Incorporation of Dynamic Capillary Pressure into the Green-Ampt Model for Infiltration

The Green-Ampt model describes infiltration of water into soil. A sharp front separates the saturated from the unsaturated zones, and capillary pressure is assumed to remain constant during infiltration. We generalized this model to account for a capillary pressure that depends on the flow velocity. Based on dimensional analysis and physical considerations, we posited a functional form for dynamic capillary pressure and assumed the nonequilibrium capillary pressure to depend on the capillary number in the form of a power law. Our model for dynamic capillary pressure describes measurements of capillary pressure versus Darcy velocity by D. A. Weitz et al. and S. L. Geiger and D. S. Durnford. Moreover, the dimensional analysis allows us to collapse three dynamic capillary pressure curves that Geiger and Durnford measured for sands of different grain size onto one curve. Furthermore our model describes capillary rise experiments performed by T. Tabuchi well. We also derived an implicit analytical solution for the front velocity.