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.
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