Title: Rheology of High-Capillary Number Flow in Porous Media,
Abstract: 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.