A continuum theory of porous media saturated by multiple immiscible fluids: II. Lagrangian description and variational structure

Abstract

The mechanical behavior of porous media is largely governed by the interactions among coexisting components. In a companion paper [Int. J. Eng. Sci. 40 (2002) 1807–1833], a continuum theory of multiphase porous media has been developed that is capable of rigorously characterizing these interactions. In this paper, the results previously obtained are used to develop a macroscale model where the state of a porous medium is described by macrostate variables measurable through experiments. The variational structure of the proposed theory is investigated. All the formulations of the macroscale model are presented in the Lagrangian setting. It is shown that the volume fractions of fluids can be considered as internal variables that microscopically represent capillary relaxation processes. By virtue of the variational description of the theory, Biot's principle of virtual dissipation [Int. J. Solids Struct. 13 (1977) 579] is rigorously recovered, and a link between the mixture theories and Biot's theory of porous media is established.