STEADY UNSATURATED FLOW IN 2-DIMENSIONAL SCALE HETEROGENEOUS POROUS-MEDIA

Unsaturated how in scale heterogeneous porous media is described by a class of nonlinear partial differential equations involving three gene ral coefficient functions. It is shown that among these, there is a la rge class of integrable models, being transformable to linear equation s even when the spatially varying geometric dilation scale factor is a n arbitrary twice differentiable function. Explicit solutions are cons tructed for basic boundary value problems that relate to field and lab oratory measurements. In one of these solutions, the flow pattern is u naffected by the heterogeneity even though the water concentration is modified. From another solution, we predict the bulk conductivity of a heterogeneous soil sample with a constant hydraulic potential differe nce maintained between the ends.