Similarity and Explicit Exact Solutions for Imbibition with Dynamic Capillary Pressure

Similarity solutions are developed to the Hassinizadeh–Gray model for nonequilibrium porous media flow, in a semi-infinite domain subject to a flux boundary condition. Power law behavior is assumed for the hydraulic diffusivity, [Formula: see text], conductivity, [Formula: see text] and relaxation coefficient, [Formula: see text], functions. We show that a simple and compact exact solution exists that is nonunique, having a stable and unstable branch. For particular values of the power law exponents, the exact solution shows that the dynamic pressure is just a translation of the equilibrium static pressure, in agreement with experimental data.