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Article Cite This: J. Phys. Chem. C 2018, 122, 2231−2237

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Controlling Nanodrop Passage through Capillary Nanovalves by Adjusting Lyophilic Crevice Structure Yu-Hsuan Weng,† Yu-En Liang,† Yu-Jane Sheng,*,† and Heng-Kwong Tsao*,‡,§ †

Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617 Department of Chemical and Materials Engineering and §Department of Physics, National Central University, Jhongli, Taiwan 32001

‡

ABSTRACT: The passage or blockage of nanodrops through a nanovalve made of a nanocrevice is explored by proof-of-concept simulations, including many-body dissipative particle dynamics and Surface Evolver simulations. Although it is generally believed that the drops wet lyophilic crevices readily, we show that the penetration of the drops into such crevices with specific structures can be prevented. The morphological phase diagram in terms of the contact angle (θY) and wedge angle (α) are constructed, and three regimes are identified: non-penetration and partial penetration, in addition to complete penetration. It is interesting to find that as long as α is small enough, the drop always runs away from the crevice even on lyophilic surfaces, leading to the non-penetration state. For intermediate α and small θY, the drop tends to break up, and only a portion of liquid wets the crevice, corresponding to the partial penetration state. Our simulation results demonstrate that a lyophilic capillary nanovalve for controlling the droplet passage can be fabricated by simply adjusting the wedge angle of the crevice.

1. INTRODUCTION Wetting phenomena exist everywhere in nature and in diverse applications, such as microfluidics, coating, and cleaning.1−3 The wettability of a surface by a drop is frequently expressed through the contact angle (CA) spanning between liquid/gas and solid/liquid interfaces. The intrinsic CA (θY) on a perfectly smooth surface relies on the chemical composition and is depicted by Young’s equation,4 cosθY = (γSG − γSL)/γLG. Here γij denotes the interfacial tension between the i and j phases, and the subscripts G, L, and S represents gas, liquid, and solid, respectively. The surface is lyophilic if θY < 90° and lyophobic if θY > 90°. For water, lyophilicity corresponds to hydrophilicity. In addition to the chemical composition, surface roughness comes into play and affects the wetting behavior seriously on real surfaces. Whether surface roughness can be wetted or not plays a key role in the wetting phenomena. Surface roughness contains grooves or crevices that are generally believed to be penetrated by liquid for lyophilic surfaces (θY < 90°) but are able to resist liquid impregnation for lyophobic surfaces (θY > 90°). Generally, the apparent contact angle of a drop on a rough surface depends on whether the groove is impregnated with liquid. For the wetted grooves, Wenzel5 generalized Young’s equation to acquire the apparent contact angle (θa), cosθa = r cos θY, where r is the area ratio of the actually wetted surface to the projected surface (r ≥ 1). As a result, surface roughness leads to the increase of lyophilicity for θY < 90° but enhances lyophobicity for θY > 90°. On the contrary, for non-wetted grooves, θa can be calculated by the Cassie−Baxter (C−B) theory,6 cosθa = f cosθY + (1 − © 2018 American Chemical Society

f)cos(180°), where f denotes the area fraction of the surface in contact with liquid (f < 1). The non-wetted grooves are considered as air pockets and thus yield an effective solid− liquid interface with θY = 180°. It has been shown theoretically that for particular groove structures, the C−B state can appear at a hydrophilic (lyophilic) surface.7 Depending on the initial conditions, the hydrophilic roughness can be non-wetted or wetted if there exists two stable states separated by an energy barrier (Wenzel and C−B) along the imbibition process. In fact, superomniphobicity was acquired from surface roughness alone irrespective of the material’s intrinsic wettability. For example, perfluorohexane with very low surface tension is prevented from wetting a silica surface made of a square array of circular posts with a specific doubly re-entrant microstructure. The solid−liquid contact fraction is very low (high liquid−air contact fraction) and renders the surface super-repellent.8 Recently, simulations also show that it is possible to fabricate lyophilic nanogrooves that can prevent impregnation. When the lyophilic surface within the cavity possesses simple patterned roughness such as shallow pits or straight trenches, liquid impregnation can be resisted until the intrinsic contact angle is lower than a critical value.9 The aforementioned studies reveal that the penetration of liquid drops into a lyophilic crevice Received: November 26, 2017 Revised: January 2, 2018 Published: January 4, 2018 2231

DOI: 10.1021/acs.jpcc.7b11624 J. Phys. Chem. C 2018, 122, 2231−2237

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The Journal of Physical Chemistry C Table 1. Dependence of the Contact Angle θY on the Attractive Parameter (−aSL) (−aSL)

15

21

23

24

28

30

35

37

39

40

θY

140°

122°

113°

108°

92°

85°

63°

46°

27°

15°

FijC = aijωa(rij)eij + bij(ρi + ρj )ωb(rij)eij

maybe be impeded if the structure of the crevice is properly designed. Valving becomes essential in order to broaden the potentiality of the fluidic microsystems. For example, miniature chemical analysis systems require injection and localization.10 These two essential functions can be achieved by employing a series of valves that control the quantity and microflow of the sample. On the basis of different physical principles, various types of valves exist, such as piezoelectric membrane actuation and magnetic plugs.11−13 They often involve challenges such as moving parts, external actuation, and implementation.10 Therefore, a simpler valving device is highly desirable. A capillary valve is constructed by a sudden enlargement of the flow channel. It is “passive”, because it does not require another energy source other than that for pumping fluid flow.14 Its principle is simple and based on the edge effect. That is, the interface of the incoming fluid is pinned on geometrical edge of the orifice unless the driving pressure exceeds a critical value (valving pressure).15 Intuitively, a nanodrop is allowed to wet the lyophilic nanocrevice, leading to the passage, but the nanodrop is resisted by the lyophobic nanocrevice. When only the lyophilic material is available, one has to design a crevice structure so that the penetration of the drop into the crevice can be prevented. If this can be achieved, the lyophilic crevice functions like a capillary nanovalve, and the passage of the drop is allowed only when the driving force exceeds a critical value.16−19 Since it is difficult to alter the surface wettability of a nanodrop on the nanocrevice, the development of a valve whose structure can be easily adjusted to modify the effective wettability is desirable as well. To explore the function of the capillary nanovalve for the drop passage, the interactions of a nanodrop characterized by the contact angle (θY) and a nanocrevice characterized by the wedge angle (α) are investigated by many-body dissipative particle dynamics (MDPD) and Surface Evolver (SE) simulations. The main goal is to control the passage of the nanodrop by tuning the wedge angle of the capillary valve, even when the valve is lyophilic (i.e., θY < 90°).

(1)

The weight function of attraction is ωa(rij) = 1 − rij/ra, while that of repulsion is ωb(rij) = 1 − rij/rb. Here rij = |rij| represents the distance between the two particles, and eij = rij/rij is a unit vector to depict the force direction. Both weight functions vary with rij and decline to 0 as rij ≥ ra for ωa and as rij ≥ rb for ωb. In our simulations, the cutoff distances of the attractive and repulsive forces are chosen as ra = 1.0 and rb = 0.75 to ensure a stable liquid−vapor interface.25−28 The strengths of attractive and repulsive forces between beads i and j are specified by the parameters aij < 0 and bij > 0, respectively. Note that the magnitude of the repulsion depends on the average local density ρi at the position of the bead i, which is determined by ρi =

∑ k≠i

2 rik ⎞ 15 ⎛ − 1 ⎜ ⎟ , if rik < rb ; 0, if rik > rb rb ⎠ 2πrb3 ⎝

(2)

The dimensionless forms are used in our simulations, and all the units are scaled by particle mass m, cutoff radius ra, and thermal energy kBT. The interaction parameters aij and bij are generally set as −40 and 25, respectively. To acquire various surface wettabilities, −aSL between solid and liquid beads is altered from 15 to 40. The relationship between the contact angle (θY) and attractive parameter (−aSL) is listed in Table 1. The number densities of liquid beads in the drop and solid beads in the substrates are 6 and 8, respectively. In our simulation system, the total number of fluid beads is 30 000, and the drop volume V is about 5000. For each simulation, at least 105 steps are run for equilibration. By the calculation of the pressure tensor, the interfacial tensions are estimated according to the Irving−Kirkwood expression.29−31 The liquid−gas interfacial tension is determined as γLG = 7.5 from the simulation of the system containing a stripe of a liquid film. 2.2. Surface Evolver (SE) Simulation. SE is a public domain software based on the finite element method.32,33 The algorithm of SE is to minimize the surface energy of the system subject to some constraints. The solid/liquid and liquid/gas interfaces are built by unions of triangles with vertices. The total free energy of our system Et is simply

2. SIMULATION METHODS 2.1. Many-Body Dissipative Particle Dynamics (MDPD) Simulation. MDPD is a modified version of the standard DPD, which is a coarse-grained particle-based approach and can be used to simulate the vapor/liquid system. On the basis of the momentum conservation, both hydrodynamics and contact line movement are taken into account simultaneously. MDPD allows simulations to be performed for wider length scales and longer time scales, compared to atomistic molecular dynamics.20−24 The three interparticle forces inherited in the DPD scheme are employed. Although the dissipation force (FDij ) and random force (FRij ) remain the same as those in DPD, the conservative force (FCij ) consists of both attractive and repulsive terms in order to acquire the liquid−vapor interface. In MDPD, both repulsive and attractive forces are linear and soft

Et = γLGALG + (γSL − γSG)ASL

(3)

where ALG is the area of the liquid−gas interface, and ASL the area of the solid−liquid interface. According to Young’s equation, the second term on the right-hand side of eq 3 becomes − γLGcosθYASL, denoting the contribution of the solid−liquid interface. In our SE simulations, all lengths are nondimensionalized by the size of the DPD bead (ra) and the free energy by γLGr2a. The system evolves gradually toward thermodynamic equilibrium. During the iterative process, the drop volume remains unchanged, and the vertices of the contact line are kept at the three-phase boundary. SE was performed to construct the phase diagram, the drop morphology as a function of the wedge angle α, and Young’s contact angle θY. For comparisons, the parameters and input conditions are in the same range as those employed in MDPD. Note that SE can provide only the final equilibrium outcome of 2232

DOI: 10.1021/acs.jpcc.7b11624 J. Phys. Chem. C 2018, 122, 2231−2237

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compared to the drop diameter (D ≈ 21) and is thus considered as infinity. For simplicity, the crevice structure is denoted by the wedge angle α = tan−1(2h/(lb − l)) for lb ≥ l. As lb < l, one has α > 90°, and the maximum value of α considered is α* = 90° + tan−1(l/2h). Obviously, the influence of the crevice structure on the penetration can be elucidated by varying α (lb) at a specified contact angle. In contrast, such an effect can also be demonstrated by varying θY at a given wedge angle. That is, as θY is altered from low to high wettability, the purpose is to find the critical value of θY associated with the transition from penetration to non-penetration, θcY(α). Note that the wetting behavior depends on α significantly but is insensitive to D/l as long as the length ratio exceeds unity significantly. First, consider the penetration into the crevice with the trapezoid structure with α ≥ 90°. The gap width is always kept the same, l = 8. As demonstrated in Figure 2, it is relatively easy to wet such crevices. For example, for surfaces with θY ≤ 92° and α ≤ 101°, the drop penetrates the crevice completely as shown in the top and side views at the bottom of Figure 2a,b. However, for the surface with θY = 92°, when α increases to 114°, the drop only partially penetrates the crevice (see the bottom of Figure 2c). When the surface has lower wettability, θY = 108°, the deposited drop can still reach the bottom of the crevice (partial penetration). However, the shape of the drop varies with the wedge angle, as can be seen from the third row of Figure 2. At θY = 113° (the second row of Figure 2), the crevices with α ≈ 101 and 114° are partially penetrated. The crevice with α = 90° represents non-penetration (drifting away). That is, the droplet stands on the crevice for a while and escapes eventually. It is driven by the random motion of the droplet on the smooth surface because of thermal fluctuations and the lack of contact line pinning associated with contact angle hysteresis.26,27 When the surface wettability is further reduced to θY = 122° (the first row of Figure 2), the crevices with α ≥ 101° are partially penetrated. However, the drop cannot reach the bottom and is trapped by the crevice (trapping), as revealed by the side views. For very lyophobic surfaces (θY = 140°), the crevice is no longer wettable, and the droplet always drifts away for all the α studied (not shown).

the system, while the dynamic process can be captured by MDPD.

3. RESULTS AND DISCUSSION The encounter of a nanodrop with a crevice may have the following consequences: complete penetration, non-penetration, and partial penetration. The first term is defined as the state for all liquid going into the crevice, and the second term corresponds to the state of no liquid in the crevice. When only a part of the liquid drop stays in the crevice, it is called partial penetration. In addition to the surface wettability, whether the crevice is wetted by a drop placed atop the crevice depends strongly on the structure of the opening of the crevice. In this work, the interaction between a nanodrop and a crevice is explored by MDPD simulations for otherwise smooth surfaces. The phase diagram, which describes the outcome varying with surface wettability and crevice structure, is also obtained by SE simulations. Particular attention is paid to the non-penetration scenario of a nanodrop on a lyophilic crevice. 3.1. Nonwetting Behavior of Crevices with the Wedge Angle Exceeding 90°. Consider a nanodrop with the volume V placed atop a crevice with the gap width l, as shown in Figure 1. The surface is smooth, and the surface wettability is

Figure 1. Nanodrop with V = 5000 atop a crevice with the gap width l = 8 and lb = 38. The opening of the crevice is wedge-like, and the wedge angle is α ≈ 34° in this diagram.

expressed in terms of θY. The cross section of the crevice structure can be depicted as an isosceles trapezoid with the height h. The lengths of the upper and lower bases are l and lb, respectively. The length of the crevice (lc = 80) is large

Figure 2. Nanodrop with V = 5000 atop a lyophobic crevice with l = 8. The wedge angles are (a) α = 90°, (b) α ≈ 101°, and (c) α ≈ 114°. 2233

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Figure 3. Nanodrop with V = 5000 atop a lyophilic crevice with the gap width l = 8. The wedge angles are (a) α ≈ 34°, (b) α ≈ 45°, and (c) α ≈ 66°.

and reaches the bottom eventually, leading to liquid accumulation at the bottom corners. Distinctly different from the classical wetting behavior associated with lyophilic surfaces, non-penetration corresponding to the nonwettable valve consists of the scenarios of splitting apart and running away. In addition, partial penetration corresponding to the valve allowing partial passage of liquid drops involves breakup and trapping. Figure 4b

Evidently, three regimes can be identified: complete penetration, partial penetration, and non-penetration. 3.2. Nonwetting Behavior of Crevices with the Wedge Angle Less than 90°. Let us proceed to the penetration of the crevice with the trapezoid structure for α < 90° and l = 8. It is generally anticipated that a lyophilic crevice (θY < 90°) can be readily wetted by liquid drops, regardless of the crevice structure. Figure 3 shows the final outcome of a drop deposited in the center of the opening of the crevice at various wettabilities θY and wedge angles α. For α ≈ 66° (Figure 3c), the deposited drop with V = 5000 and θY ≥ 63° tends to wet the crevice upon contact. Nearly complete penetration is observed for θY = 46°, but a small amount of liquid (1%) is left on the surface. For even lower CAs, θY = 27°, more liquid residues (50%) are observed to stay on the surface, corresponding to partial penetration. According to top and side views, there are two residual drops located on both sides of the crevice and a pool of liquid sitting on the bottom of the crevice. It is interesting to find that in this case, as the wettability is increased (decreasing θY), the crossover from complete penetration to partial penetration takes place. For α ≤ 45° (Figures 3a,b), the deposited drop seems to be repelled by the crevice and starts to run away from the opening immediately upon contact for θY= 85°. Since the drop on the lyophilic surface possesses lower surface energy than that atop the crevice, the drop prefers to run away from the opening of the crevice. That is, the lyophilic crevice is able to resist the penetration of the drop by repelling it from the opening as the wedge angle is small enough. As the surface wettability is further increased (θY ≤ 63°), the crevice with α ≤ 45° is still able to resist the penetration by splitting the drop apart. The final morphology of the breakup drops with θY = 27° on the surface is demonstrated from the top and side views shown at the bottom of Figure 3a,b). The shapes of the two drops are like spherical caps, and the contact angle is about θY = 27°. Note that for small θY, a small amount of liquid goes into the crevice, and slight penetration is observed. When the wedge angle is as low as α ≈ 34°, less than 5% liquid penetrates into the crevice and hangs on the upper part of the slanted surfaces. However, for α ≈ 45°, about 10% liquid goes into the crevice

Figure 4. Dynamics of a nanodrop with V = 5000 deposited on a lyophilic crevice with l = 8. The wedge angles are α ≈ 45°, and the surface wettabilities are (a) θY = 46°, (b) θY = 63°, and θY = 85°.

illustrates the non-penetration dynamic process of splitting apart on the lyophilic crevice (θY = 63°). The drop is symmetrically in contact with both sides initially. After a while, it becomes asymmetric due to serious thermal fluctuations. Because of the Marangoni effect (interfacial tension gradient), it moves toward one side eventually, but the capillary force on the other side is able to grab a small portion of the liquid (∼1%), leading to the breakup of the drop. A number of independent runs have been performed. The mass ratio between the two split parts varies case by case due to thermal fluctuations, but its average value is about 1% in Figure 4b. Note that for more wettable crevices (e.g., θY = 46°), more liquid (∼14%) is captured by the other side, but an uneven partition still results, as illustrated in Figure 4a. However, as the crevice becomes less wettable (θY = 85°), the pinning force 2234

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criterion associated with the partial penetration state is rather stringent. The partially penetrated drop remains intact for large θY and α (upper right part of Figure 5) but experiences breakup for small θY and intermediate α (lower middle part of Figure 5). The wetting behavior generally changes from non-penetration to complete penetration, as the wedge angle (α) is large enough. In contrast, the wetting behavior may be altered from complete penetration to non-penetration, as the contact angle (θY) is large enough. The competition between those two trends results in the regime of partial penetration (intact). According to the morphology phase diagram, one is able to construct lyophilic nanocrevices that show liquid repellency by suitable structural design. The non-penetration state occurring on a lyophilic surface can be attributed to the energy barrier associated with penetration and the Marangoni flow. For the wedge angle less than 90°, the symmetric advance of the contact line into the crevice leads to the growth of both the solid−liquid and liquid−gas areas. While the former lowers the surface energy, the latter elevates the system energy, and this contribution is getting significant with decreasing α. For a small enough α at a given θY, the latter becomes dominant over the former. That is, the penetration of the drop into the crevice corresponds to the rises of the system energy and there exists an energy barrier to resist wetting of lyophilic crevices by nanodrops. As the penetration of the drop is arrested, the state of sitting on the opening of the crevice is also unstable. The base of the drop can be divided into two regions. The liquid−solid contact region has lower interfacial energy (smaller θY area) because of the lyophilic nature. In contrast, the liquid−gas contact region (opening of the crevice) possesses higher surface energy (larger θY ≈ 180° area). As a result, the drop base is subject to the gradient of the interfacial tension, and the liquid in the drop is driven to flow by the Marangoni effect from the center (larger θY) to the edge (smaller θY). The environmental disturbance may result in uneven Marangoni stresses on both sides and lead to splits of the drop. When the Marangoni stress on one side wins over that on the other side, the runaway state takes place. On the basis of the morphological phase diagram, a capillary nanovalve with a specific lyophilic surface (fixed θY) can be fabricated to control the passage of the nanodrop by tuning the

provided by the other side is too weak to capture any liquid, yielding runaway of the drop, as shown in Figure 4c. 3.3. Phase Diagram for Capillary Valve. For symmetric deposition of a drop atop the crevice, the equilibrium state is a function of the contact angle θY and wedge angle α. The morphological phase diagram can be obtained mainly by SE combined with MDPD. Most of the regimes in the diagram can be acquired by the two methods independently. However, the regime of partial penetration (breakup) can only be simulated by MDPD. Figure 5 shows the final outcome for a nanodrop

Figure 5. Morphology phase diagram of a drop on a crevice with various surface wettabilities and crevice structures obtained by SE and MDPD.

with V = 5000 and the gap width l = 8. Three regions corresponding to non-penetration, partial penetration, and complete penetration are clearly identified. For large enough wedge angles (e.g., α ≈ 50°), the non-penetration state occurs generally on lyophobic surfaces, but the complete penetration state takes place on lyophilic surfaces, as anticipated. However, the critical CA between the two states depends on the wedge angle, and θcY grows with increasing α. It is interesting to note that as long as α is small enough (e.g., α ≤ 45°), the drop always runs away from the crevice, even on lyophilic surfaces. Also, as with non-penetration and complete penetration, the

Figure 6. Nanodrop with V = 5000 subject to the force f encounters a capillary valve made of a crevice with l = 8. (slightly tilted 5°). 2235

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angle. At θY = 63° and l = 8, non-passage is always achieved for f < fc(α) regardless of the wedge angle. As f > fc(α), complete passage can be observed at α = 34° (see Figure 7b), while partial passage is acquired at α = 90° (see Figure 7a). At the onset point of complete passage (e.g., α = 34°), the deformed drop cannot wet the crevice due to the strong edge effect but is able to reach the other side of the opening. In contrast, at the onset point of partial passage (e.g., α = 90°), the deformed drop wets the crevice first but touches the other side of the opening eventually. The invasion to the new surface and breakup of the drop leads to partial passage. The residue inside the valve can be tuned by the external force. Note that the depth and width of the crevice will affect the passage amount of the nanodrop. If the trench becomes very deep and a little wider, the drop can still be driven laterally across the opening, but the passage amount is significantly reduced.

wedge angle of the crevice. Consider nanodrops with their sizes greater than the gap width (l) of the valve. Those drops move toward the valve by applying a weak external field ( f) such as an electric force. As demonstrated in Figure 6a, they are allowed to pass the lyophilic nanovalve if the wedge angle is changed to a large enough value (corresponding to complete penetration). The drop is symmetrically in contact with both sides of the capillary valve initially, goes into the crevice completely, and tends to stay at the opening (t = 700). As the external force is large enough, it passes the valve. On the contrary, as depicted in Figure 6b, the passage of the drop is prevented as α (≈ 34°) is adjusted to be less than a certain value (corresponding to nonpenetration), which depends on θY. The drop is also symmetrically in contact with both sides initially. After a while, it becomes asymmetric as a result of thermal fluctuations. The Marangoni effect (interfacial tension gradient) makes it move toward one side eventually, leading to the non-passage phenomenon. Certainly, when the wedge angle is tuned to the partial penetration regime, only a portion of the liquid drop is permitted to go through the valve, as shown in Figure 6c. Note that the initial applied force is the same for the three cases, f = 0.001. After the relaxation of the drop colliding with the capillary valve, the force is increased to a certain value, f = 0.05 (t = 700) in Figure 6a and f = 0.3 (t = 500) in Figure 6c, so that the nanodrop can pass the valve. The front surface of the valve is slightly tilted (5°) so that the drop that cannot pass (nonpassage and partial passage) will be forced to slide away by the external field. Throughout this work, the opening is strip-like. However, the shape of the opening is an important factor. The quantitative result depends on the shape of the opening, but the qualitative behavior is essentially the same. In fact, our simulations for the imbibition of a nanodrop atop a cubic nanogroove yield similar results to those of strip-like openings. When the drop motion is along the substrate surface, the crevice can also function as a valve to control the passage of the drop from the left side to the right side, as demonstrated in Figure 7. The drop is always halted at the left edge of the valve if the external force (f) parallel to the surface is small. However, the drop passes the crevice as the force exceeds the critical value ( fc), which depends on both the wedge angle and contact

4. CONCLUSIONS The passage or blockage of a nanodrop through a lyophilic nanocrevice is explored by proof-of-concept simulations. Although it is believed that the drops wet the lyophilic crevice readily, we have shown that the penetration of the drop into the crevice can be prevented by specific structures. As a result, a lyophilic capillary nanovalve for controlling the droplet passage can be constructed by simply adjusting the wedge angle of the crevice. Whether the drop is able to penetrate the crevice or not depends on the contact angle θY and wedge angle α. The morphological phase diagram is obtained mainly by SE simulations combined with MDPD simulations. Three regimes are identified: non-penetration, partial penetration, and complete penetration. When only a part of the liquid drop goes into the crevice, it is called partial penetration. It is interesting to observe that as long as the wedge angle is small enough, the drop always runs away from the crevice regardless of the contact angle. For large wedge angles, the drop tends to penetrate the crevice if the contact angle is lower than the critical value. Our simulation results demonstrate that it is possible to fabricate capillary nanovalves that exhibit low contact angles (lyophilic).

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (Y.-J.S.) *E-mail: [email protected] (H.-K.T.) ORCID

Yu-Jane Sheng: 0000-0002-3031-8920 Heng-Kwong Tsao: 0000-0001-6415-8657 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Y.-J.S and H.-K.T. thank the Ministry of Science and Technology of Taiwan for financial support. Computing times, provided by the National Taiwan University Computer and Information Networking Center and National Center for High-Performance Computing (NCHC) are gratefully acknowledged.

Figure 7. Passing dynamics of an adhered nanodrop with V = 5000 and θY = 63° from the left side of a lyophilic valve. As f exceeds the critical force, the drop can pass (a) with residue and (b) without residue in the crevice. 2236

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DOI: 10.1021/acs.jpcc.7b11624 J. Phys. Chem. C 2018, 122, 2231−2237