Modeling and simulation of wetting and spreading

Abstract

We present a mathematical model for the slow three-dimensional motion of a liquid coating on a substrate with wetting and de-wetting edges. The equilibrium contact angle is considered to be a material property of the liquid-substrate system. Substrate chemical heterogeneity, or physical roughness, may also be an important determinant of edge motion. Conversely, dynamic contact angle information is not required by the model; it is predicted as part of the solution. Calculated results are compared with experimental observation with good agreement. Many industrial applications involve liquid coating and wetting considerations are usually quite important. References Deryaguin, B. V., Theory of the capillary condensation and other capillary phenomena taking into account the disjoining effect of long-chain molecular liquid films, Zhur. Fiz. Khim. 14 , 137 (1940) [In Russian]. Eres, M. H., Schwartz, L. W., and Roy, R. V., Fingering phenomena for driven coating films, Physics of Fluids 12 , 1278--1295, 2000. Frumkin, A. N., On the phenomena of wetting and sticking of bubbles, Zhur. Fiz. Khim. 12 , 337 (1938) [In Russian]. Haze, R. and Lammers, J. H., ``Liquid height measurement through light absorption,'' Philips Research Laboratory, Report No. UR 819/99, Eindhoven, Netherlands, 1999. Huh, C. and Scriven, L. E., Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, J. Colloid Interface Sci. 35 , 85, 1971 . Levich, V. G., Physiochemical Hydrodynamics , 1962, Prentice--Hall, Englewood Cliffs. Moriarty, J. A. and Schwartz, L. W., Effective slip in numerical calculations of moving-contact-line problems, J. Engineering Math. 26 81--86, 1992. Peaceman, D. W. and Rachford, H. H., The numerical solution of parabolic and elliptic differential equations, SIAM J. 3 , 28, 1955. Podgorski, T., Flesselles, J.-M., and Limat, L., Corners, cusps, and pearls in running drops, Phys. Rev. Lett. 87 , 1--4, 2001. Schwartz, L. W., Roy, R. V., Eley, R. R. and Petrash, S. Dewetting Patterns in a Drying Liquid Film, J. Colloid Interface Science 234 , 363--374, 2001. Atherton, R. W. and Homsy, G. M., On the derivation of evolution equations for interfacial waves, Chem. Eng. Comm. 2 , 57, 1976. Schwartz, L. W. and Roy, R. V., Theoretical and numerical results for spin coating of viscous liquids, Physics of Fluids 16 , 569--584, 2004. Schwartz, L. W., Roux, D. and Cooper-White, J. J., On the shapes of droplets that are sliding on a vertical wall, Physica D 209 , 236--244, 2005. Seeberg, J. E. and Berg, J. C.. Dynamic wetting in the low capillary number regime. Chem. Eng. Sci. 47 4455--4464, 1992. Sherman, F. S., Viscous Flow , 1990, McGraw--Hill, New York. Benney, D. J., Long waves on liquid films, J. Math. and Phys. 45 , 150, 1966. Blake, T. D., ``Dynamic contact angles and wetting kinetics.'' In: J. C. Berg (ed.) Wettability , Marcel Dekker, New York, 251--309, 1993. Cazabat, A. M, Heslot, F., Carles, P. and Troian, S. M., Hydrodynamic fingering instability of driven wetting films, Adv. Colloid Interf. Sci. 39 , 61--75, 1992.