Length scale of viscous fingers in multiphase flow through porous media

When a less viscous fluid displaces a more viscous one in a porous medium, the displacement front is unstable, and the hydrodynamic instability that ensues is referred to as viscous fingering. The displacement pattern is characterized by branching structures, with an intrinsic length scale that depends on the fluid properties, essentially viscosity and surface tension between the fluids, as well as the structure of the porous space, the wetting properties of the system, and the injection rate. Here we present a continuum model of two-phase flow in porous media that reproduces the experimental patterns of displacement. We describe the properties of our model in simple quasi-1D displacements, and in unstable two-dimensional flow. Using our macroscopic model, we discuss the scaling properties of the intrinsic finger length scale.