FLUID PENETRATION THROUGH A CRACK IN A PRESSURE-GRADIENT

We investigate invasion percolation fingers in a quenched medium in wh ich the randomness has a gradient following a power law both in the di rection of the flow and perpendicular to it. The first gradient corres ponds to a pressure gradient, the second one to the density of microcr acks that arises in a self-organized way around a large crack. We give an argument for the value of the fractal dimension as found in previo us simulations. We calculate the roughness exponent of the fingers and find a value consistent with 1/2 as predicted by the argument.