Ind. Eng. Chem. Res. 2008, 47, 3639-3644
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Vertical Spreading of Aqueous Trisiloxane Solution Driven by a Spontaneously Developing Surface Tension Gradient Anoop Chengara, Alex D. Nikolov, and Darsh T. Wasan* Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, Illinois 60616
This article reports the results of experiments conducted on the spontaneous climbing of an aqueous film of trisiloxane surfactants (“superspreaders”) on a vertical strongly hydrophobic solid surface. The final height achieved is much in excess of that expected purely on the basis of the capillary wetting action and suggests that a spontaneously developing surface tension gradient aids in film climbing. Maxima are observed in both the spreading rate and the height achieved as a function of the surfactant concentration, similar to the spreading of a superspreader drop on a horizontal hydrophobic surface. Introduction Trisiloxane surfactants are among the best water spreading agents on hydrophobic surfaces. They are commonly used as adjuvants for agrochemicals. Since the work of Ananthapadmanabhan et al.,1 there have been many studies aimed at understanding the mechanism behind the extent and rate of spreading of aqueous trisiloxane surfactants on hydrophobic surfaces. (For recent reviews, see Hill.2,3) In this article, we report on the spreading characteristics of an aqueous trisiloxane surfactant on a vertical flat plate. The purpose of this study was to verify whether the spreading dynamics of a trisiloxane surfactant on a hydrophobic surface (such as polystyrene) is indeed driven by a spontaneously developing surface tension gradient at the air-liquid interface as proposed in our previous work.4-6 Whereas our previous work focused on the spreading rate and total area achieved by a sessile drop of aqueous trisiloxane on a horizontal hydrophobic surface, here, we examine the rate of climb and the maximum height to which a liquid film of trisiloxane solution will rise on a vertical hydrophobic plate. In this case, the liquid film must climb against the force of gravity, whereas gravity contributes to the spreading rate of a sessile drop. Furthermore, the spreading rate behavior of the liquid film is not limited by the volume of solution (as it was in the case of a sessile drop) because the film is in contact with a large reservoir of solution. A comparison of the spreading behavior of a drop with that of a vertical thin film using the same surfactant solution provides evidence that the spontaneous surface tension gradient drives the rapid spreading of aqueous trisiloxane solutions on hydrophobic surfaces. Most controlled experiments7-9 have depended on the imposition of an external surface tension gradient (usually in the form of a known temperature gradient) to drive a liquid film against the force of gravity. We seek to understand what drives climbing films of aqueous trisiloxane solutions on vertical hydrophobic surfaces and to elucidate the superspreading phenomenon. Materials and Methods The trisiloxane surfactant chosen for this study was the same as reported in our earlier studies, namely, Silwet L77 (a * To whom correspondence should be addressed. E-mail: wasan@ iit.edu. Tel.: 312-567-3001. Fax: 312-567-3003.
commercial form with eight ethoxy groups), obtained from Witco Osi, Tarrytown, NY. Aqueous dispersions were formed by dissolving the surfactant in 18 MΩ cm deionized water obtained from a Millipore filtration unit. The solid surface used in the study was the interior of polystyrene (PS) containers (6.5 cm × 6.5 cm × 13 cm) obtained from Amac Plastic, Sausalito, CA. These containers were chosen for their good optical qualities, as well as their hydrophobicity. Each of these boxes was washed in DI water and dried at room temperature before use in the experiments. On visual inspection, the contact angle of water on these polystyrene surfaces was very close to 90°, making them of the same hydrophobicity as the polystyrene Petri dishes used in the experiments in our previous work. A fresh box was used in each experimental run. A schematic of the experimental setup is shown in Figure 1. Instead of a single plate being immersed in a bath of liquid to serve as a vertical surface for the film to climb, the four walls of the container served as four different vertical surfaces in a single experiment. This approach provided a simple method for assessing the reproducibility of the measurements with less experimental effort. A graduated millimeter scale was attached to one outer face of each box in order to read the instantaneous height of the climbing film. About 2 cm3 of Silwet L77 solution of a specified concentration was dispensed into the bottom of the polystyrene container using a pipet. The dropped solution quickly spread over the bottom surface and began to climb up the walls of the container as soon as it reached them. The front wall of the container was illuminated with diffuse incident white light (Figure 1), and the angle of observation was about 45°. Using this arrangement, the dark front of the climbing film was clearly outlined against the more brightly illuminated background on three of the four faces of the container. The film climbing process was recorded using a Sony TRV-310 digital video camera. The recorded segent was played back, and the height of the liquid film was read from the attached scale at the time displayed on the tape’s counter (of at least 1/30 of a second). There was no appreciable corner effect on the height of the rising film, and the variation among the height readings on the four walls of the container was less than 10%. The optical setup was adjusted to pick up the incident light reflected from two surfaces of the climbing film: the solid/liquid surface and the air/liquid surface. Because of interference between the two reflected light beams, colored fringes were observed toward the end of the spreading process, near the bottom of the film. The order of interference provided information about the thickness of the climbing liquid film.
10.1021/ie070862+ CCC: $40.75 © 2008 American Chemical Society Published on Web 01/30/2008
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Figure 1. Schematic of experimental setup for studying the climbing of a liquid film from a solution of Silwet L77.
hydrostatic pressures. The prediction of the height of the climbing film (L) above the flat interface of a liquid with surface tension σ and density F as a function of the contact angle with the wall (θ) is given by a relation based on the Laplace equation
L)
Figure 2. Final height of climbing film as a function of Silwet L77 concentration.
Experiments were conducted at 25 °C and at two different values of humidity (measured using an Amprobe TH-2 digital hygrometer, Lynbrook, NY). For the set of experiments conducted at 35% relative humidity (RH), no saturation of the container with water vapor was needed. For the set of experiments conducted at 65% RH, a porous pad wetted with water was attached to the lid of the box, and the closed atmosphere was allowed to saturate for about 3 h prior to each experiment. Small droplets of water condensed on the top of the walls during the experiments; a closed atmosphere was maintained by means of a hole in the lid through which the surfactant solution was dosed. We describe the consequences of high humidity in the next section, along with the experimental results. Results and Discussion Maximum Height of the Climbing Film. Figure 2 shows a plot of the maximum height to which the film rose as a function of surfactant concentration for experiments conducted at 35% RH. The final (equilibrium) height was always achieved in less than 3-4 min for all concentrations studied. The final value passed through a maximum at around 0.1 wt %, as was the case for the drop area experiment studied previously.5 This is not surprising given that the solid surfaces on which the spreading occurred in the two sets of experiments were hydrophobic to the same degree. However, it is remarkable that the maximum height to which the film rose was in excess of what would be expected from a balance of only capillary and
x2σFg(1 - sin θ)
(1)
For all concentrations above the critical micelle concentration (CMC), σ ) 22 dyn/cm, and the maximum height achieved corresponds to perfect wetting conditions (i.e., θ ) 0), which, from eq 1, is 0.2 cm. Figure 2 shows that there is an excess force that causes the liquid film to rise above the meniscus limit determined by the capillary/gravity action. This is a significant result because it is difficult to draw conclusions with the same degree of accuracy about the equilibrium radius of a drop perfectly wetting a solid surface (θ ) 0). (This inaccuracy is a consequence of the fact that the solution of the Laplace equation requires large values for the apex curvature that accompany a perfectly wetted drop, which results in a large variation in the calculated radius of the drop for very small changes in the contact angle.10) Although it was not possible to determine whether there was a force in excess of the gravitational and capillary force from the radius measurement of the aqueous Silwet L77 solution drop, the method using the climbing film clearly demonstrates the presence of an excess force (i.e., the surface tension gradient). Experiments conducted by Churaev et al.11 using a 0.16 wt % aqueous solution of a similar surfactant (trisiloxane with eight ethoxy groups, but a methyl end cap) showed that the wetting film climbed beyond the capillary limit on an inclined hydrophobized glass plate. However, although their surface was as hydrophobic as ours (with a water contact angle between 90° and 95°), the maximum distance above the meniscus was only 1.5 cm. The discrepancy might be due to the surfactant’s chemical structure or the fact that the experiments were conducted in a water-saturated atmosphere. However, when we conducted the experiments at 65% RH, we found that the maximum height of the film was about 4.5 cm above the flat liquid interface, even more than that reported in Figure 2. Moreover, it was observed that, under saturation conditions, the maximum height was a very weak function of the surfactant concentration, unlike the curve in Figure 2. Dynamics of Film Climbing. Figure 3 shows a plot of the instantaneous height of the film as a function of time for the
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(surface tension gradient) that was discussed in our previous work. The second scenario is based on the disjoining pressure gradient as proposed by Churaev et al.11 We begin with the Marangoni stress effect. As in the case of a drop, we expect that the surfactant concentration at the airliquid interface near the expanding edge of the film is less than its concentration where the meniscus meets the liquid reservoir. This is reasonable given that the expansion of the interface is closer to the leading edge than the bottom of the film, leading to a local depletion of surfactant at the edge. This nonuniformity in the surfactant concentration leads to a surface tension gradient in the upward direction, causing the film to rise. Cazabat et al.8 showed that there is a region where the climbing film is almost flat and has a thickness (ho) (Figure 1) that is related to the surface tension gradient (τ) as Figure 3. Height of the climbing film as a function of time.
ho ≈
13τ2 σ2C3
(3)
where the curvature at the base of the meniscus (C) is given by
C-1 )
Figure 4. Film climbing rate as a function of Silwet L77 concentration.
0.1 wt % Silwet L77 sample. For most of the spreading process, the height [L(t)] versus time can be approximated with the relation
L(t) ≈ R t1/2
(2)
where the constant (R) takes the value 0.4; this value is close to the value of 0.6 used to fit the radius vs time of a drop for the same Silwet L77 concentration spreading on a horizontal polystyrene surface.5 This again suggests that the spreading behaviors of Silwet L77 (“superspreader”) are very similar, irrespective of geometry (drop vs film) or the action of gravity. The fact that the film’s spreading process continues for much longer is because it is connected to a large reservoir of liquid, unlike a drop. Because the experimental data for height follow the form of eq 2 for all concentrations, the square of the height [L2(t)] varies linearly with time. Figure 4 shows a plot of the climbing rate expressed as the (constant) slope of the L2(t) vs time plot for various surfactant concentrations. The climbing rate shows a maximum as a function of the surfactant concentration, with the peak value occurring at 0.1 wt %, just as in the case of the sessile drop geometry. However, the descending part of the rate curve does not match well with the rate curve of the sessile drop geometry: in the latter case, the decrease in the areal spreading rate is not as sharp a function of surfactant concentration. This is probably due to the water droplet condensation effect on spreading and is explored further in the next section. Mechanism of Film Climbing. In this section, we examine two different scenarios to explain the spreading features reported above. The first scenario we evaluate is the Marangoni effect
x2σFg
(4)
Substituting values for the surface tension (σ) equal to 22 dyn/ cm and the density (F) equal to 1 g/cm3 yields a C-1 value of 0.2 cm-1. Approximately the same value of curvature is obtained if the curvature (0.15 cm-1) is calculated as the inverse of the distance (d) between the two opposite walls of the container, as d ) 6.5 cm. Further, the average rising velocity (U) in the early stages of film climbing (considering that the rate of climbing is driven by the balance between the surface tension stress and viscous force) is given by
U)
τh0 Fgh02 2µ 3µ
(5)
For the 0.1 wt % solution, the average rising velocity in the initial stages is 0.1 cm/s (2 cm covered in 20 s; Figure 3). Using this value for U and solving eqs 3 and 5 gives τ ≈ 1 dyn/cm2 and ho ≈ 2 µm. For comparison, the value of the surface tension gradient regressed from the drop spreading experiment for the same concentration was also between 0.5 and 1 dyn/cm2 in the range of 5-10 s of spreading.5 This close match of the surface tension gradient values in the two different geometries also suggests that the driving mechanism is the Marangoni stress created by a spontaneously developing surface tension gradient at the rim (bump) of the film spreading front. The gravitational term in eq 5 is negligible compared to the surface tension gradient term because of the small value of ho. As a further confirmation on this value of ho, interference patterns of order 7-8 were observed toward the base of the meniscus. Because green and red interference patterns were observed in the reflected white light at the base of the climbing film, a film thickness of about 3-4 µm is implied, and the film is expected to be even thinner in the upper regions. This small value of ho explains why the spreading rates are nearly the same when spreading occurs against gravity (film experiment) as when it occurs in the direction of gravity (drop experiment). It is also interesting to note that, in the case of spreading of a sessile drop, the drop thickness was on the order of a few hundred microns, leading to a higher gravitational forcesbut still consistent with our assumption, this was balanced by a large capillary force. In the film’s vertical spreading, the capillary force is smaller in the early stages but becomes significant in the last stage when the
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spreading front (the bump) breaks into ridges (“fingers”) (see the photograph inset in Figure 1). It appears that, in the early stages of spreading, the climbing film rate is governed by the balance between the meniscus base curvature (capillary force) and the spontaneously developing surface tension gradient; during the last stage of film climbing, the rate is driven by the developing surface tension gradient at the spreading bump and the feedback bump’s capillary pressure. Finally, the liquid film close to the leading edge (the bump) is unstable and breaks up into ridges (see the photograph in Figure 1). This is consistent with the fact that the film thickness (ho) satisfies the condition for film breakup,7 i.e., that it be less than the critical value (hcr) given by
hcr )
3τ ) 8 µm 4Fg
(6)
The calculated value of surface tension gradient (τ ≈ 1 dyn/ cm2) was used in eq 6. As the film climbs, the fingers at the top of the film become clear. The height of the rim of the fingers can be predicted by the Rayleigh instability criterion for a constant surface tension gradient applied to this geometry8
B ) 6hR
(3µU σ )
1/3
(7)
Applying this equation to the experimentally observed spreading velocity, with U ≈ 0.1 cm/s, ho ) 3 µm (as estimated from interference patterns), viscosity of water ) 0.01 g cm/s, and σ ) 22 dyn/cm, the value of the rim height is 0.035 cm, and the distance between adjacent fingers is 4B or 0.13 cm. This predicted distance between fingers correlates well with the experimental value of 0.1 cm and serves as a check for the assumption of a constant surface-tension-gradient-driven flow. The existence of maxima in the climbing rate and the total height as a function of the surfactant concentration supports the Marangoni stress hypothesis. At low concentrations (0.01 wt %), the surfactant is depleted in all regions of the interface, leading to a low spatial tension gradient and a lower rate. At intermediate concentrations (0.05-0.2 wt %), the surfactant is depleted more at the leading edge than near the base of the meniscus, driving the process faster. At very high concentrations (0.5 wt % and higher), the stretching of the interface cannot overcome the high surfactant flux to the interface, leading to a lower tension gradient and lower spreading rate. As discussed above, the spreading rate falls off more rapidly in the case of a film than it does in the case of a drop, as the surfactant concentration increased beyond 0.1 wt %. This might be because gravity (for the drop) aids the spreading, particularly in the initial regime. At high surfactant concentrations, when the surface tension of the drop remains essentially at its lowest value of 22 dyn/cm, the force of gravity actually spreads the drop faster because the capillary pressure resistance is at its lowest. In contrast, such a contribution to the spreading rate from the gravitational force is not available to drive the film vertically upward; gravity always acts to retard the spreading of the film. This difference might account for the fact that the climbing rate of a film decreases more sharply as a function of the surfactant concentration than the spreading rate of a drop. A comment on the effect of humidity on the maximum height is in order. The maximum height to which the film climbed was almost independent of the surfactant concentration at high humidity (65% RH). This is probably because the surface of the wall was covered by small condensed water droplets
surrounded by a thin film of water from the saturated atmosphere. This possibility was suggested by the visible condensation of water drops at the upper reaches of the wall (close to the saturating pad). If this were the case, the rising film would have spread on a thin layer of water instead of on a bare polystyrene surface. The spreading of the film would be akin to that of a monolayer driven by a positive spreading coefficient,12 and the predominant mechanism would not be the Marangoni stress created by a nonuniform surfactant concentration along the length of the interface. This might explain the lack of a well-established maximum in the total height as a function of the surfactant concentration. The experimental conditions of low humidity (35% RH) did not create an additional Marangoni stress due to water evaporation. If this were the case, the evaporation of water would be greater at the thinner edge of the film, leading to an excess concentration of the surfactant at the leading edge relative to that at the base of the meniscus. In this case, the surface tension gradient would be reversed in direction, and the film would not be driven upward, in contradiction to the observed phenomena. The surfactant itself is stable, eliminating any effect of its evaporation on the gradient at low humidity. Thus, it appears that the experiments conducted at low humidity are relevant in understanding the mechanism of spreading of aqueous trisiloxane dispersions. Churaev et al.11 suggested that the disjoining pressure in the film causes the climb observed in our experiments. They postulated that the rising film has two metastable thicknesses: the thinner one at the leading edge stabilized by van der Waals forces and a thicker one behind it, stabilized by the disjoining pressure created by the ordered structure of surfactant vesicles. They further estimated that the driving force for the film motion is given by the linear gradient in the disjoining pressure between these two films. However, in their model, the exact nature of the disjoining pressure isotherm between the thick and thin films is unimportant: only the slope of the straight line connecting the disjoining pressures at the two thicknesses is important. Although Churaev et al. observed a linear dependence of the film height on the square root of time as we did, their climbing velocity showed a maximum value of 0.01 cm/s, which is 1 order of magnitude less than what we observed. Further, to stabilize the thick film, the disjoining pressure was assumed to be created by vesicles with a radius of 20 nm. However, using their value for the surfactant monomer concentration (0.16 wt %), we found a volume fraction of vesicles of only 0.2%. The volume fraction of particles (in this case vesicles) would need to be at least 30% in order for the structural disjoining pressure to be significant, even at a film thickness in the range of tenths of a micrometer (i.e, a few multiples of the diameter of the vesicle). Therefore, we cannot expect the disjoining pressure created by the surfactant vesicles to be strong enough to drive the film at the rate observed in our experiments. Furthermore, as the surfactant concentration increased, the film became more structured with more particle layers, and the film disjoining pressure gradient increased, so no maximum in the spreading rate would be expected. There is another reason for not invoking the presence of a precursor film to explain the observed spreading kinetics as has been done previously.13 Numerical simulations have shown that, irrespective of the kinetics of the spreading of the precursor film, the kinetics of the spreading of the main drop (in a horizontal geometry) is unaffected14 and is described by the classical Tanner’s law, R ∼ t1/10. The measured spreading rate of the macroscopic drop in our experiments was much higher, i.e., R ∼ t1/2, a phenomenon that cannot be
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explained by the rate of spreading of the precursor film. Further, as discussed in a previous work,5 this is unable to explain the observed rate of spreading, either because of the slow kinetics of rearrangement of molecules in the precursor film15 or because of the high disjoining pressures required to stabilize the suggested precursor film.11 The same explanation is expected to be valid for the case of vertical film spreading because the solid surface characteristics are the same, as are the observed experimental spreading rates, and they show the same dependence on surfactant concentration. From the above analysis, it appears that the surface-tensiongradient-driven mechanism explains the climbing rate behavior better than the disjoining-pressure-gradient-driven mechanism. Two further points need to be made with regard to the surface tension gradient mechanism. First, one might expect the film height to decrease from its maximum value after the surface tension gradient has died out because of surfactant transport to all parts of the surface. This was not observed until 5 min had elapsed, and it probably occurred as a result of hysteresis on the solid surface resulting in the pinning of the contact line. We did observe the drainage of the film due to gravity at longer times (∼1 min), as seen from the interference pattern near the base of the meniscus; however, this was not accompanied by the retraction of the contact line. Rather, at longer times, the evaporation of water occurred near region of the contact line, effectively preventing its downward movement. It must be emphasized that we do not claim a failure of eq 1 in describing the equilibrium state of the system. Our results are applicable only in the transient regime. The equilibrium state of the system, i.e., the final spreading height, is difficult to measure because of hysteresis effects due to drainage of the vertical film by gravity and the pinning of the contact line. The situation is further exacerbated by the small thickness of the final wetting film, which is different from the thick spreading film that was observed visually and measured in our experiments. The second point refers to the initiation of the Marangoni process. In the case of the drop geometry, it was hypothesized that the tension gradient is initially created by gravity pressing the drop onto the solid surface. However, such an explanation is not valid for a film rising against the force of gravity. A better explanation for the initiation of the tension gradient appears to be the stretching of the three-phase contact region due to the wetting of the solid surface by the surfactant solution through capillary action. However, the capillary action alone is inadequate to explain the observed high rate of spreading or the maximum in the area (or height) as a function of the surfactant concentration, resulting in the need to invoke a mechanism driven by Marangoni stress (surface tension gradient).
Conclusions This study was undertaken to verify whether the surfacetension-gradient-driven mechanism proposed in our previous work4-6 explains the superspreading behavior of aqueous Silwet L77 solutions. In this work, we allowed the surfactant solution to climb a vertical plate in the form of a thin film. The major differences from the sessile drop studied in the previous work are that the vertical spreading here was not limited by the availability of the fluid and the climbing of the film was opposed by the capillary force rather than gravity. The solid surfaces used in this set of experiments were polystyrene of the same hydrophobicity (water contact angle ) 90°) as the Petri dishes in the drop spreading experiments. We observed that the height of the climbing film also followed
a square root law as a function of time, just as the radius of the drop did. The rate of climb of the film was very close to the rate of spreading of the drop, implying that the influence of the gravitational force was quite small. Additionally, the rate of climb passed through a maximum as a function of surfactant concentration, consistent with the observations on the spreading drop. The final height of the film also showed a maximum with respect to the surfactant concentration and, for all concentrations studied, was in excess of that expected from a balance of capillary and hydrostatic forces. The excess force driving the movement of the film could possibly be the spontaneous surface tension gradient that arises from the inability of the surfactant molecules to rearrange from a bulk configuration to the equilibrium surface configuration in the region of the expanding interface. Indeed, a simple calculation of the surface tension gradient required to move the film at the rate observed experimentally showed that it is very close in magnitude to that required to move the spreading drop at the experimentally observed rate. The driving force is dependent only on the surfactant concentration, consistent with the physical picture of the origin of the tension gradient. An alternate possibility based on the disjoining pressure gradient in the climbing film does not adequately explain the observed spreading rate data. It appears that the salient features of the spreading of aqueous trisiloxane dispersions can be rationalized in terms of the model of a spontaneously generated surface tension gradient. The gradient is attributed to the molecular structure of the superspreaders, particularly for their ability to maintain the surface tension gradient at the spreading edge. More work needs to be done to identify the reasons why trisiloxane surfactants are able to sustain the surface tension gradient whereas other nonionic surfactants are not able to do so.
Acknowledgment Financial support for this study was provided by the National Science Foundation, Grant CTS-0553738.
Literature Cited (1) Ananthapadmanabhan, K. P.; Goddard, E. D.; Chandar, P. A Study of the Solution, Interfacial and Wetting Properties of Silicone Surfactants. Colloids Surf. 1990, 44, 281. (2) Hill, R. M. Superspreading. Curr. Opin. Colloid Interface Sci. 1998, 3, 247. (3) Hill, R. M. Silicone SurfactantssNew Developments. Curr. Opin. Colloid Interface Sci. 2002, 7, 255. (4) Nikolov, A. D.; Wasan, D. T.; Chengara, A.; Koczo, K.; Policello, G. A.; Kolossvary, I. Superspreading Driven by Marangoni Flow. AdV. Colloid Interface Sci. 2002, 96, 325-338. (5) Chengara, A.; Nikolov, A.; Wasan, D. Surface Tension Gradient Driven Spreading of Trisiloxane Solution on Hydrophobic Solid. Colloids Surf. A: Physicochem. Eng. Aspects 2002, 206, 31. (6) Chengara, A.; Nikolov, D.; Wasan, D. Spreading of Water Drop Triggered by Surface Tension Gradient Created by Localized Addition of Surfactant. Ind. Eng. Chem. Res. 2007, 46, 2987. (7) Ludviksson, V.; Lightfoot, E. N. The Dynamics of Thin Liquid Films in the Presence of Surface Tension Gradients. AIChE J. 1971, 17, 1166. (8) Cazabat, A. M.; Fournier, J. B.; Carles, P. Wetting Films Driven by Surface Tension Gradients. In Fluid Physics; Velarde, M. G., Christov, C. I., Eds.; Non-linear Science Series B; World Scientific: Singapore, 1995; Vol. 5. (9) Kataoka, D. E.; Troian, S. M. A Theoretical Study of Instabilities at the Advancing Front of Thermally Driven Coating Films. J. Colloid Interface Sci. 1997, 192, 350. (10) Hartland, S.; Hartley, R. W. Axisymmetric Liquid-Liquid Interfaces; Elsevier: Amsterdam, 1976.
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(11) Churaev, N. V.; Esipova, N. E.; Hill, R. M.; Sobolev, V. D.; Starov, V. M.; Zorin, Z. M. The Superspreading Effect of Trisiloxane Surfactant Solutions. Langmuir 2001, 17, 1338. (12) Joos, P.; Van Hunsel, J. Spreading of Aqueous Surfactant Solutions on Organic Liquids. J. Colloid Interface Sci. 1985, 106, 161. (13) Stoebe, T.; Hill, R. M.; Ward, M. D.; Scriven, L. E.; Davis, H. T. Surfactant Enhanced Spreading. Langmuir 1996, 12, 337. (14) Haley, P. J.; Miksis, M. J. The Effect of the Contact Line on Droplet Spreading. J. Fluid Mech. 1991, 223, 57.
(15) Tiberg, F.; Cazabat, A. M. Spreading of Thin Films of Ordered Nonionic Surfactants: Origin of the Stepped Shape of the Spreading Precursor. Langmuir 1994, 10, 2301.
ReceiVed for reView June 22, 2007 ReVised manuscript receiVed November 27, 2007 Accepted December 4, 2007 IE070862+
