Liquid Conservation and Non-local Interface Dynamics in Imbibition

TL;DR

This paper studies how liquid interfaces move and roughen in disordered media, revealing the effects of conservation laws and disorder on interface dynamics and scaling behavior.

Contribution

It introduces a phase-field model with conserved dynamics to analyze non-local interface behavior in imbibition, highlighting the impact of conservation and disorder.

Findings

Conservation slows interface propagation and creates an intrinsic correlation length.

The interface exhibits self-affine roughness with a global roughness exponent of approximately 1.25.

The interface shows anomalous scaling behavior.

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 \xi_\times \sim H^{1/2} on the spatial fluctuations of the interface. The interface is statistically self affine in space, with global roughness exponent \chi \simeq 1.25 and exhibits anomalous scaling.