contributes to the base and shell formation. The preferential particle accumulation is supposed to lead to a concentration gradient across the left and right lobes of the droplet. This difference, denoted by (NH − NL), is, however, possible only if the particle agglomeration process is sufficiently fast and comparable to the residence timescale. Details of the particle agglomeration mechanism and the diffusion process are explained next. The process of agglomeration is mainly governed by perikinetic and orthokinetic mechanisms. Perikinetic agglomeration takes into consideration the collision-induced particle agglomeration resulting from the Brownian motion, whereas orthokinetic agglomeration takes into consideration the collision of particles resulting from the shear flow inside of the fluid domain. Smoluchowski derived the expression for the rate of perikinetic agglomeration at any time t by considering a diffusive flux of particles as38 Jperi = −

single droplet) and

(3)

where N is the particle concentration (number of particles per unit volume) at time t, k is the the Boltzmann’s constant, μ is the dynamic viscosity, and T is the temperature. Using eq 3, the time scale of perikinetic agglomeration is defined as

τperi =

12

δ21 δ22

dN 8kTN 2 = dt 3μ

≈ 0.2 (at BB′; paired droplets). Note

3μ 8kTN

(4)

For a pair of droplets at t = 0 and considering the initial concentration as N ≈ 3.6 × 1022 numbers/m3 (40 wt %), the perikinetic agglomeration time scale τperi is ∼2.3 × 10−6 s. Similarly, the rate of orthokinetic agglomeration at any time t (by considering the collision of particles moving in different streamlines) can be calculated using

that the deviation in the measurements of shell thickness is limited to ∼5%−6%. This comprehensively suggests why buckling occurs at B′ (at a nonzero buckling angle) rather than the apex. This further supports our argument about nonuniform shell growth, where particle deposition is primarily governed by the inherent flow pattern. 2.3.2. Agglomeration Kinetics. For a pair of nanocolloidal droplets, during the initial phase of evaporation, the average velocity magnitude (vavg) as stated earlier corresponds to ∼15 μm s−1 and the length scale of fluid flow is approximately equal to the diameter of the droplet (D ≈ 1500 μm). The residence time scale of a cluster of particles during one cycle of the single⎛ D ⎞ toroid flow ⎜τflow = V ⎟ corresponds to ∼1.0 × 102 s. At any ⎝ avg ⎠ time instant (t), the number of particles transported in the first half-cycle of the toroid motion (NH: from the suppressed evaporation edge to free evaporation edge) is expected to be greater than in the second half-cycle of the toroid motion (NL)

Jortho = −

4γḋ 3N 2 dN = dt 3

(5)

where γ̇ is the velocity gradient and d is the particle diameter. The time scale of orthokinetic agglomeration at any time t can be defined as τortho =

3 4γḋ 3N

(6)

Similarly, substituting N ≈ 3.6 × 10 numbers/m , the orthokinetic agglomeration time scale at t = 0 is obtained as τortho ≈ 196 s. It is important to note that the orthokinetic agglomeration and particle transport time scales are of the same 22

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global phenomenology remains unaltered, there are local variations such as the degree of contact angle asymmetry, extent of contact line pinning (mode of evaporation), and variation in the buckling angle (ψb) across differently pinned droplets with varied particle loading. These variations are explained in detail (Figures 5−7) in the following sections.

order [O (2)]. This in turn proves that the deposition rate of particles during the half flow cycle is sufficient to cause preferential accumulation near the free edge of the droplet compared with the suppressed side. In addition, enhanced vaporization [diffusion-based evaporation time scale ∼O (10−1) s] near the free edge also contributes to rapid accumulation of particles as compared with that of the evaporation suppressed zone. The flow-induced differential particle accumulation pattern is represented in Figure 4. One would normally expect diffusion of NPs from a high concentration zone to a low concentration zone to relax this gradient. The time scale of such particle D2

diffusion is defined as τDiff = L , where D is the characteristic length scale of diffusion and L is the diffusion coefficient given kT by the Stoke−Einstein equation, L = 3πμd (where k is the

Boltzmann’s constant, μ is the dynamic viscosity, d is the particle diameter, and T is the temperature). During the initial phase of evaporation, the value of τDiff is ∼1.16 × 105 s. Hence, the ratio τDiff ≈ 700 ≫ 1 signifies that the diffusion processes cannot τ flow

relax this ever-increasing concentration gradient. Also, the ratio τDiff ≈ 77 ≫ 1 signifies that the evaporation process is fast t

Figure 5. Evolution of nondimensional contact angle asymmetry with nondimensional time (te is the corresponding droplet evaporation duration) through suppressed evaporation (Phase I), relaxation (Phase II), and buckling (Phase III). (a) The weakly pinned droplet on substrate S1 demonstrates lower contact angle asymmetry (∼15°) and complete recovery before the onset of buckling. (b) The strongly pinned droplet on S2 demonstrates higher contact angle asymmetry (∼20°), and permanent asymmetry is sustained because of shorter Phase II. In both cases, suppressed evaporation (shaded gray) is relaxed (shaded white) before buckling (shaded blue). Plots are provided for pure deionized water (0 wt %) and two levels of PLR (5 or 10 and 30 wt %).

e

enough (compared to diffusion) for shell formation and subsequent buckling. 2.3.3. Buckling Dynamics in Paired Nanocolloidal Droplets. Prevailing theories in particle transport (evaporation-driven flow), particle agglomeration (orthokinetic and perikinetic), and buckling dynamics (thin-shell theory) are in good agreement with the present observations, as explained through the preceding sections. Thus, placing a second droplet does not completely alter the buckling dynamics or the occurrence of buckling. However, to adapt to the disparities in the system due to suppressed evaporation flux, the droplet undergoes spatiotemporal variations in flow and the consequent particle deposition. This results in a reorientation of the weak spot on the drop, and hence the final residues (a single droplet, Figure 2c vs paired droplets, Figure 2d) look very different. A plausible reason for unaltered buckling dynamics is the return of the paired droplets to the single droplets during the later stages of evaporation (when L0/D → 2). This is explained as follows: Evaporation from the nanomenisci (Figure 4) of the viscoelastic shell develops a capillary pressure (Pcap) responsible for buckling as given by eq 2. It is clear that the capillary pressure depends on the evaporation flux given by Pcap ∝ J. Therefore, if evaporation is continued to be suppressed, that is, J is sufficiently lowered for a long period, then the required Pcap necessary for overcoming the critical buckling pressure (Pcr) may never be attained during the droplet lifetime. Evaporation will eventually dry out the solvent to agglomerate the solid. However, in the present system of paired droplets, the evaporation flux is dynamically relaxed and the buckling is not inhibited as t/te → 0.6, L0/D → 2, and k → 1. Nevertheless, shell formation and buckling are delayed in paired droplets because of slow evaporation.

3.1. Contact Angle Asymmetry. As explained earlier, suppression of evaporation leads to contact angle asymmetry. Figure 5 shows the temporal variation in the contact angle asymmetry (δθ = θR − θL; Figure 2b) for different substrates and PLRs. The degree of asymmetry is enhanced as we increase the PLR from 0 to 30 wt %. This is because during asymmetric evaporation, differential particle agglomeration results in a tilted dome structure. Although the suppressed evaporation zone gradually relaxes, the rigidity of the dome helps the droplet to maintain its tilted geometry. At 30 wt %, the asymmetry in the contact angle is ∼1.4−2 times that of pure water. However, for a low PLR ( 0.75), the shell is completely developed and no further slip is possible irrespective of the substrate and the PLR (CCR mode; both S1 and S2). Another interesting corollary is the decreased value of total slip% or enhanced CCR mode with the increase in the PLR (Table 1). This suggests that for the same substrate (S1 or S2), the droplet separation or evaporation relaxation (k → 1) is delayed with increased PLR (also shown in Figure 5a,b).

4. CONCLUSIONS In the foregoing sections, we will undertake a methodical study to analyze the effect of paired nanocolloidal drops placed on a hydrophobic substrate. The results suggest major variation in the morphology of the final residue because of sidewise buckling or angular buckling, that is, ψb > 0. Also, the dynamic behavior of the contact line slip and the contact angle asymmetry is locally altered. Local mode of evaporation with variations in slip as large as 25% (in the same drop) is an observation of its kind in sessiledroplet studies. Furthermore, for paired droplets, the longevity of the suppressed evaporation determines the buckling and nonbuckling conditions. If vapor relaxation is delayed, the critical pressure for buckling may never be achieved and hence buckling is subdued. Late relaxation of vapors can also induce permanent asymmetry as observed for a strongly pinned droplet on a GDL substrate (S2). In other words, it is hitherto important to understand the mechanism of these variations and design a controlled assembly of droplet systems. An example of such applications is shown in Figure 8, where the smaller

Table 1. Comparison of Total Slip% for Single and Paired Nanocolloidal Droplets across Different PLRs PDMS (S1)

GDL (S2)

Φ (wt %)

5

30

10

30

single droplets paired droplets

21 19.5

16.24 14.5

6.82 5.97

4.81 4.5

3.3. Variation in the Buckling Angle (ψb) and the Critical Buckling Concentration (ϕm). In section 2.3, we explained the universal phenomenon of sidewise buckling (ψb > 0) observed for all paired droplets placed at L0/D ≤ 1.2. We also observed the effect of concentration and substrate on variations in contact angle asymmetry (Figure 5), mode of evaporation (Figure 6), and total slip (Table 1). These delicate dissimilarities affect the exact location of the weak spot, and hence ψb is sensitive to PLR and the droplet-pinning characteristics. Table 1 suggests that with increased PLR, CCR mode is enhanced. The increased CCR mode delays the droplet separation (L0/D → 2−2.5) and subsequent vapor relaxation (k → 1). Thus, shell formation in the suppressed evaporation zone is stifled for a longer duration. From Figure 5, it is confirmed that the relaxation phase (Phase II) indeed decreases with an increase in the PLR for all substrates examined here. As a result, the weak spot (of minimum shell thickness) is developed closer toward the suppressed edge (toward the second drop; Figure 7a), that is, ψb increases as shown in Figure 7b (ψb ≈ 40°−50° for 30 wt %). Although the trend of ψb vs ϕ (increasing function) is consistent for both strongly pinned and weakly pinned droplets, there is a downward shift in the graph with the increased pinning of the droplet’s contact line (Figure 7b). This is because as the droplet is pinned to the substrate (S2) for a considerable duration (∼60% of its lifetime), the base continuously builds up and the average base height increases. However, for a relatively moving contact line (S1), the average base height (for S1) is nearly half of that of S2 (illustrated in Figure 7a). The dome is formed over the base, and inevitably, the taller base on S2 would result in a lower value of buckling angle when compared with identical particle loading on S1. Figure 7c shows the necessary condition required for buckling, that is, aspect ratio (hb/Rb, where hb and Rb are the droplet height and radius at the buckling onset, respectively) should be greater than 1 for any substrate as also explained by Basu et al.35 This is due to the loss of the dome-shaped structure below a critical initial PLR (ϕm), resulting in the formation of a disk-shaped final precipitate. Hence, buckling is observed only for ϕi > ϕm, and ϕm varies across substrates (5 wt % for S1 and 10 wt % for S2). Because of the stick−slip behavior on S1, the dome can be maintained for concentrations as low as ∼5 wt %. On the other hand, for S2, buckling is inhibited at concentrations below 10 wt %. However, there is a marginal increase in ϕm (3 to 5 wt % on S1) for paired droplets when

Figure 8. One-dimensional arrangement of interacting nanocolloidal droplets (30 wt %) of different sizes at different pitches placed on a hydrophobic substrate (S2). Final precipitates show that small droplets buckle facing the bigger ones. Small discrepancies in pitch are due to the time lag in deploying five droplets of different volumes one after another.

droplets in a linear array buckle facing the larger droplets. This is evident from the fact that the larger droplet has a greater field of influence (vapor-suppressed zone) and hence more dominant in the vapor-mediated interactions. It can also be extended to a complex droplet patterning wherein evaporation is suppressed at multiple sites at different levels (depending on the droplet-todroplet separation), enabling custom tailoring of the final precipitates. The present study can provide important information to researchers in surface patterning and colloidaldroplet studies. 10341

DOI: 10.1021/acs.langmuir.6b03024 Langmuir 2016, 32, 10334−10343

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first window size of 64 × 64 pixels, the second window of 32 × 32 pixels, and a 50% overlap between the two windows. The instantaneous vector fields thus obtained were temporally averaged to obtain the average flow field vectors as shown in Figure 3.

5. EXPERIMENTAL SECTION 5.1. Solution and Substrate Preparation. Nanosilica particles (LUDOX TM40 from Sigma-Aldrich, U.S.) of average particle diameter 25 ± 2 nm were dispersed in deionized water by sonication using an ultrasonicator (Trans-O-sonic, Mumbai, India). Solutions were diluted to different concentrations (5 to 30 wt %) under ambient conditions of temperature (25 °C) and relative humidity (45%). PDMS substrates were prepared from the PDMS Sylgard 184 solution (Dow Corning, Wiesbaden, Germany). The solution was spincoated on glass slides precleaned in a sonication bath using the 2propanol solution. PDMS substrates are hydrophobic with an apparent static contact angle of ∼115° and a contact angle hysteresis (CAH) of ∼8°. GDL substrates, with a static contact angle of ∼125° and a CAH of ∼14°, were obtained from Sainergy Fuel cell Inc. The average surface roughness for PDMS and GDL substrates were measured as 40 nm and 12 μm, respectively, using atomic force microscopy. 5.2. Experimental Setup. A contact angle measuring instrument (Holmarc, India) attached to an adjustable XY traverse platform coupled with the horizontal Vernier scale (least count of 50 μm) was used for all experiments. The setup was enclosed to prevent convection effects (Figure S1). Ambient conditions were maintained at 25 °C and 45% RH. Nanocolloidal droplets (from the prepared solutions) of 3 μL volume were deployed on the substrates (PDMS or GDL) using a syringe pump (Holmarc). The flow rate was maintained at 70 μL/min. After deployment of the first droplet, the injection system was translated by the droplet separation distance (or pitch) L0. Then, the second droplet was deployed with an uncertainty in pitch less than 10%. The time delay between consecutive drops was nearly 10 ± 2 s (very small when compared with the total lifetime of the droplets of ∼22 min). For larger time intervals (above 20 s), the droplets became uneven in size. 5.3. Imaging and Postprocessing. Two different kinds of images were taken with back light illumination (shadowgraphs) and front light illumination (clear view). For shadowgraphs, side-view images were acquired at 3 fps using an NR3S1 (IDT vision) fitted to a Navitar 4.5× zoom lens (spatial resolution, 2.8 microns/pixel). The droplet was illuminated with a back light arrangement (cold light source) as shown in Figure S1. The acquired images were processed using inbuilt MATLAB codes and ImageJ software. To capture the buckling front and the cavity propagation, images were taken using Nikon D7200 fitted to the same Navitar zoom lens. Front light illumination and reflectors were placed as shown in Figure S1. A video is provided in Movie S1. 5.4. Flow Visualization. We perform two different kinds of flow visualization: side view using a continuous thin laser sheet and bottom view using a pulsating laser. In both cases, a 40 wt % nanocolloidal droplet is seeded with 0.008 vol % solution of rhodamine-coated polystyrene particles (Thermo Fisher Scientific, average particle diameter of 1 μm). For sidewise visualization as seen in Movie S2, a thin laser sheet (175 micron thickness) was created using a cobalt− samba laser (wavelength, 532 nm) with a spherical lens assembly (see Figure S2). The laser sheet was passed through the meridional plane of the droplet, and side-view images were acquired at 50 fps using the NR3S1 camera fitted to the same Navitar zoom lens. To quantify the flow field, μPIV techniques were performed on the bottom view images (Movie S3) recorded using an Imager Intense (Lavision) camera fitted on a Flowmaster Mitas microscope (Figure S3). An Nd:Yag laser (NanoPIV Litron Laser) was used for illumination. Images were acquired at 5 fps through a 5× objective lens having a field of view (FOV) of 1200 × 900 μm and depth of view of 28 μm. The plane of imaging was kept at two-thirds of the droplet height taken from the bottom. Because of particle jamming, focusing was difficult near the base. One thousand images were acquired for each runat the beginning (t/te ≈ 0), intermediate (t/te ≈ 0.5), and final (t/ te ≈ 0.75) stages. All images were first preprocessed by applying background subtraction and a 3 × 3 Gaussian filter, and then subjected to time series PIV analysis that involved cross-correlation of consecutive image pairs. We used multipass postprocessing with the

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b03024. Experimental setup (PDF) Buckling in paired NP-laden droplets taken from top view (AVI) Flow transitions (double to single toroid) taken from side view (AVI) Bottom view microscopic imaging of single and paired droplets (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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