Wrinkling of stable fronts in viscous flow

Stable wrinkled fronts were often observed in experiments on fluid invasion into porous media, when the invaded phase is less viscous than the invading one. Recent experiments by a group at the Weizmann institute, show that capillary wetting of paper may also lead to rough self-affine fronts. A dominant factor controlling the interface roughening in these systems is the nature of the two-dimensional viscous fluid flow in the medium behind it. Since the disorder in the medium modifies this flow, it also determines the roughness of the interface. We present a theoretical analysis of the connection between the nature of randomness in the medium and the resulting roughness of the fronts.