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Drop Behavior on a Thermally-Stripped Acrylic Polymer: Influence of Surface Tension Induced Wetting Ridge Formation on Retention and Running Gang Pu, Jun Ai, and Steven J. Severtson* Department of Bioproducts and Biosystems Engineering, University of Minnesota, 2004 Folwell Ave., St. Paul, Minnesota 55108 Received May 4, 2010 Results are reviewed from a study on retention and running of water and other liquids on tilted, polymer coated surfaces. The polymer is a thermally-stripped, solvent-borne acrylic composed primarily of the monomer 2-ethylhexyl acrylate, providing a soft and viscoelastic substrate absent of contaminants. It is shown that drop retention does not obey standard models, which assume dominance of capillary forces in offsetting drop weight for tilted plates. For these surfaces, maximum volumes correlate with capillary lengths, and distinct deformations, which vary in magnitude depending on location, are apparent over the entire drop perimeter. Deformation images indicate that running, which in real time appears to be continuous motion, actually proceeds through a series of steps beginning with the failure of the front edge wetting line. This produces a relatively large translation of the drop’s front edge down the plate surface stretching the drop. This is followed by multiple failures at the rear edge producing a series of small translations, contracting the drop volume to a more spherical-like geometry. Repetition of this mechanism results in the appearance of propagation similar to that employed by an inchworm. The proposed mechanism is consistent with images of drop movement and deformations induced on polymer surfaces, which are apparent subsequent to the running process.
Introduction Movement of water droplets down an angled surface is a familiar phenomenon.1,2 Motion is typically induced by increasing the volume of a sessile drop or tilting the surface. These changes throw out of balance the forces from the pull of gravity and capillary pressure present along the wetting line, which circles the base of the drop.3-8 Set on an angled surface, droplets will assume a distinct leaning geometry due to differences in the contact angle induced at its front and rear edges to counter gravitational forces. While the leading edge will assume an angle greater than that for the drop on a horizontal surface, the contact angle at the rear edge will be smaller. This configuration generates capillary forces that act to resist motion, or, in the case of chemically heterogeneous surfaces, promote it.9-11 In this paper, resistance to motion and running of pure liquids are examined for a substrate, which is tilted to various angles. Given the ubiquitous role these processes play in nature and technology, it is not surprising that they have been studied extensively. However, the focus has been almost exclusively on rigid surfaces for which chemical composition and topology are the characteristics affecting both drop adhesion and motion. Here, *To whom correspondence should be addressed. E-mail: sever018@ umn.edu. Phone: (612) 625-5265. Fax: (612) 625-6286. (1) de Gennes, P. G.; Brochard-Wyart, F.; Quere, D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves; Springer: New York, 2003. (2) Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Rev. Mod. Phys. 2009, 81, 739–805. (3) Frenkel, F. Y. I. J. Exptl. Theoret. Phys. (USSR) 1948, 18, 659–668. (4) Furnidge, C. G. L. J. Colloid Sci. 1962, 17, 309–324. (5) Dussan, E. B. J. Fluid Mech. 1985, 151, 1–20. (6) Extrand, C. W.; Gent, Y. N. J. Colloid Interface Sci. 1990, 138, 431–442. (7) Yadav, P. S.; Bahadur, P.; Tadmor, R.; Chaurasia, K.; Leh, A. Langmuir 2008, 24, 3181–3184. (8) Pierce, E.; Carmona, F. J.; Amirfazli, A. Colloids Surf., A 2008, 323, 73–82. (9) Chaudhury, M. K.; Whitesides, G. M. Science 1992, 256, 1539–1541. (10) Daniel, S. D.; Chaudhury, M. K.; Chen, J. C. Science 2001, 291, 633–636. (11) Ichimura, K.; Oh, S.; Nakagawa, M. Science 2000, 288, 1624–1626.
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results demonstrating the influence of surface tension induced wetting ridge formation on drop motions are presented and discussed. Studies are carried out on smooth (Ra = 61 nm), homogeneous coatings composed of a highly viscoelastic, thermoplastic elastomer. Previously, the authors demonstrated the influence of film substrates cast from this polymer on both static and dynamic wetting.12-14 For many liquids, surface tension acting perpendicular to the surface can produce an immobile deformation ridge tens of micrometers in height and clearly visible when the liquid is removed. Because the average distances between formed ridge patterns (i.e., pinning distances) are often different when advancing versus receding, the complexity of motion for a drop is substantially increased. In the case of water, pinning distances are significantly greater when the contact line is advancing. For a moving water drop, these circumstances result in a sequence that begins with meniscus failure at the front contact line, which is advancing, followed by multiple meniscus failures at the rear contact line, which is receding, to produce what can best be described as “inchworm” propagation. This motion for water and other liquids will be documented and discussed below. Given that pinning distances are controlled by properties of both the liquid which composes the drop and the polymer surface, motion can be modified and engineered to some extent. The system studied here is of great interest in fields such as microfluidics. Use of microfluidic devices has received considerable attention recently for applications in biotechnology, medical diagnostics and in the administration of pharmaceuticals. In practice, microfluidics is concerned with the propagation of small volumes of liquid along flat surfaces and through narrow channels composed of soft materials. The general platform of a microfluidic device is manufactured using nonrigid materials such as (12) Pu, G.; Guo, J.; Larry, G. E.; Severtson, S. J. Langmuir 2007, 23, 12142– 12146. (13) Pu, G.; Severtson, S. J. Langmuir 2008, 24, 4685–4692. (14) Pu, G.; Severtson, S. J. Appl. Phys. Lett. 2009, 94, 134101–134103.
Published on Web 07/07/2010
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PDMS (polydimethylsiloxane).15 Intricacies such as those described here make it apparent that movement of fluids in such systems can be governed by energy dissipation at the wetting line. Strong capillary forces can damage the micro channels and modify flow behavior, which must be considered in device designs.16 The described research also contributes to our understanding of biological processes such as cell migration and adhesion involving interactions between a complex fluid and soft matrix.
Materials and Methods The acrylic polymer is a thermoplastic generated via solvent polymerization primarily from the monomer 2-ethylhexyl acrylate with lesser amounts of amide and vinyl aromatic comonomers. The polymer has a glass transition temperature of less than -50 °C and, at room temperature, a Young’s modulus in the range of 10-100 kPa, similar to that of hydrogels and biological tissues. Dynamic mechanical analysis of acrylic polymer film was carried out with an AR-2000 ex rheometer (TA Instruments Ltd., Fleming Way, U.K.). Frequency sweeps ranged from 1 to 340 rad/s at a temperature ranging from -20 to þ70 °C with a 0.1% strain. These data show that for low deformation rates carried out at room temperature, the polymer demonstrates more viscous behavior and both its storage modulus, G0 , and loss modulus, G00 , are below 10 kPa. Films of the polymer were generated via spin coating on new, precleaned glass slides. Liquids used in wetting experiments including formamide, diiodomethane, and glycerol were purchased from Mallinckrodt Chemicals (Philipsburg, NJ) with 99% purity. The water used was purified to 18 MΩ cm with Type II Laboratory SpectraPure Water System (Tempe, AZ). The surface tension of water with a small amount of surfactant added was 30 N m/m. Shape profiles of wetting ring ridges were obtained by drying water drops on coated plate surfaces. These plates were coated with 50 A˚ of platinum and imaged using a Veeco Wyko NT1100 Optical Profiler (Edina, MN). Tilted plate experiments were carried out on an in-house constructed platform with the capability to incline up to 90 degrees. The platform was attached to a Kruss DSA10 Drop Shape Analysis System (Hamburg, Germany). During experiments, liquid was added to the top of the drop in the center region using a 0.5 mm syringe with an accuracy of 0.017 μL. The initial drop volume for all tilt angles was 0.9 μL. Digital pictures of coated plates were captured with a Nikon (Melville, NY) Coolpix 4500 digital camera immediately following running experiments. Video was recorded using automatic software provided with the DSA 10 system at a frame rate of 15 s-1.
Results Figure 1 shows optical profilometry data for polymer-coated plates subsequent to the evaporation of 20 μL water droplets. Figure 1a shows the typical ring ridge structure left behind by a drop placed on a level plate and then evaporated. The ridges produced by the vertical component of the surface tension are on the scale of micrometers in height and millimeters in width. Figures 1b and 1c show profiles for the front and rear ridges of drops, respectively, that have been tilted to various angles. As would be expected little or no difference is found in the ridge height between the front and rear drop edge when placed on a horizontal surface. In contrast significant differences in the magnitude and shape of deformations can be found when the (15) Haeberle, S.; Zengerle, R. Lab Chip 2007, 7, 1094–1110. (16) Yang, J. L.; Tze, J. Y.; Yn, C. T. J. Micromech. Microeng. 2004, 14, 220– 225.
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Figure 1. (a) Optical profilometry image of a typical residual ring structure on the polymer film subsequent to complete evaporation of a water droplet: topological details for the (b) front wetting ridge and (c) rear wetting ridge formed at various tilt angles. (Ridge profiles are centered at their maximum heights.) Table 1 height wetting ridge (μm) R (degrees)
front edge
rear edge
0 45 80
14 18 21
14 7 3
plate is placed at an angle. As shown in the figures, the height of the front wetting ridge increases with tilt angle (R), whereas the height of the rear wetting ridge decreases. Table 1 shows the DOI: 10.1021/la101786r
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Figure 2. Optical images showing droplet progression for a variety of tilt angles including (a) 2°, (b) 25°, (c) 45°, and (d) 60°. Drop outlines result from wetting line collapse induced through the incremental addition of water to sessile drops. Each collapse event produces a circular ridge pattern on the surface.
Figure 3. Equivalent drop radius versus number of collapse events for a range of tilt angles.
maximum and minimum ridge height for the front and rear wetting ridge with tilt angle. In Figure 2 optical images are shown that outline the progression of droplet motion induced through incremental addition of water to sessile drops. Drops were placed on polymer coated surfaces tilted to various angles including (a) 2°, (b) 25°, (c) 45°, and (d) 60°. Deformation ridges formed at 3-phase lines for different drop volumes show the sequence of events that eventually lead to the running of drops down plate surfaces. The concentric outlines are indicative of stick and break behavior, in which induced deformation ridges pin wetting lines. Continued propagation is only possible through the failure of the meniscus forced through the addition of greater amounts of water to increase drop volume. At 2° the drop shows essentially random collapse behavior in that no distinct direction or change in drop shape is obvious. With increasing tilt angle, the drop elongates in the direction gravitational forces are acting and widens to a lesser extent. The collapse appears to occur at the wetting line composing the front edge of the drop, i.e., the three-phase line running from each side at the maximum width of the drop around to the point furthest down the plate. Figure 3 plots equivalent drop radius versus the number of collapse events for each of the tilt angles. (Equivalent drop radius is simply the radius of a sphere with the same volume as the drop, and 12698 DOI: 10.1021/la101786r
a collapse event involves the failure and re-establishment of the wetting line; a step in the stick and break motion.) In all cases, linear relationships exist. The dotted line is a guide added for comparison between the different tilt angles. It can be seen that for the same drop volume, a greater number of collapse events occur for higher tilt angles, e.g., in reaching the indicated volume, a drop originally placed on a plate with R = 85° collapses 6 times while a drop with the same volume history originally placed on a plate at a 2° only collapses 3 times. In other words, the slopes of the lines decrease with increasing tilt angle. Figure 4a shows the maximum tilt angle (designated Rmax) as a function of drop volume for various liquids. This is the R necessary to induce continuous motion of a drop down the plate surface or running. In all cases there is an inverse relationship as indicated by the curves. It can be seen that for the same volume the maximum tilt angle was measured for water followed by an aqueous solution containing glycerol, pure formamide, water with surfactant, and pure diiodomethane, in order of decreasing angles. Figure 4b plots sin Rmax versus V-2/3 where V is the drop volume. Another correlation identified is shown in Figure 4c, for which slopes from the lines shown in Figure 4b are plotted against capillary lengths for the different liquids tested. A fairly linear relationship was found for all liquids tested (r2 > 0.86), indicating that higher capillary lengths provide greater retention angles. The series of images shown in Figure 5 are for a water droplet with a volume of 35 μL. The drop was placed on a polymer-coated plate at an 85° tilt angle and the drop volume was increased to induce rapid movement down the plate or running. Time zero corresponds to the moment just prior to meniscus failure at the front edge of the sessile drop. The lower and upper lines in the images indicate positions of the front and rear wetting lines, respectively. Top and bottom sequences each demonstrate a cycle in the movement of the drop down the plate, which involves collapse of the front edge of the drop followed by the collapse of its rear edge. It can be seen that the collapse at the front drop edge requires less than 40 ms to complete, while collapse at the rear line involving recession is substantially slower requiring more than 20 s (>500 times greater). During the collapse, advancements at the front edge of the drop appear to occur in single events or steps, which are about 1.4 mm in length, while the rear drop edge remains pinned. This is followed by the slow progression of the rear edge down the plate, which increases volume over the wetting line (see the volume accumulating under the lower line) and contact angle at the front edge of the drop. Figure 6 shows the deformation remaining after a water drop with a volume of 60 μL has run off a polymer-coated plate with a 45° tilt angle without any apparent stops. The ridge deformation caused by pinning at the contact line is consistent with the process Langmuir 2010, 26(15), 12696–12702
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different outcomes.17-20 For example, angles required to initiate the running of drops down plate surfaces, i.e., critical angles, are dependent on whether the drop is placed on surfaces already at an incline or those that are level when the drop is deposited and then tilted.21,22 Another aspect of these experiments identified as producing variations is needle position during volume addition to suspended drops.20 In general, measurement issues appear to result from an inadvertent addition of kinetic energy for example through small induced vibrations. Also, contributing to repeatability problems is the assumption of simple circular symmetry for drop profiles, which are often skewed due to the pinning of rear edges as droplets are placed. Our results were repeatable and demonstrate a novel mechanism for drop retention and movement on tilted surfaces. Below, the observed behavior is distinguished from what has previously been reported and an explanation is provided for both retention and running processes based on differences in contact line behavior at the front and rear edges of the drop on the viscoelastic surface. Drop Retention on Viscoelastic Surface. Drop volume (V) and its advancing (front edge) (θa) and receding (rear edge) (θr) contact angles have been found to be related through a theoretical expression of general form1,3,6 FgV sin R ¼ γωKðcos θr - cos θa Þ
Figure 4. (a) Maximum tilt angle (Rmax) versus drop volume for
various liquids: (b) sin Rmax versus V-2/3 for various liquids: (c) The slopes from lines in Figure 4b versus capillary lengths for the liquids.
In eq 1, the left-hand side is the component of the drop’s body force acting down a tilted plate where g is acceleration due to gravity, F is liquid density, and R is again the tilt angle of the plate. This is countered by the capillary forces with the terms γ, ω, and κ corresponding to the surface tension of the liquid, the width of the drop, and a numerical constant that corrects for irregular drop geometry, respectively. Drop profiles typically vary with increasing volume, diverging from their original circular geometry. The κ term is found to linearly increase with the length-to-width (aspect) ratio of the drop for an elliptical contact line.6 Another well-documented aspect of drop retention experiments is a relationship between the maximum drop volume, Vmax, and advancing and receding contact angles and tilt angle.5 This is different from eq 1, which describes the equilibrium balance between body and capillary forces. In this case, variables correspond to conditions that initiate the running of a drop down a surface. Again, for the acrylic polymer, behavior veered significantly from what has previously been reported. Data plotted in Figure 4a was fit by Dussan’s equation Vmax ¼
described in Figure 5. Although the motion of the drop appeared to be continuous, clues left behind on the highly viscoelastic surface indicate it is actually composed of a series of distinct steps of the front and rear wetting lines. The evenly spaced, crescent-shaped ridges are indicative of pinning followed by collapse at the front contact line. The ridges caused by the rear contact lines were smaller in both magnitudes and separation distances as shown in the inset. The picture was enhanced by increasing contrast to show three smaller reversed crescent shape ridges, pointed out by the arrows, caused by stick and break motion of the receding contact line.
Discussion Precision is often an issue in tilted plate studies. Small variations in experimental techniques can produce significantly (17) ElSherbini, A. I.; Jacobi, A. M. Prog. Colloid Polym. Sci. 2004, 128, 57–62.
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ð1Þ
Fg sin R - 3=2 96 1=2 ½ðcos θr - cos θa Þ3=2 ð1 γ π
þ cos θa Þ3=4 ð1 - ð3=2Þ cos θa þ ð1=2Þcos3 θa Þððcos θa þ 2Þ3=2 ð1 - cos θa Þ9=4 Þ - 1
ð2Þ
Realistic advancing and receding, θa and θr, contact angle values, i.e., between 0 and 180°, were used as parameters to obtain the best fit. As can be seen from Figure 4a, fits were better in the high R regions where the drop volumes are still small. The Dussan equation is reportedly more accurate for smaller drops and contact angle hysteresis values. Values show a high hysteresis, but more importantly, advancing and receding values for all of the (18) (19) (20) (21) (22)
Krasovitski, B.; Marmur, A. Langmuir 2005, 21, 3881–3885. Tadmor, R.; Yadav, P. S. J. Colloid Interface Sci. 2008, 317, 241–246. Pierce, E.; Carmona, F. J.; Amirfazli, A. Colloids Surf. A 2008, 323, 73–82. Extand, C. W.; Kumagai, Y. J. Colloid Interface Sci. 1995, 170, 515–521. Berejnov, V.; Thorne, R. E. Phys. Rev. E 2007, 75(066308), 1–6.
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Figure 5. Movement of a 35 μL water droplet down a plate coated with the acrylic polymer and tilted to 85°.
liquids are all quite similar, i.e., the bracketed term in eq 2 is relatively constant. This is demonstrated in Figure 4c in that the slopes of lines in Figure 4b show a linear correlation with capillary length, (Fg/γ)1/2. It was also noticed that maximum drop volumes on the acrylic polymer were significantly greater than those reported for other polymeric surfaces. From our drop data for water and other liquids on the acrylic polymer, no clear relationship between front and rear edge contact angles, drop volume and tilt angle is distinguishable. Contact angles are determined by drop volume rather than capillary forces. The maximum drop volume is related to the capillary length for a given liquid, rather than measures of its surface tension balance with the surface. Owing to the unique wetting behavior for our system, this was not unexpected. The formation of a wetting ridge structure is not exclusive to highly viscolelastic surfaces. However, the observed magnitude of deformation for the acrylic polymer and great extent to which this impacts wetting and drop movement appears to be novel. It is possible that in other systems for which ridge formation occurs to lesser extents the same influence exists but manifests itself in more subtle ways. For example, Extrand studied drop retention on an elastomeric surface, for which it was noted that the vertical surface tension could induce ridge formation with heights ranging from 5 nm to 1 μm.21 These wetting ridges were visible for several seconds before relaxing back into the surface. There is also evidence from other studies that incremental adjustments to achieve a more stable wetting line position occur at the front edge of the drop for the advancing angle, as was observed here.4,22 Numerical modeling shows that if the contact line could freely displace to minimize the free-energy, the small discrete jumps would occur along the advancing line.23,24 Berejnov et al. showed that the pinning along the contact line is not homogeneous on a tilted plate. The instability of the advancing contact line is considerably greater than that of the receding line and nearly independent of drop volume.22 In all these cases, the instability region of the contact line is small compared with drop size. The relationship between the instability of drops and the volume fraction in the front edge is shown in Figure 7. Here the reciprocal slopes from linear fits of data shown in Figure 3 are (23) Dimitrakopoulos, P.; Higdon, J. J. L. J. Fluid Mech. 1999, 395, 181–209. (24) Iliev, S. D. J. Colloid Interface Sci. 1997, 194, 287–300. (25) Quere, D. Annu. Rev. Mater. Res. 2008, 38, 71–99.
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plotted against the calculated fraction of drop volumes held in the front portion of tilted drops. It is assumed that the weight distribution of drops is divided by a vertical plane, which includes the drop center. On a level plate, the front and rear portions of the contact line support an equal amount of water whereas on a vertical plate, the entire volume (weight) of the drop is supported by its front contact line. By assuming that the drop has a spherical cap geometry, the drop volume fraction supported by the front contact line, νfront, is calculated as νfront ¼ 0:5 þ ðR=180°Þ
ð3Þ
The slopes of lines plotted in Figure 3 are the equivalent drop volumes required to produce a collapse of the drop’s front edge. Thus, the reciprocal value is the collapse frequency for a given equivalent volume at the different R values. As would be expected, the greater the tilt angle, the higher the frequency. In fact these values show a linear correlation. Drop Running on the Polymer Surface. Drop retention results reviewed above are interesting in that they demonstrate how wetting behavior on the polymer is dominated by the pinning of the 3-phase line due to ridge formation. Once its volume is increased beyond what its capillary force can sustain, a drop will run down a tilted surface driven by gravity. The mechanics involved in this motion are dependent on the nature of the surface.26-30 For rigid hydrophilic surfaces, water droplets tend to slide as a solid body with little or no internal motion. This leaves behind a microscopic film, such as that observed when rain drops slide down a clean windshield. For hydrophobic surfaces, the drop will tend to roll like a wheel. The classic example of this is the so-called “lotus effect”, which involves the rolling of water droplets down leaf surfaces to remove dirt and debris.31,32 Shanahan et al. described so-called “viscoelastic braking” for the movement of wetting lines on soft polymer surfaces in which the contact line carries the ridge deformation forward. The energy dissipated (26) (27) (28) (29) 131. (30) (31) (32)
Dorrer, C.; Ruhe, J. Soft Matter 2009, 5, 51–61. Allen, R. F.; Benson, P. R. J. Colloid Interface Sci. 1975, 50, 250–253. Mahadevan, L.; Pomeau, Y. Phys. Fluids 1999, 11(9), 2449–2453. Hodges, S. R.; Jensen, O. E.; Rallison, J. M. J. Fluid Mech. 2004, 512, 95– Richard, D.; Quere, D. Europhys. Lett. 1999, 48, 286–291. Neinhuis, C.; Barthlott, W. Ann. Bot. 1997, 79, 667–677. Gao, L.; McCarthy, T. J. Langmuir 2006, 22(7), 2966–2967.
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Figure 7. Reciprocal of slopes from lines shown in Figure 3 versus the calculated drop volume fraction supported by the front contact line of tilted drops (shaded regions for inset schematics).
Figure 6. Deformations left behind from a droplet of water, which had run down a plate tilted to 45°. Insert shows the smaller wetting ridges caused by the receding contact line.
through the viscoelastic deformation cycle can impede the motion of the wetting line.33,34 The acrylic polymer used in our studies has an enhanced ability to dissipate energy, which prevents propagation of the wetting ridge forward. Motion of a drop requires failure of the existing and establishment of a new wetting line, i.e., stick and break propagation, shown in Figure 5. In the case of drop running, significant differences exist in the magnitude of deformation induced at the front and rear edge of the drop. This leads to significant differences in the stick and break propagation at the front and rear of the drop, which alters drop motion as it moves (33) Carre, A.; Gastel, J. C.; Shanahan, M. E. R. Nature 1996, 379, 432–434. (34) Shanahan, M. E. R.; Carre, A. Langmuir 1994, 10, 1647–1649.
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down an inclined plate. It leads to what we have described in the Introduction as “inchworm” propagation. In this section, a more detailed description, as well as an explanation, is offered for the observed motion. This mechanism is demonstrated for drop motion on highly viscoelastic surfaces, however it is also possible in systems for which there exists a considerable contact angle hysteresis. As discussed in detail elsewhere, the wetting ridge is critical to how strongly the wetting line can be pinned. The spacing (pinning distances) and extent to which stick and break motion occurs is dependent on the magnitude of ridge formation. On a tilted surface, the front wetting ridge is significantly larger than the rear ridge and this difference increases with tilt angle. The forcedisplacement curves from rod wetting experiments indicate the quasi-periodic patterns during receding were significantly smaller in magnitude and pinning distances than when advancing.14 For example, for the same distance, 10 mm, of rod movement, the advancing contact line collapsed 13 times and the receding contact line collapsed 40 times.14 Such results are consistent with results shown in Figure 6. The liquid front advances through a rolling motion in which the volume (weight) increases over the wetting line to the point where it can no longer be supported by the meniscus. This leads to its collapse spilling the supported liquid into the region in front of the three-phase line and establishment of a new wetting line. Due to the drag effect from the rear of the drop, the front contact line could support a higher contact angle and consequently collapse a larger distance than that observed in wetting experiments utilizing a rod. Movement of the receding wetting line for water is similar to what is observed in general on hydrophilic surfaces. There is a high affinity with the surface due to the pinning of the receding contact line. As a result the contact angle is pulled to near 0° and a thin film of water is left behind as the wetting line recedes. This liquid film quickly contracts forward and a new wetting line is established. This mechanism results in less deformation to the polymer surface and shorter distances between wetting lines (pinning distances). The stick and break motion described above for the advancing (front edge) and receding (rear edge) wetting lines of a drop running down the surface of a tilted plate provides a possible explanation for the observed motion described as inchworm propagation. The front edge of the drop, which involves an advancing wetting line, moves through a rolling motion in a series of relatively large steps, whereas the rear edge, which involves a receding wetting line, is closer to a sliding motion involving small DOI: 10.1021/la101786r
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Figure 8. Schematic for proposed mechanism involved in running of liquid down tilted plate coated with the acrylic polymer. Shown are the (a) side view and (b) top view.
pinning distances. An analogy to this set of circumstances is the running of a water drop down a tilted plate composed of both hydrophobic and hydrophilic horizontal stripes with widths similar to the drop radius. Thus the drop is always in partial contact with both hydrophilic and hydrophobic regions of the surface. Numerical and experimental studies of water drop motions on such surfaces indicate strong oscillations in both drop shape and velocity.35,36 These drops adopt two stable shapes depending on location; a “butterfly” configuration in which the drop spans the space between two hydrophilic stripes and a “diamond” shape where the drop is contracted over a single hydrophilic stripe. This is a result of the advancing line quickly vacating the hydrophobic regions, whereas the receding line shows strong adhesion to the hydrophilic areas. Thus, as a drop moves over such a surface, its shape and length oscillates. The proposed mechanism involved in the running of a drop of liquid down a tilted plate coated with the acrylic polymer is shown schematically in Figure 8. Much like the motion involved in the running of water on alternating hydrophobic-hydrophilic patterned surfaces, propagation on the polymer demonstrates an oscillation in drop shape. In contrast, the oscillation on the polymer surface is induced by strong and weak interactions at the front and rear edge wetting lines, respectively. The solid profile in the schematic shows the initial drop position and shape on the tilted plate. Increasing the drop volume or tilting the plate increases the front edge (advancing) contact angle due to pinning, indicated by the blue profile. Increasing drop volume eventually forces the collapse of the meniscus and the wetting line is reestablished resulting in the movement of the drop’s front edge down the plate (red profile). This changes the shape of the drop as its axis perpendicular to the motion is extended, which reduces the contact angle at the drop’s rear edge promoting propagation. This motion involves a series of several significantly smaller steps, which act to increase the volume of liquid supported by the meniscus at the drop’s front edge (green profile), eventually forcing its collapse and a repeat of the described mechanism. The above analysis indicates that the mechanism for the running of a drop down a highly viscoelastic surface is deceptively (35) Leopolds, J.; Dupuis, A.; Bucknall, D. G.; Yeomans, J. M. Langmuir 2003, 19(23), 9818–9822. (36) Kusumaatmaja, H.; Leopldes, J.; Dupuis, A.; Yeomans, J. M. Europhys. Lett. 2006, 73(5), 740–746.
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complex. What appears to be constant and uninhibited motion can be broken down into series of steps all of which have dependencies on properties of the liquid and polymer involved as well as the rate at which the drop is moving. Predicting or engineering this motion is challenging because the shear modulus for the polymer in our experiments can not be assumed to remain constant. Increasing the wetting rate reduces the surface deformation consistent with greater elastic behavior for higher deformation frequencies. Also, due to the hydrophilic characteristics of the receding contact line, the volume of a drop is reduced as it propagates down a surface. For a large drop, a stable high velocity could likely be found for which the surface deformation is negligible, but for smaller drops at lower wetting rates deformation is likely to greatly influence behavior. It is expected that there exist some critical transition points for drop movement associated with the volume and velocity. With a sufficiently high wetting rate, viscous dissipation would be expected to dominate drop motion as is found for rigid surfaces. Further investigation is underway.
Conclusions Results demonstrate that both drop profile and motion on the viscoelastic polymer show complex behavior due to the strong pinning effect caused by surface deformation. The simple “rolling” or “sliding” models are not sufficient to describe drop motion on such surfaces. We have suggested the described inchworm model for such motion. The proposed model may be generally applicable for the wetting by liquid drops having large hysteresis values (>100°) on soft viscoelastic surfaces at sufficiently low rates. Reported results have significant ramifications for fields such as microfluidics. It is apparent that precise control on such surfaces will require knowledge of the viscoelastic properties of the platform layer in order to superimpose the effect of solid surface deformation on classical results. Acknowledgment. The authors thank Mr. Andrew Sipple of Boston Scientific Corporation for his generous assistance in collecting optical profilometry data. This research is financially supported in part by a grant from the U.S. Postal Service, Stamp Acquisition and Distribution and the U.S. Department of Energy Project No. DE-FC36-04GO14309.
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