Phase Field Model of Capillary Rise Between Two Walls

We model the dynamics of a liquid-gas interface rising between two chemically inhomogeneous walls under the influence of capillary forces. The system is described by a phase field-model with conserved dynamics similar to [1]. Liquid conservation leads to a slowing down of the average interface position. Spatial disorder of the walls is introduced through a quenched random field. Disorder in the walls causes roughening of the contact line and fluctuations of the local contact angle. Values of scaling exponents are discussed. We also study the effect of single defects on the contact line and contact angle in three dimensions [2]. [1] M. Dubé, M. Rost, K. R. Elder, M. Alava, S. Majaniemi and T. Ala-Nissila, Phys. Rev. Lett. 83 (1999) 1628 [2] J. A. Marsh and A. M. Cazabat, Europhys. Lett. 23 (1993) 45