INTERFACE FLUCTUATIONS IN RANDOM-MEDIA

We study a stochastic model of an interface moving through a random medium. This model differs from the standard Kardar-Parisi-Zhang equation by the fact that the fluctuations are quenched random variables. We find an intermediate scaling regime with roughness exponent approximately equal to 0.75; this compares favorably with recent experiments [M. A. Rubio, C. A. Edwards, A. Dougherty, and J. P. Gollub, Phys. Rev. Lett. 63, 1685 (1989)] on multiphase flow through a bead pack.