  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 is in agreement with previous experiments on imbibition in
paper and collections of glass beads.

Statistical Mechanics;Soft Condensed Matter