Fluid invasion in porous media: viscous gradient percolation.

We suggest that the dynamics of stable viscous invasion fronts in porous media depends on the volume capacitance of the media. At high volume capacitance, our network simulations provide numerical evidence of a scaling relation between the front width and its velocity. In the low volume capacitance regime, we derive a new effective scaling supported by network simulations and that is in agreement with previous experiments on imbibition in paper and collections of glass beads.