Conserved dynamics and interface roughening in spontaneous imbibition: A phase field model

The propagation and roughening of a fluid-gas interface through a disordere d medium in the case of capillary driven spontaneous imbibition is consider ed. The system is described by a conserved (model B) phase-field model, wit h the structure of the disordered medium appearing as a quenched random fie ld alpha(x). The flow of liquid into the medium is obtained by imposing a n on-equilibrium boundary condition on the chemical potential, which reproduc es Washburn's equation H similar to t(1/2) for the slowing down motion of t he average interface position H. The interface is found to be superrough, w ith global roughness exponent chi approximate to 1.25, indicating anomalous scaling. The spatial extent of the roughness is determined by a length sca le xi(x) similar to H-1/2 arising from the conservation law. The interface advances by avalanche motion, which causes temporal multiscaling and qualit atively reproduces the experimental results of Horvath and Stanley (Phys. R ev. E 52, 5166 (1995)) on the temporal scaling of the interface.