Water movement in a porous material whose interconnected pores are filled only partially with water is defined as unsaturated water flow. Important phenomena occurring in the hydrological cycle, such as infiltration, drainage, redistribution of soil water, water uptake by plant roots, and evaporation, all involve flow of water in unsaturated soil.
Historically, the development of the physical theory of water flow in unsaturated porous media was promoted by Richards , who considered the original Darcy law for saturated flow, and therefore its underlying physical meaning, still valid under unsaturated conditions. In the unsaturated zones, the gaseous phase (generally, air and water in the vapor phase) is assumed to be continuous and interconnected at a constant pressure value, usually at atmospheric pressure. Moreover, the flow of the interconnected air or gas is neglected because it is a nearly frictionless flow. The presence of the gaseous phase reduces the hydraulic conductivity of the system in different ways from point to
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