Liquid Conservation and Nonlocal Interface Dynamics in Imbibition

Abstract

The propagation and roughening of a liquid-gas interface moving through a disordered medium under the influence of capillary forces is considered. The system is described by a phase-field model with conserved dynamics and spatial disorder is introduced through a quenched random field. Liquid conservation leads to slowing down of the average interface position $H$ and imposes an intrinsic correlation length ${\ensuremath{\xi}}_{\mathsf{x}}\ensuremath{\sim}{H}^{1/2}$ on the spatial fluctuations of the interface. The interface is statistically self affine in space, with global roughness exponent $\ensuremath{\chi}\ensuremath{\simeq}1.25$, and exhibits anomalous scaling.