Dynamics of stable viscous displacement in porous media

We investigate the stabilization mechanisms of the invasion front in two-dimensional drainage displacement in porous media by using a network simulator. We focus on the process when the front stabilizes due to the viscous forces in the liquids. We find that the capillary pressure difference between two different points along the front varies almost linearly as a function of height separation in the direction of the displacement. The numerical results support arguments that differ from those suggested earlier for viscous stabilization. Our arguments are based upon the observation that nonwetting fluid hows in loopless strands (paths) and we conclude that earlier suggested theories are not suitable to drainage when nonwetting strands dominate the displacement process. We also show that the arguments might influence the scaling behavior between the front width and the injection rate and compare some of our results to experimental work.