Morphology and dynamics of interfaces in random two-dimensional media

Abstract

We study the morphology and dynamics of an interface driven through a disordered two-dimensional medium by an applied force. At large length scales the interface is self-affine with roughness exponent α=1/2. The structure at small scales may be self-similar or self-affine, depending on the degree of disorder. Simulations of wetting invasion produce self-affine interfaces with α=0.8 and a power law distribution of local interface velocities. Numerical results are in excellent agreement with expreiment. A technique that distinguishes between true self-affine scaling and a crossover is presented, and applied to the invasion model and a model for magnetic domain growth.