CROSSOVER FROM FRACTAL TO COMPACT FLOW FROM SIMULATIONS OF 2-PHASE FLOW WITH FINITE VISCOSITY RATIO IN 2-DIMENSIONAL POROUS-MEDIA

The effect of the viscosity ratio (M = mu(D)/mu(I)) in changing the nature of viscous fingering was studied using a simple, physical model of miscible, dispersionless, two-phase, linear flow in model two-dimensional porous media. For all viscosity ratios, the initial flows had an unstable, fractal character which crossed over to stable, compact flow on a time (or length) scale which increased with the viscosity ratio. An empirical scaling of the data enables an asymptotic characterization of both this time scale tau almost-equal-to M(phi)t, where phi(t)=0.17+/-0.03, as well as the front velocity upsilon almost-equal-to M(epsilonphi)t where epsilonphi(t)=0.07+/-0.02. A comparison with identical simulations of radial flow indicates that the same characteristic length scale applies in both linear and radial geometries l almost-equal-to M(phi)l where phi(l) = 0.24+/-0.06, while the time scales differ because of the different relations between time and size in the two geometries.