Scaling Properties of Pinned Interfaces in Fractal Media

Experimental data for rupture lines and wetting fronts in various kinds of paper suggest that the scaling properties of interfaces pinned in such fractally correlated media are governed by the fractal dimension, D, of the medium. Specifically, the phenomenological relation ζ=D-(d-1), where d is the spatial dimension of the system, satisfactorily describes the local roughness exponent, ζ, of a pinned interface. The relation is supported by analysis of the competition between an elastic restoring force and correlated pinning force in an elastic fractal media, under the assumption that the pinning force correlations decaying with distance, r, as r^-η with 0<η=d-D<1.