Immiscible fluids flowing at high capillary numbers in porous media may be characterized by an effective viscosity. We demonstrate that the effective viscosity is well described by the Lichtenecker-Rother equation. The exponent $\alpha$ in this equation takes either the value 1 or 0.6 in two- and 0.5 in three-dimensional systems depending on the pore geometry. Our arguments are based on analytical and numerical methods.
Categories: physics.flu-dyn