Macroscale thermodynamics and the chemical potential for swelling porous media

The thermodynamical relations for a two-phase, N-constituent, swelling poro us medium are derived using a hybridization of averaging and the mixture-th eoretic approach of Bowen. Examples of such media include 2-1 lattice clays and lyophilic polymers. A novel, scalar definition for the macroscale chem ical potential for porous media is introduced, and it is shown how the prop erties of this chemical potential can be derived by slightly expanding the usual Coleman and Noll approach for exploiting the entropy inequality to ob tain near-equilibrium results. The relationship between this novel scalar c hemical potential and the tensorial chemical potential of Bowen is discusse d. The tensorial chemical potential may be discontinuous between the solid and fluid phases at equilibrium; a result in clear contrast to Gibbsian the ories. It is shown that the macroscopic scalar chemical potential is comple tely analogous with the Gibbsian chemical potential. The relation between t he two potentials is illustrated in three examples.