Liquid conservation and nonlocal interface dynamics in imbibition

The propagation and roughening of a liquid-gas interface moving through a d isordered medium under the influence of capillary forces is considered. The system is described by a phase-field model with conserved dynamics and spa tial disorder is introduced through a quenched random field. Liquid conserv ation 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 fluc tuations of the interface. The interface is statistically self affine in sp ace, with global roughness exponent chi similar or equal to 1.25, and exhib its anomalous scaling.