Influence of buoyancy on drainage of a fractal porous medium

The influence of stabilizing hydrostatic pressure gradients on the drainage of a fractal porous medium is studied. The invasion process is treated with invasion percolation (IP) in a gradient. Fractality is mimicked by randomly closing bonds of a network. Two length scales govern the problem: the characteristic length of the pore structure xi(s) and a length scale xi(g) above which buoyancy determines the structure of the cluster. When xi(s)xi(g), gravity becomes important and xi(g) scales with the bond number B as xi(g)proportional toB(-0.57), as in ordinary IP, while the fractal dimension becomes equal to the Euclidean one. When xi(g)xi(s) the fractal dimension of the invading cluster equals the Euclidean one and xi(g)proportional toB(-0.69)