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Langmuir 1997, 13, 7258-7264
The Spreading of Silicone Oil Droplets on a Surface with Parallel V-Shaped Grooves Stina Gerdes,*,† Anne-Marie Cazabat,‡ and Go¨ran Stro¨m§ Institute for Surface Chemistry, P.O. Box 5607, S-114 86 Stockholm, Sweden, Colle` ge de France, 11, Place Marcelin-Berthelot, 75231 Paris Cedex 05, France, and Stora Corporate Research AB, S-791 80 Falun, Sweden Received February 11, 1997. In Final Form: September 29, 1997X In this paper we report on dynamic wetting studies on model rough surfaces. A series of well-defined model surfaces has been manufactured, and the dynamic wetting of silicone oil droplets on these surfaces has been studied. The surface structures are etched, parallel, V-shaped grooves with varying width and spacing. Spreading has been studied in two different time regimes with two different techniques. At “short times”, the liquid does not penetrate significantly inside the grooves ahead of the edge of the main drop. At “long times”, the penetration of liquid inside the grooves is significant and the grooves are practically filled up at the edge of the main drop, which we consider as the “contact line”. In both regimes, contact line velocity, v, and dynamic contact angle, θ, are measured in the flat parts between grooves. The spreading parallel to the grooves is described by Tanner-like laws in both cases but with different characteristics: At short times, the spreading velocity increases with the area covered by grooves. At long times no effect of the grooves is observed until the distance between the grooves is smaller than approximately 30 µm. In this case, it appears that the effect is correlated with the disturbance of the contact line due to the interaction of the groove “defects”.
Introduction Dynamic wetting of rough surfaces is important in many industrial applications, for example, printing and coating. A common problem in newsprint and inkjet printing1 is when the ink spreads faster in the narrow grooves formed between the fibers than on the smoother areas of the surface, which may give rise to bad print quality. The problem is pronounced in water-based gravure, where the inks dry slower and are less viscous than in many other printing processes. There is a need to understand how the dynamics of liquid spreading is affected by surface roughness. Wetting on rough surfaces has been studied for at least 60 years, when Wenzel did his pioneering work on effects of surface roughness on the static contact angle.2 However, while the dynamics and kinetics of wetting have been studied extensively on smooth surfaces,3-36 very few * Author to whom correspondence is addressed. † Institute for Surface Chemistry. ‡ Colle ` ge de France. § Stora Corporate Research AB. X Abstract published in Advance ACS Abstracts, November 15, 1997. (1) Wa˚gberg, P.; Wågberg, L. Ink Jet Printing on Uncoated Fine Papers. 1996 International Printing and Graphic Arts Conference, Minneapolis, MN, 1996; TAPPI Press: Atlanta, GA, 1996; p 187. (2) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988. (3) Blake, T. D. The Contact Angle and Two Phase Flow. Ph.D. Thesis, University of Bristol, 1968. (4) Blake, T. D.; Haynes, J. M. J. Colloid Interface Sci. 1969, 30, 421. (5) Brenner, M.; Bertozzi, A. Phys. Rev. Lett. 1993, 71, 593. (6) Brochard-Wyart, F.; Hervet, H.; Redon, C.; Rondelez, F. J. Colloid Interface Sci. 1990, 142, 518. (7) Brochard-Wyart, F.; de Gennes, P. G. Adv. Colloid Interface Sci. 1992, 39, 1. (8) Cazabat, A. M.; Cohen-Stuart, M. A. PhysicoChem. Hydrodyn. 1987, 9, 23. (9) Cazabat, A. M.; Cohen-Stuart, M. A. Mol. Cryst. Liq. Cryst. 1990, 179, 99. (10) Cazabat, A.-M. Adv. Colloid Interface Sci. 1992, 42, 65. (11) Chen, J.-D. J. Colloid Interface Sci. 1988, 122, 60. (12) Cherry, B. W.; Holmes, C. M. J. Colloid Interface Sci. 1969, 29, 174. (13) Cox, R. G. J. Fluid Mech. 1986, 168, 169. (14) de Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827. (15) Dodge, F. T. J. Colloid Interface Sci. 1988, 121, 154. (16) Hayes, R. A.; Ralston, J. Langmuir 1994, 10, 340. (17) Hayes, R. A.; Ralston, J. Colloids Surf., A 1994, 93, 15. (18) Hocking, L. M.; Rivers, A. D. J. Fluid Mech. 1982, 121, 425.
S0743-7463(97)00139-X CCC: $14.00
studies have been reported on dynamic wetting of rough surfaces.37-47 . In this paper we report on dynamic wetting studies on a series of structured surfaces that models those of a paper surface. Paper is a fibrous material, and on the surface of an uncoated paper a network of grooves is formed between the fibers. The model material is made from smooth oxidized silicon wafers with etched, parallel, V-shaped grooves. The groove widths range from 5 to 90 (19) Hocking, L. M. Q. J. Mech. Appl. Math. 1983, 36, 55. (20) Hocking, L. M. J. Fluid Mech. 1992, 239, 671. (21) Hoffman, R. L. J. Colloid Interface Sci. 1983, 94, 470. (22) Kalliadasis, S.; Chang, H.-C. Phys. Fluids 1993, 6, 12. (23) Lopez, J.; Miller, C. A.; Ruckenstein, E. J. Colloid Interface Sci. 1976, 56, 460. (24) Marmur, A. Adv. Colloid Interface Sci. 1983, 19, 75. (25) Ngan, C. G.; Dussan, V. E. B. J. Fluid Mech. 1982, 118, 27. (26) Petrov, J. G.; Radoev, B. P. Colloid Polym. Sci. 1981, 259, 753. (27) Petrov, P. G.; Petrov, J. G. Langmuir 1992, 8, 1762. (28) Petrov, J. G.; Sedev, R. V. Colloids Surf. 1993, 74, 233. (29) Ruckenstein, E. J. Colloid Interface Sci. 1995, 170, 284. (30) Shikhmurzaev, Y. D. Fluid Dyn. Res. 1994, 13, 45. (31) Starov, V. M.; Kalinin, V. V.; Chen, J.-D. Adv. Colloid Interface Sci. 1994, 50, 187. (32) Summ, B. D.; Yushchenko, V. S.; Shchukin, E. D. Colloids Surf. 1987, 27, 43. (33) Tanner, L. H. J. Phys. D: Appl. Phys. 1979, 12, 1473. (34) Teletzke, G. F.; Davis, H. T.; Scriven, L. E. Chem. Eng. Commun. 1987, 55, 41. (35) Thompson, P. A.; Brinckerhoff, W. B.; Robbins, M. O. J. Adhes. Sci. Technol. 1993, 7, 535. (36) Voinov, O. V. Fluid Dyn. 1976, 11, 714. (37) Cazabat, A. M.; Cohen Stuart, M. A. J. Phys. Chem. 1986, 90, 5845. (38) Cox, R. G. J. Fluid Mech. 1983, 121, 1. (39) Fraaije, J. G. E. M.; Cazabat, M.; Hua, X.; Cazabat, A. M. Colloids Surf. 1989, 41, 77. (40) Gerdes, S.; Stro¨m, G. Colloids Surf., A 1996, 116, 135. (41) Lenormard, R.; Zarcone, C. Role of roughness and edges during imbibition in square capillaries. 59th Annual Technical Conference of the SPE, Houston, TX, 1984. (42) Mann, J. A. J.; Romero, L.; Rye, R. R.; Yost, F. G. Phys. Rev. E 1995, 52, 3967. (43) Marsh, J. A.; Cazabat, A. M. Phys. Rev. Lett. 1993, 71, 2433. (44) Rye, R. R.; Mann, J. A., Jr.; Yost, F. G. Langmuir 1996, 12, 555. (45) Yost, F. G.; Michael, J. R.; Eisenmann, E. T. Acta Metall. Mater. 1995, 43, 299. (46) Bouillault, A.; Cazabat, A. M.; Cohen Stuart, M. A. C. R. Acad. Sci., Se´ r. II 1986, 301, 525. (47) Cazabat, A. M.; Cohen Stuart, M. A. C. R. Acad. Sci., Se´ r. II 1985, 301, 1337.
© 1997 American Chemical Society
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µm, and the distance between the grooves varies from 10 to 1000 µm. Dynamic wetting is studied by following how a small silicone oil droplet spreads out over the model surface. Spreading was studied in two regimes: The fast spreading of the droplet at high spreading velocities was studied as a function of the apparent dynamic contact angle, obtained from the silhouette of the spreading droplet. At low contact angles, the local dynamic contact angle between the grooves is measured by an interferometric technique. The materials were chosen such that the liquid spreads out completely over the solid surface. Hence, we are dealing with complete wetting and equilibrium contact angles of 0°. Theoretical Background Spreading on smooth surfaces has been investigated for many years, and there exist two fundamentally different approaches for the interpretation of the obtained data. Tanner,33 de Gennes,14 Cox,13 Voinov,36 and Starov et al.31 have derived an approximate expression for liquid spreading from hydrodynamic considerations, in some cases supplemented by disjoining pressure terms.14,31 This mesoscopic approach is in contrast to the molecular theory put forward by Blake and Haynes3,4 and Cherry and Holmes,12 who consider the adsorption/desorption kinetics of the fluid phases as the liquid front advances over the surface. This theory, which can predict spreading behavior at high contact angles, is mostly used in forced spreading. It is shown here that it is possible to fit spreading data on model rough surfaces as a function of the same type of hydrodynamic derivation that those by Tanner, Cox, de Gennes, Voinov, and Starov13,14,31,33,36 yield for smooth surfaces. The derivation is outlined below. Consider a liquid droplet thin enough that the flow of liquid as the drop spreads out can be approximated as one-dimensional, i.e., where the pressure, P, is constant in the vertical direction, z, and where inertial forces may be ignored. The lubrication approximation of the NavierStokes equations23,33,36 allows one to calculate the spreading velocity vx in the droplet in the x-direction, assuming that the dependence of film thickness, h, on radial position is small enough (i.e., the slope of the interface ,1).
0)-
∂2vx ∂P +η 2 ∂x ∂z
(1a)
∂P ∂z
(1b)
0)-
Then vx is obtained by integrating eq 1a twice with respect to z. The mean velocity, v, is then given by the expression
v)-
2
3
1 ∂P z h ∂P ∫0hvx dz ) - ηh ∫ ∂x 2 dz ) - 3η ∂x
1 h
(2)
The pressure difference in the x-direction is the driving force for spreading. ∂P/∂x is a sum of several contributions
∂3h ∂π ∂h ∂P ) -Fg - γlv 3 + ∂x ∂x ∂x ∂x
(3)
where F, γlv, and g refer to liquid density, surface tension, and gravitational acceleration, respectively, and π refers to the disjoining pressure. Several authors have derived the time dependence of the radius and contact angle of a spreading droplet. As the droplet spreads out, different kinetic regimes are encountered depending on the forces that dominate the spreading. The capillary pressure is the main driving
force for spreading11,32,33 when gravity can be ignored. The disjoining pressure term plays only when the droplet is very thin and can therefore be ignored in this study. For this situation eq 2 can be solved by introducing eq 3. When the solutions10 by de Gennes,14 Tanner,33 Voinov,36 and Cox13 are combined, an approximate formula for the dynamic contact angle θ of a liquid wedge spreading on a dry surface can be derived
(
θ3 - θeq3 ) 9Ca ln
R +Q Λ
)
(4)
where Ca, the capillary number, refers to the dimensionless quantity ηv/γlv, R is a typical length scale of the system, θeq is the equilibrium contact angle, and Λ is a microscopic cutoff which has to be introduced in order to avoid a singularity in the solution. Q is a dissipative term which originates from the Cox derivation and refers to the dissipation at the contact line. Q is zero for complete wetting systems.13 For complete wetting, eq 4 can be written as
θ3 ) 9Ca ln
R Λ
(5)
The length Λ depends on Ca. In the de Gennes14 analysis
Λ ≈ a(Ca)-2/3
(6)
where a is a molecular length. Equation 5 then becomes
(
θ3 ) 9Ca ln
R 2 + ln Ca a 3
)
(7)
As Λ plays only in a logarithmic term, eqs 5 and 7 are often approximated to the so-called Tanner law
θ3 ≈ 9K(Ca)
(8)
where K is approximately constant. The Tanner law has been shown to be valid up to dynamic contact angles of 150°.36 The Tanner law is also the result of the zero-order approximation of a more general treatment of the problem, where the movements of the three phase contact line are treated with perturbation theory, as described by Cox.13 Among the few studies on spreading dynamics on rough or structured surfaces are refs 37-47. When Bouillault, Cazabat, and Cohen Stuart37,46,47 studied spreading of PDMS droplets on roughened glass surfaces, they found the same time dependence of the main drop radius as was previously observed for the spreading on smooth glass surfaces in the gravity-controlled spreading regime, i.e., R(t) ∝ t1/8. Ahead of the droplet they also observed a rim of liquid, spreading in the roughness. This film was spreading at a steady rate Rrim(t) - Rdrop(t) ) ∆R(t) ∝ t1/2, implying that a constant capillary pressure is the driving force for spreading of the film. Lenormand and Zarcone41 have also predicted faster spreading in roughened capillaries, especially at low capillary numbers in their theoretical study of spreading and displacement in a gridlike network of capillaries. In a theoretical study on a surface with parallel shallow grooves, Cox38 predicts faster spreading in the direction of the grooves and slower spreading perpendicular to them. All studies were performed with complete wetting liquids. Bouillault et al.46 studied the spreading on smooth hydrophobic glass surfaces of liquids which had equilibsmooth , ranging from zero to 45°. rium contact angles, θeq smooth Liquids with θeq up to about 20° were all found to spread completely on the hydrophobic roughened glass
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surfaces. Moreover, the spreading of the rim of liquid in front of the macroscopic droplet was independent of smooth θeq . This has been verified for the SnPb solder/Cu surface system studied by Yost et al.45 A SnPb solder smooth droplet with θeq ) 30° on a Cu surface spread out completely on a roughened Cu surface. Methods Fast Regime. A Fibro dynamic absorption tester 1100 (Fibro Systems AB, Stockholm, Sweden) was used to monitor the drop shape versus time. This equipment, originally developed for parallel studies of dynamic wetting and absorption in paper surfaces, was modified for the use of solid surfaces in general. The instrument is used to measure contact angles and to study fast absorption and wetting processes. During the first second of measurement the analyzing unit of the dynamic absorption tester collects 50 images of the spreading drop, i.e., one image every 20 ms, with the shutter open for 1 ms. Slower processes, over several minutes, can be followed as well, with 5-10 images collected every 1s. A predefined volume is pumped out by a motor attached to a syringe containing the liquid. The syringe is connected via a Teflon capillary to a thin needle on which the droplet is formed. The needle has inner and outer diameters of 0.2 and 0.5 mm, respectively. It is coated with Teflon to prevent any liquid from remaining outside the tip. The drop is applied on the surface by a short stroke from an electromagnet. The strength of the stroke was kept at a minimum in order to avoid effects on the spreading process. A strong stroke will cause an oscillation of the drop height in the few images after application. No such oscillations were observed in our measurements; the first few images were nonetheless omitted to ensure that these effects were not incorporated in the data. The instrument setup is such that rectangular surfaces are easily aligned along a wall parallel to the camera. The images from the video camera are evaluated by an image analysis system, which measures the base width and height of the droplet. The drop silhouette is always well-defined and not distorted from the grooves at the length scale observable here. From these parameters the contact angle is calculated and the data are stored on the hard disk. The high-speed video camera is connected to a display on which the spreading process is visualized. The pixel width is 15.8 µm and the height is 12.6 µm. The maximum errors in width and height are therefore 32 and 25 µm, respectively. For base widths over 3 mm the absolute error is hence less than 1%. Low-Velocity Regime. Since the silicon surfaces are reflecting light and the silicone oil is transparent, an interferometric pattern can be observed as the liquid spreads over the flat surface. Each fringe represents a constant thickness of the liquid and the distance between two fringes corresponds to a change in thickness by λ/2n, where λ is the wavelength of the reflected light and n is the refractive index of the liquid. A green filter was used to filter the light beam to a wavelength band around 546 nm. The contact angle was calculated from the measurement of the distance between the fringes close to the contact line. The spreading experiments were recorded at a magnification of 600× in real time by a CCD camera attached to a OPTIPHOT-2 Nikon microscope. Individual frames were analyzed by an image analysis software, NIH image. The distance between the fringes was measured, and thus the contact angle was calculated on the flat surface at the midpoint between the grooves perpendicular to the advancing front and is presented as a function of spreading velocity.
Figure 1. Profile of the liquid in a channel, approximately 17 s after drop application. Each step corresponds to a height difference of 0.14 µm. The width of the groove is 40 µm. Note that the z-scale is around 20× the scale of the x and y axes. The pattern is obtained using a Mirau lens.
Profile of Liquid in Grooves. The profile of the liquid in the grooves in Figure 1 is calculated from the distance between the fringes as observed with a Mirau lens. In the Mirau lens the interferometric pattern is obtained from a reflection of the light between the liquid surface and a semitransparent mirror in the lens. The distance between the fringes then corresponds to a height difference of λ/2n, where λ is the wavelength of the reflected light and the refractive index n then is the refractive index of the air. This technique allows the study of the liquid surface topography over a nonreflecting solid surface or of thick liquid layers. The images were recorded on a VCR and then analyzed in an image processing program, where the constant distance between the fringes was transferred to a threedimensional surface. Materials Surfaces. The surface structures are chemically etched on thin silicon wafers. The measurements presented here are made on surfaces with parallel surface grooves, with different widths and spacings. Due to the crystal structure of silicon, the etched grooves become V-shaped and meet the horizontal surface with a 54° angle. After etching, a silicon oxide layer was deposited on the surface to ensure a uniform surface free of possible heterogeneities obtained in the etching process. The chemical vapor deposition is performed in a reactor at atmospheric pressure at a temperature between 300 and 350 °C. Gas-phase SiH4 and oxygen are introduced to form a solid silicon oxide layer. The thickness of the silicon oxide layer is between 1000 and 1500 Å. All surfaces were examined by a Philips SEM 505 scanning electron microscope. An atomic force microscope was also used to check the surfaces. The exact groove widths and spacings were calculated from the SEM pictures. These are presented in Table 1. The surfaces were also examined in order to identify any defects. Very few defects were found, and it was in all cases possible to localize a defect-free area for the spreading measurements. The surfaces were prepared by Department of Solid State Electronics, Chalmers University of Technology. Liquid. The liquid is a silicone oil from Brookfield (Engineering Laboratories, Inc., Stoughton, MA) with a standard viscosity of 995 mPa‚s and surface tension of 20 mN/m. The silicone oil used in the SEM image in Figure 2 is from the same manufacturer but has a viscosity of 4995 mPa‚s.
Results A SEM image of the spreading silicone oil droplet on the model surfaces is shown in Figure 2. The image is taken a few minutes after drop application and corresponds to the low-velocity region. The volume of liquid inside the grooves when they are completely filled has been calculated and compared to the typical volume of a droplet. This volume was found to be negligible.
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Table 1. Dimensions of the Grooves, Manufacturers Width and Spacing, and the Width and Spacing As Measured from SEM Images surface
nominal width (µm)
nominal spacing (µm)
measured width (µm)
measured spacing (µm)
1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 2-1 2-3 2-8 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8
5 5 5 5 5 5 10 10 5 5 10 10 10 20 20 40 40 20 80
10 20 50 100 200 1000 20 50 10 50 50 100 200 50 200 50 200 100 200
6.8 6.7 6 5.60 6.3 7.1 12.5 11 5.5 5.30 12 12 12 25 24 46 46 23.7 90
12 24.9 56.8 100 230 1 mm 23.2 53 10.4 54 55 100 207 53 212 54 214 107 214 est.
Figure 2. SEM image of a spreading silicone oil droplet on a model surface.
High-Velocity Regime. In the high-velocity regime the contact angle and spreading velocity is obtained from the silhouette of the spreading droplet as described in the experimental section. A silicone oil droplet spreading on a smooth homogeneous surface will spread uniformly in all directions, and when capillarity is the main driving force, the droplet will take the shape of a spherical cap. In our case, spreading parallel to the grooves is enhanced while the liquid is rather reluctant to spread across the grooves. In fact, the liquid stops spreading perpendicular to the grooves very soon after droplet application. The base width and dynamic contact angle measured parallel and perpendicular to the grooves for a spreading droplet on a grooved surface is shown in Figure 3a,b. The base width of the droplet increases rapidly parallel to the grooves, while the droplet stops spreading perpendicular to the grooves after about 1-2 s. On this surface it corresponds to about 10 grooves. Figure 3b shows that the apparent dynamic contact angle, θapp, is around 55° when the spreading stops. The decrease in θapp perpendicular to the grooves after spreading has stopped is due to drainage in the other direction. In the following only spreading parallel to the grooves will be considered. In Figure 4 the spreading velocity is shown as a function of the apparent dynamic contact angle, θapp, for measurements performed on a series of grooved
Figure 3. (a) Base width of a droplet spreading parallel and perpendicular to the grooves on the 10/100 surface. (b) Dynamic contact angle of a droplet spreading parallel and perpendicular to the grooves on the 10/100 surface.
surfaces with the same spacing, 50 µm, but different widths of the grooves, 5, 10, and 40 µm. The spreading on a smooth surface is shown for comparison. The effect of channel size is pronounced when the grooves are very wide, while the difference is small when the groove width is relatively small. At the 40/50 surface the spreading velocity at θapp ) 40° is approximately twice the spreading velocity of the smooth surface. The Tanner law (eq 8) was verified for spreading on the smooth surface. The data are shown in Figure 5 as θapp 3 versus xv together with data from the model surfaces. It was found that the spreading on the model surfaces also displays a straight line when plotted as θapp versus x3 v; however it shifted along the x-axis. In fact, data from the spreading measurements on all the surfaces can be described with an equation of the form
v1/3 ) k1θ + k2
(9)
k1 appears to be roughly constant for all the groovy surfaces except the roughest one, the 40/50 surface. k2 and therefore the x-axis intercept θ0 ) -k2/k1 is, however, not constant. On the contrary, this shift is correlated with the fraction of the surface area covered by grooves. In Figure 6a the shift θ0 is shown vs the fraction of the surface covered by grooves, Xgroove, i.e., groove width/spacing. The
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Figure 4. Spreading velocity, v, versus the apparent dynamic contact angle, θapp, for a silicone oil droplet spreading parallel with the grooves on the 5/50, 10/50, and 40/50 surfaces plus the smooth surface.
Figure 6. (a) x-axis intercept of eq 9, θ 0, versus the fraction of the surfaces covered by grooves, Xgroove. The interpolation of θ0 to Xgroove ) 1 appears to be correlated with 90° - 54° ) 36°. (b) Prefactor to the Tanner law, k1 in eq 9, versus Xgroove.
Figure 5. Cubic root of the spreading velocity, v1/3, versus the apparent dynamic contact angle for the 5/50, 10/50, and 40/50 surfaces.
extrapolated value of θ0 to Xgroove ) 1 (the broken line in Figure 6a) is compatible with the slope of the groove walls (see the Surfaces section), 90° - 54° ) 36°. For completeness k1 is shown versus Xgroove in Figure 6b. The prefactor of the Tanner law, k1, deserves some attention. The value of the prefactor was calculated from the measurements and compared to the value predicted by the analysis of Cox and de Gennes.10,13,14 From eq 5 the prefactor is 9 ln (R/Λ). R is the macroscopic length scale and is approximately 1 mm, while the molecular length scale Λ is on the order of a nanometer, which makes the prefactor around 120. The prefactors calculated from the measurements were for the smooth surface 0.010 25 and for the grooved surfaces about 0.009 75, which correspond to 99 and 115 in the units of eq 8. Low-Velocity Regime. In the high-velocity regime we studied the apparent dynamic contact angle, θapp,
calculated from the macroscopic dimensions of the droplet. In the later stages of spreading, when the dynamic contact angle is low, we were able to study the local dynamic contact angle on the flat surface between the grooves with an interferometric technique, as described in the experimental section. The highest contact angle that could be measured with the interference technique is just above 10°. When the droplet reaches this contact angle, the spreading velocity is less than the velocity with which the liquid spreads in the grooves. They are therefore filled up with liquid ahead of the macroscopic drop front. The local contact angles at the flat parts between the grooves were measured as a function of the local velocity of that particular segment of the contact line. A snapshot of the liquid front on the 20/50 surface is shown in Figure 7. Just as in the highvelocity regime, a smooth surface was studied for reference purposes. In Figure 8 v1/3 ∝ θlocal is shown for the smooth reference surface and the 5/20, 10/20, and the 10/200 model surfaces. The Tanner law was again verified for the smooth surfaces; moreover, the data from the surfaces with a large spacing could not be distinguished from the data from the smooth surfaces. However, when the flat areas between the grooves become more narrow, the spreading rate increases. In the high-velocity region the prefactor k1 in eq 9 was
Spreading of Silicone Oil Droplets
Figure 7. Example of the interferometric pattern observed between the grooves in the low-velocity regime. Surface 20/50. The grooves appear dark since they are too deep for interference patterns to be observable, and the reflected intensity is low in comparison with the flat smooth parts. The liquid is moving from the top to the bottom.
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Figure 9. Prefactor to the Tanner law, k1, from linear regression of eq 9 to the low-velocity data. The open symbol refers to the smooth surface.
Conclusions and Summary
Figure 8. v1/3 versus local dynamic contact angle (low-velocity regime) for the 10/20, 5/20, 10/200, and smooth reference surfaces.
roughly constant for all surfaces except the very roughest (the 40/50 surface). In the low-velocity region k1 is still constant at large spacing. However, when the flat areas between the grooves become more narrow, k1 increases rapidly. In Figure 9 k1 from eq 9 is shown versus the distance between the grooves for the low-velocity data. The increase in k1 is correlated with the curvature of the liquid front. When the spacing is large, the liquid front is undisturbed by the grooves at the midpoint between the grooves, but when the distance between the grooves is smaller, the disturbances from the grooves (curvature of the contact line) overlap and the contact line is disturbed at the midpoint between the grooves where the contact angle is measured. Interaction between the grooves appears to start when the distance between the grooves is approximately 30 µm and increases rapidly as the spacing decreases. These results are in line with the results by Marsh et al.43,48 where they studied the effect of individual heterogeneity defects on liquid spreading and also found an onset of contact line curvature effects at around 30 µm. (48) Cazabat, A.-M.; Heslot, F. Colloids Surf., A 1990, 51, 309.
The spreading of an oil droplet was studied on a series of model rough surfaces, with parallel grooves of different width and spacing. At short time an automatic equipment, the DAT, was employed. The DAT calculates the base and the contact angle from the silhouette of the droplet. The liquid was found to spread faster in the direction of the grooves when the grooves were larger and more closely spaced. No spreading perpendicular to the grooves was observed except during the seconds after droplet application. The contact angle versus spreading velocity parallel to the grooves was found to follow the Tanner law on the grooved surfaces; however, it shifted along the x-axis by a constant amount, θ0, which was found to correlate with the relative surface area covered by grooves, Xgroove, rather than the size or spacing of the grooves. Several surfaces with the same Xgroove but with different groove witdths, and therby different spacing yield the same θ0. The liquid does not penetrate very far into the grooves ahead of the macroscopic contact line during this regime; however, the drop front is rather distorted. A profile of the drop front in a groove after approximately 17 s after drop application is shown in Figure 1. This is in the end of the high-velocity regime. The grooves start to be filled up at the drop front around 60-120 s depending on the groove size. At long times when the grooves are filled, we were able to measure the local dynamic contact angle as a function of spreading velocity on the smooth areas between the grooves. The Tanner law is obeyed in this regime as well, and no effect of the grooves can be seen until the grooves are very close together. An increase in the prefactor to the Tanner law, k1 in eq 9, was found when the distance between the grooves approached 30 µm. The drop front is not distorted when the grooves are filled; however, the contact line has an intricate shape. The grooves can be regarded as defects which do not play until the defect density is high enough for the defects to interact, i.e., the curvature of the contact line caused by the grooves overlap, which appears to occur around 30 µm. Then the prefactor in the Tanner law increases rapidly with spacing; see Figure 9. When the grooves are liquid filled at the drop front, the friction between the spreading liquid and the solid surface is reduced, since the liquid is essentially spreading on itself. However, no correlation of k1 to the fraction of the surface area covered by grooves, Xgroove, could be found. This might
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rather large, and the (2/3) ln Ca term in eq 7 that emerges when substituting eq 6 into eq 5 cannot be ignored. While the change in Ca is roughly (5)3, i.e., 125 (corresponding to a change in v from 1 to 0.008 mm/s), the (2/3) ln Ca term changes from -2 to -5.2, i.e., a change of 3.2. This yields a difference in K/9 (see eq 8) from, at large velocities, K/9 ≈ 12.8 to, at low velocities, K/9 ≈ 12.8 - 3.2 ≈ 9.6; the ratio 12.8/9.6 is 1.33, which is compatible with experimental data. In Figure 10 data for the two regions are plotted on the same graph for spreading on the surface 40/200 and are compared to the low- and high-velocity regions of the smooth surface. A crossover region can clearly be observed for the groovy surface. The crossover is believed to depend on the point where the liquid in the grooves starts spreading decoupled from the macroscopic droplet.
Figure 10. Low-velocity and high-velocity data shown for the 40/200 surface and the smooth surface.
be due to the presence of a precursor film on the surface so that the drop is already spreading on a thin liquid layer. The prefactor in the Tanner law on the smooth surfaces is different in the low- and high-velocity regimes. The difference is approximately 40%. The velocity interval is
Acknowledgment. The department of Solid State Electronics at Chalmers Technical University is gratefully acknowledged for manufacturing the model surfaces. This work was supported by the Swedish Research Council for Engineering Sciences (TFR). S.G. expresses her gratitude to “Stiftelsen Gunnar Sundblads Forsknings Fond” for a travel grant. Olle Paulsson is acknowledged for skillful laboratory assistance with the DAT measurements. LA970139W
