THE NONEQUILIBRIUM THERMODYNAMICS OF THE SOIL-WATER SYSTEM - A VARIATIONAL APPROACH

A variational principle for extended irreversible thermodynamics (Vazquez, F., del Rio, J.A., Rev. Mex. Fis., 35 (1990), 71) is reformulated to incorporate the spatial inhomogeneities of the non-conserved variables in their time evolution equations. This approach is applied to water transport through soils and an exact time evolution equation for the water flux is derived as an Euler-Lagrange equation. In the structure of this equation the Forchheimer correction of Darcy's Law (applied to non-stationary problems) can be identified.