Interfacial Stability of Immiscible Displacement in a Porous Medium

We study patterns formed by the viscous fingering instability in a porous medium. The wetting properties of the medium have a profound influence on the width of the individual fingers and consequently on the shape of the overall pattern. If the displaced fluid preferentially wets the medium, the finger width is comparable to the pore size, independent of other parameters. In contrast, if the displacing fluid preferentially wets the medium, the finger width is much larger than the pore size, and, when normalized by the square root of the permeability, is found to scale with the capillary number approximately as $N_{\mathrm{Ca}}^{-\frac{1}{2}}$.