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

摘要

The propagation and roughening of a fluid-gas interface through a disordered medium in the case of capillary driven spontaneous imbibition is considered. The system is described by a conserved (model B) phase-field model, with the structure of the disordered medium appearing as a quenched random field α(x). The flow of liquid into the medium is obtained by imposing a non-equilibrium boundary condition on the chemical potential, which reproduces Washburn's equation H ～ t~(1/2) for the slowing down motion of the average interface position H. The interface is found to be superrough, with global roughness exponent x ≈ 1.25, indicating anomalous scaling. The spatial extent of the roughness is determined by a length scale ξ_x ～ H~(1/2) arising from the conservation law. The interface advances by avalanche motion, which causes temporal multiscaling and qualitatively reproduces the experimental results of Horvath and Stanley (Phys. Rev. E 52, 5166 (1995)) on the temporal scaling of the interface.