Unsaturated Water Movement
Many soil physicists and hydrologists have assumed that Darcy’s law and the diffusion equation are applicable to unsaturated flow at any water content. Many researchers have used the diffusion equation to predict change of water content with time in phenomena such as infiltration, drainage, and evaporation. W. G. Gray and S. M. Hassanizadeh introduced an unsaturated flow theory derived from basic principles of continuum mechanics with a thermodynamic analysis. They took explicit account of the interfaces. From a practical point of view the interface between air and water is an important attribute of unsaturated flow. The relationships between flow velocity and hydraulic gradient for three materials: a Newtonian liquid, a non-Newtonian liquid, and a Bingham material. S. V. Nerpin and A. F. Chudnovskii introduced basic equations for film water flow using the equation of continuity, the Navier-Stokes equations for the three velocity components, and the heat transfer equation.