We demonstrate through numerical simulations and a mean field calculation
that immiscible two-phase flow in a porous medium behaves effectively as a
Bingham viscoplastic fluid. This leads to a generalized Darcy equation where
the volumetric flow rate depends quadratically on an excess pressure difference
in the range of flow rates where the capillary forces compete with the viscous
forces. At higher rates, the flow is Newtonian
