Anomalous interface roughening: The role of a gradient in the density of pinning sites

We study the effect on interface roughening of a gradient ∇p in the density of pinning sites p. We identify a new correlation length, ξ, which is a function of ∇p: ξ~(∇p)−γ/α, where α=ν⊥/ν|| is the roughness exponent, and γ=ν⊥/(1+ν⊥). The exponents ν⊥ and ν|| characterize the transverse and longitudinal correlation lengths. To investigate the effect of ∇p on the scaling properties of the interface in (1+1) and (2+1) dimensions, we calculate the critical concentration, pc, and the exponents γ and α from which ν⊥ and ν|| can be determined. Our results are in qualitative agreement with some of the features of imbibition experiments.