Incompressible porous media models by use of the theory of mixtures

This work illustrates the use of the thermodynamics of mixtures to formulate incompressible porous media models. An incompressible porous material is a mixture where the solid and the fluid constituents are each incompressible. Among the results are formulas which show how the chemical potentials for the constituents determine the stress tensor for the mixture and the pore pressure for each pore fluid. The general results are specialized to the forms necessary to produce models used in the applications. For example, the classical models used to study the flow of immiscible fluids in deformable and rigid solids are given.