Rheology of high-capillary number two-phase flow in porous media

Flow of immiscible fluids in porous media at high capillary numbers may be characterized by an effective viscosity. We demonstrate that the effective viscosity is well-described by the Lichtenecker-Rother equation. Depending on the pore geometry, wettability, and viscosity of the fluids, the exponent α in this equation can have different values. We find α = 1 when fluids are well-mixed with small bubbles, α = 0.6 in two- and 0.5 in three-dimensional systems when there is less mixing with the appearance of big bubbles, and α = −0.5 when lubrication layers are formed along the pore walls. Our arguments are based on analytical and numerical methods