A thermodynamic basis for the derivation of the Darcy, Forchheimer and Brinkman models for flows through porous media and their generalizations

In this study we use a general thermodynamic framework which appeals to the criterion of maximal rate of entropy production to obtain popular models due to Darcy and Brinkman and their generalizations, to describe flow of fluids through porous solids. Such a thermodynamic approach has been used with great success to describe various classes of material response and here we demonstrate its use within the context of mixture theory to obtain the classical models for the flow of fluids through porous media and more general models which are all consistent with the second law of thermodynamics.