Liquid conservation and nonlocal interface dynamics in imbibition

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(x) similar to H-1/2 On the spatial fluctuations of the interface. The interface is statistically self affine in space, with global roughness exponent chi similar or equal to 1.25, and exhibits anomalous scaling.