Article pubs.acs.org/Langmuir
Influence of Substrate Elasticity on Droplet Impact Dynamics Azar Alizadeh,*,† Vaibhav Bahadur,† Wen Shang,† Yun Zhu,† Donald Buckley,† Ali Dhinojwala,‡ and Manohar Sohal§ †
General Electric Global Research, Niskayuna, New York 12309, United States The University of Akron, Akron, Ohio 44304, United States § Idaho National Laboratory, Idaho Falls, Idaho 83145, United States ‡
S Supporting Information *
ABSTRACT: Droplet impact dynamics is vital to the understanding of several phase-change and heat-transfer phenomena. This work examines the role of substrate elasticity on the spreading and retraction behavior of water droplets impacting flat and textured superhydrophobic substrates. Experiments reveal that droplet retraction on flat surfaces decreases with decreasing substrate elasticity. This trend is confirmed through a careful measurement of droplet impact dynamics on multiple PDMS surfaces with varying elastic moduli and comparison with impact dynamics on hard silicon surfaces. These findings reveal that surfaces tend to become more wettable upon droplet impact as the elastic modulus is decreased. First-order analyses are developed to explain this reduced retraction in terms of increased viscoelastic dissipation on soft substrates. Interestingly, superhydrophobic surfaces display substrate-elasticity-invariant impact dynamics. These findings are critical when designing polymeric surfaces for fluid−surface interaction applications.
1. INTRODUCTION Water droplet impact on surfaces is an important consideration for the development of applications in the areas of heat transfer and phase change (ice formation,1−9 condensation,10 and boiling11,12). Droplet impact dynamics can show markedly different characteristics depending on the impact velocity, surface chemistry and structuring, liquid properties, and environmental conditions (temperature, pressure, and humidity). These parameters determine the nature of the fluid− structure interaction when a droplet strikes a surface; the outcome of droplet impact determines the performance of these systems. As an illustration, the interfacial contact area after droplet impact determines the probability of freezing for supercooled droplets and is an important parameter for the characterization of icephobic coatings.1 For high-temperature applications, the nature of droplet impact affects convection patterns in the droplet, which determines the heat removal capacity of the droplet. An analysis of the existing literature13−16 reveals a significant number of studies on the role of surface structuring, chemistry, and impact conditions on impact dynamics. In contrast, there are fewer studies17−20 on the role of temperature and pressure on droplet impact dynamics. There are even fewer studies on the role of substrate elasticity on wettability. Most existing studies on wettability on soft substrates analyze static droplets21−23 on soft polymeric surfaces. The concept that a static droplet on a soft substrate will form a wetting ridge at its perimeter has been experimentally demonstrated20 and analyzed by multiple researchers.21,22 This wetting ridge is the result of surface tension deforming and pulling up the © 2013 American Chemical Society
substrate vertically at the three-phase contact line; a corresponding dimple is left on the surface below the droplet. The height of this wetting ridge has been experimentally measured and depends on the substrate elastic modulus. Pericet-Camara et al.21 have measured a height of about 700 nm for a substrate with an elastic modulus of 25 kPa. Carre et al.24−26 have shown that the existence of the wetting ridge leads to energy dissipation as the contact line moves on the deformable substrate. This energy loss is termed viscoelastic dissipation and is different from the viscous dissipation phenomenon20 that depends on the viscosity and velocity profile on the surface. Sokuler et al.27 have demonstrated faster rates of condensation of water droplets on soft surfaces. Rioboo et al.28 have carried out static and dynamic contact angle measurements to quantify contact angle hysteresis on soft surfaces. Pepper et al.29 studied the dynamics of a droplet impacting a stretched elastic membrane; however, the objective was to analyze the influence of membrane tension on impact behavior. There is no existing study in the available literature that has analyzed or measured the influence of substrate modulus on droplet impact dynamics behavior. The present study is a fundamental analysis of the role of substrate elasticity on droplet impact dynamics. Multiple poly(dimethylsiloxane) (PDMS) surfaces of contrasting elastic properties have been utilized in this study. The results of droplet impact on soft surfaces are compared to the impact on a Received: December 1, 2012 Revised: January 24, 2013 Published: February 11, 2013 4520
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= 138 at room temperature (where d is the initial droplet diameter, ρ is the density, V is the impact velocity, and γ is the surface tension of water). In all cases, the droplet was maintained at room temperature. A high-speed camera (Phantom V7.3 from Vision Research, 3000 frames/s) was utilized to capture the details of droplet impact. The high-speed camera images were utilized to obtain the transient position of the contact line. Videos of droplet impact on these surfaces are provided in the Supporting Information section. Figure 1 shows the variation of the transient droplet diameter as a function of time for four flat substrates. The droplet impact can be
hard surface (silicon). It should be noted that the surface chemistry is maintained the same on all the surfaces considered in this study; the difference in droplet dynamics can then be directly attributed to a difference in elastic properties.
2. SURFACE FABRICATION AND EXPERIMENTAL SETUP The details of the substrates used in the present study are summarized in Table 1. Flat, polished silicon wafers (functionTable 1. Details of Surfaces Utilized in the Present Study sample Si−F PDMS (1:10) PDMS-F (1:10) PDMS (1:25) PDMS-F (1:25) PDMS (1:40) PDMS- F (1:40) Si-STex-F PDMS-STex
description flat Si (fluorinated) flat PDMS 1:10 flat PDMS 1:10 (fluorinated) flat PDMS 1:25 flat PDMS 1:25 (fluorinated) flat PDMS 1:40 flat PDMS 1:40 (fluorinated) textured Si (fluorinated) textured PDMS (1:10)
shear modulus G (MPa) at 20 °C 170 × 103 3
0.6
0.25
Figure 1. Transient spreading diameter of a water droplet on fluorinated Si, PDMS (1:10), PDMS (1:25), and PDMS (1:40) substrates at room temperature. The two insets show droplets after they come to rest on fluorinated Si (bottom) and fluorinated PDMS(1:40 (top)) substrates. It is clearly seen that the droplet retracts more on the high-elastic-modulus silicon substrate. The horizontal dashed lined represents the spreading diameter corresponding to the gentle positioning of the droplet on the fluorinated surfaces. This static spreading diameter has been calculated from the measured static contact angle data assuming a spherical cap geometry. In all cases, the dynamic (impact) spreading diameter is larger than the static spreading diameter. The scale bar in the figures is 1 mm.
alized with a thin tridecafluoro-1,1,2,2-tetrahydrooctyl trichlorosilane (Mw = 482 g/mol) coating to render the surface hydrophobic with a contact angle of 110 ± 5°) were the highest elastic modulus substrates in this study. PDMS flat substrates with three different elastic moduli were prepared by controlling the ratio of curing agent to prepolymer (the curing agent/ prepolymer weight ratios were 1:10, 1:25, and 1:40, respectively). Some PDMS substrates were also functionalized with a thin fluoropolymer layer (tridecafluoro-1,1,2,2-tetrahydrooctyl trichlorosilane (Mw = 482 g/mol)) to maintain the same chemistry as on the silicon substrate. The static contact angles of a water droplet on PDMS surfaces before and after functionalization were equal to 115 ± 10 and 119 ± 10°, respectively. The elastic moduli of all of the PDMS substrates were obtained from a dynamic mechanical analysis (DMA). Along with the flat substrates, textured Si and PDMS (1:10) substrates (with periodic arrays of post structures) were also prepared using standard photolithography and replication techniques. These textured substrates were fluorinated with tridecafluoro-1,1,2,2-tetrahydrooctyl trichlorosilane (Mw = 482 g/mol) to render them superhydrophobic. Water contact angles on the textured Si and PDMS surfaces were equal to 142 and 147°, respectively. Advancing, receding, and roll-off contact angles of sessile DI water droplets were measured on all of the samples at room temperature using a VCA Optima setup from AST Products, Inc. The details of surface fabrication and characterization are described in the Supporting Information section.
divided into spreading and retraction stages. It should be noted that the spreading phase is much faster than the retraction phase. As evident in Figure 1, the spreading stage does not show any dependence on the substrate modulus. In contrast, the retraction phase on these substrates varies significantly, and a clear trend of decreased retraction with reduced elastic modulus is observed. The insets in Figure 1 are the images of two droplets after coming to rest on the fluorinated silicon and 1:40 PDMS surfaces, respectively. A significantly reduced droplet retraction is observed for the softer fluorinated 1:40 PDMS surface. This finding has important implications on the use of polymeric surfaces for droplet impact applications because it implies that a material with an ultralow elastic modulus may compromise the benefits (of inherent hydrophobic surface chemistries) associated with commonly used polymers such as PDMS. Another noteworthy point stems from the role of the impact velocity of the droplets. Even at a low impact velocity of 2.2 m/s, the velocity-dependent impact pressures were sufficient to deform the substrate such that droplet retraction was adversely affected. It is anticipated that at higher impact velocities a low-modulus substrate will retard droplet retraction to an even greater extent. Droplet impact dynamics experiments were also conducted on textured superhydrophobic surfaces with various elastic moduli. Figure 2 shows the droplet dynamics results for impact on textured superhydrophobic surfaces made of silicon and PDMS (1:10). It is seen that the curves are almost identical; on the Si surface, the droplet is completely repelled, but on the PDMS surface, the droplet comes very close to being repelled from the surface. (See the Supporting
3. EXPERIMENTAL MEASUREMENTS OF DROPLET IMPACT Two-millimeter-diameter deionized (DI) water droplets (at room temperature) impacted the substrates, with the surface temperature set at either 20 °C or −15 °C. The impact velocity was 2.2 m/s, corresponding to a Reynolds number (measure of the inertial to viscous forces in the droplet) of Re = (Vdρ)/μ = 4400 and a Weber number (measure of fluid inertia to surface tension) of We = (ρV2d)/γ 4521
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The instantaneous viscoelastic energy dissipation of the droplet can be estimated as dEv = f
γ 2u(t ) (πD(t )) dt 2πGε
(2)
where D(t) is the instantaneous droplet diameter and f is the dissipation factor (a measure of how much elastic energy is irrecoverable). f is computed from the experimental data as the ratio of the imaginary and real components of the elastic modulus. (See the Supporting Information for more details.) The total viscoelastic energy dissipated during the spreading and retraction processes can now be estimated as ΔEv = f Figure 2. Transient spreading diameter of a water droplet on superhydrophobic silicon and PDMS substrates (at room temperature). The SEM images in the insets show the structure of the surfaces (with a scale bar of 1 μm).
γ2 2Gε
∫0
tc
u(t ) D(t ) dt
(3)
where tc is the spreading and retraction time of the droplet. The above equations can be used to estimate the viscoelastic energy losses accompanying the droplet impact on the silicon substrate and the PDMS substrates. The instantaneous droplet diameters and contact line velocities can be obtained from the plots in Figure 1. In Figure 3, the variation of the retention factor (defined as the ratio of the final contact area to the maximum contact area)
Information for videos of droplet impact on these surfaces.) These results imply that, in contrast to the case of flat surfaces, substrate elasticity does not influence the droplet impact on textured surfaces. The above finding reveals that structured polymeric substrates retain the superior water-repelling properties of harder substrates. This is important because polymeric superhydrophobic surfaces have substantial cost and manufacturability benefits associated with them.
4. ANALYSIS OF ENERGY DISSIPATION DURING DROPLET RETRACTION The decrease in droplet retraction with decreasing substrate elasticity, in the case of flat surfaces, can be understood by an analysis of the energy dissipation phenomena occurring during droplet spreading and retraction. On a rigid substrate, viscous dissipation and contact line friction30 act to dissipate the total energy of the droplet (which consists of the surface and kinetic energies). The extent of energy loss determines the degree to which the droplet retracts. On a soft substrate, however, additional energy is dissipated into the substrate because of the deformation of the substrate. The existence of a wetting ridge (Figure 2, schematic on the right) at the three-phase line for a droplet on a soft surface has been experimentally demonstrated.21 This ridge occurs because the soft substrate is pulled up at the contact line, leading to a dimple below the droplet; the height26 of the wetting ridge depends on the elastic modulus of the substrate and is on the order of γ/G, where G is the shear elastic modulus. As the contact line moves on such a surface, additional energy is expended in moving the wetting ridge; this viscoelastic dissipation influences the wetting kinetics very strongly. The work done by the droplet per unit time per unit length of the contact line to move on a soft surface can be estimated from the following equation as26
Figure 3. Relation between viscoelastic dissipation and droplet retraction on a silicon surface and three PDMS substrates with varying elastic moduli. All experiments were conducted at room temperature. The schematic shows droplet spreading/retraction on hard and soft surfaces and highlights the dominant energy loss mechanisms.
is plotted as a function of the viscoelastic energy loss as defined in eq 3. It is clearly seen that increased viscoelastic dissipation retards retraction. This analysis suggests that subsequent to impact a droplet will end up with a larger footprint on the surface after retraction. This suggests that soft surfaces tend to act in a more wettable manner upon droplet impact; this is a very significant finding of the present work. At the other extreme, a droplet should almost completely retract on hard surfaces; indeed much higher retraction is observed on the hydrophobic silicon surface (Figure 1). It should be noted that along with viscoelastic dissipation, droplet retraction is also influenced by surface chemistry and viscous dissipation20 effects. This explains the lack of complete retraction on the hydrophobic silicon surface (leftmost data point in Figure 2) even though the viscoelastic losses are negligible.
γ 2u (1) 2πGε where U is the instantaneous contact line velocity and ε is an empirically determined distance near the triple line (and is assumed to be 1 μm in the present study). Equation 1 is based on Carre and Shanahan’s formulation25,26 to predict droplet motion on soft surfaces and captures the contribution of the viscoelastic dissipation to the total energy loss of the droplet. The effect of viscous dissipation is analyzed in a subsequent portion of the Article. Wv =
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It is important to estimate the strength of viscoelastic dissipation (on soft surfaces) against viscous dissipation at the surface−liquid interface. To a first order, the viscous dissipation energy loss associated with a single droplet impact on a flat surface can be estimated using31 viscousloss =
π 2 2 1 ρV ddmax 3 Re
Article
ASSOCIATED CONTENT
* Supporting Information S
Surface fabrication and characterization. Droplet impact dynamics on soft substrates at low temperatures. Videos of droplet impact. This material is available free of charge via the Internet at http://pubs.acs.org.
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(4)
where dmax is the maximum spreading diameter and Re is the Reynolds number corresponding to droplet impact conditions. (The other parameters in this equation were defined earlier.) A comparison of the two losses reveals that the viscoelastic losses are higher than viscous losses by 3 orders of magnitude even for the hardest (lowest viscoelastic loss case) PDMS substrate in this study (G = 0.25 MPa). This dominance of viscoelastic losses implies that viscous dissipation will not play a dominant role in influencing droplet impact dynamics on such soft surfaces. This hypothesis is directly verified by conducting droplet impact tests on the PDMS substrates at −15 °C. The viscosity of water at −15 °C is greater than that at room temperature by a factor of 6, which implies a significant increase in viscous dissipation at −15 °C. However, the impact dynamics at −15 °C does not change significantly as compared to room-temperature impact dynamics, implying the negligible influence of viscous dissipation on such soft surfaces. (See Supporting Information for more details on impact dynamics at −15 °C.) It should be noted that such viscosity-independent impact dynamics (for cases where dynamics is predominantly determined by viscoelastic dissipation) was previously demonstrated by Carre and Shanahan32 by using liquids with different viscosities. In contrast to the flat surfaces, the liquid contact line on textured surfaces rests on a composite solid−air interface, which hinders the formation of a continuous wetting ridge and eliminates the associated viscoelastic losses accompanying contact line motion. It is also important to note that the movement of the contact line on textured surfaces comprising an array of pillars could induce the bending of the pillars.33 However, for the present low-aspect-ratio post structures, the bending of pillars is expected to be negligible. This hypothesis is confirmed by the close match of the curves in Figure 2, which indicates no difference in energy losses on the two surfaces (by the bending of pillars or by viscoelastic dissipation). The minor differences in the retraction curves of the two superhydrophobic surfaces in Figure 2 can be potentially explained by understanding that the textures on the two surfaces are not exactly identical. As evident in Figure 2, the silicon pillars are undercut, which is a consequence of the silicon etching process, whereas the PDMS pillars do not have such features.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We are very thankful to Maria LaTorre, Sheng Zhong, Lauraine Denault, Chris Keimel, Oliver Boomhower, Ken Conway, Jim Ruud, Scott Miller, and Margaret L. Blohm for their assistance and support of this work. The Nanotechnology Advanced Technology Program at GE Global Research, the Department of Energy (award number DE-AC07-05ID14517), and the National Science Foundation (grant number 1006764) are acknowledged for financial support. This Article has been authored by Battelle Energy Alliance, LLC, under contract no. DE-AC07-05ID14517 with the U.S. Department of Energy. The publisher, by accepting the Article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this Article, or allow others to do so, for United States Government purposes.
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5. CONCLUSIONS This work presents new insights into the dynamic interaction of droplets with soft substrates; it is clearly seen that substrate elasticity plays a significant role in influencing the nature of droplet impact dynamics along with surface chemistry and texture. The findings of this work will be important in the design of flat and textured polymer-based surfaces for droplet− structure interaction-based applications. The present results combined with recent advances34 in fabricating polymer-based (variable stiffness and anisotropic) textured surfaces offer immense possibilities for enhanced performance and control of droplet-based phenomena. 4523
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