On multicomponent, multiphase thermomechanics with interfaces

Abstract The thermomechanics of a multiphase multicomponent mixture are developed in the spirit of modern continuum physics. A new axiom of constitution, “equipresence of constituents”, is stated and employed to obtain macroscale equations of constitution which are consistent with their microscale counterparts. Here we are assuming a scale separation wherein the classical microscale theory of mixtures applies within each phase and interface, and a hybrid theory of mixtures, which is a homogenization of the microscale mixture theory over phases and interfaces, applies at the macroscale. We thus postulate the existence of a two-scale hierarchy of overlaying continua. Such scale separation is common to many types of porous media. Exploitation of the entropy inequality in the sense of Coleman and Noll and application of equilibrium constraints produces a complex list of functional relations forming a macroscale theory of constitution. In a three-phase system linearization of several of these relations produces novel analogs of Fick's first law of diffusion and Darcy's law of fluid transport in deforming porous media. These analogs of Fick's and Darcy's laws are significantly different from their traditional forms in that they contain an “interaction potential”. The authors feel that the contribution fo the interaction potential to fluid flow dynamics could be of crucial importance in swelling and shrinking colloidal systems. Another especially important consequence of the theory of constitution is the development of the experimentally observed exponential relation between disjoining (swelling) pressure and the pore width in a smectitic clay-water system. This relation cannot be developed using classical Gibbsian thermostatics.

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