  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 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 flows 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.
