Analysis of a new model for unsaturated flow in porous media including hysteresis and dynamic effects

A new model for unsaturated flow in porous media, including capillary hysteresis and dynamic capillary effects, is analyzed. Existence and uniqueness of solutions are established and qualitative and quantitative properties of (particular) solutions are analyzed. Some results of numerical computations are given. The model under consideration incorporates simple 'play'-type hysteresis and a dynamic term (time-derivative with respect to water content) in the capillary relation. Given an initial water content distribution, the model determines which parts of the flow domain are in drainage and which parts are in imbibition. The governing equations can be recast into an elliptic problem for fluid pressure and an evolution equation for water content. Standard methods are used to obtain numerical results. A comparison is given between J.R. Philip's semi-explicit similarity solution for horizontal redistribution in an infinite one-dimensional domain and solutions of the new model.