Fluid invasion in porous media: Viscous gradient percolation

Viscous gradient percolation for fluid invasion fronts in porous media with low volume capacitance was derived. The regime was characterized by realistic features including highly hysteric capillary flow and long-range propagation of pressure distributions. It was observed that there is two distinct scalings depending on the volume of liquid that can be extracted from the porous medium locally per unit decrease in pressure. It was suggested that the dynamics of stable viscous invasion fronts in porous media depends on the volume capacitance of the media.