Clarifying mixture theory and the macroscale chemical potential for porous media

• Published in: International journal of engineering science 1996-11, Vol.34 (14), p.1611-1621
• Main Authors: Bennethum, Lynn Schreyer, Cushman, John H., Murad, Márcio A.
• Format: Article
• Language: English
• Subjects: Chemical thermodynamics; Chemistry; Exact sciences and technology; General and physical chemistry; General. Theory
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/S0020-7225(96)00042-0

Hybrid mixture theory (HMT) consists of classical mixture theory applied to a multiphase system with volume averaged field equations. HMT is applicable to a multiphase mixture in which the characteristic length of each phase is ‘small’ relative to the extent of the mixture. A porous body is the canonical model of a system to which HMT is applicable. When a phase contains N constituents, the linearized fluxes derived through HMT are historically expressed relative to the Nth constituent, e.g. Fick's law for the jth species is expressed in terms of a gradient of the jth chemical potential relative to the Nth. This is in contrast to classical Gibbsian thermodynamics, which gives rise to results of similar form, but with absolute (non-relative) driving forces. Here we modify HMT to construct results which are completely analogous to Gibbsian thermodynamics. This is accomplished by modifying the way the entropy inequality is exploited and by re-examining the definition of the averaged chemical potential of a constituent and the averaged Gibbs energy of a phase. Particular emphasis is placed on the relations between the scalar chemical potential of Gibbs and the tensorial chemical potential of Bowen. Previous HMT results gave rise to an averaged chemical potential that may experience a jump between the solid and fluid phases at equilibrium; a result in clear contrast to Gibbsian theories. This discontinuity in the potential is due to an ‘effective’ external field (e.g. the effective stress induced by a load in the solid phase). A notable consequence of the approach proposed herein is a HMT chemical potential in complete analogy with the Gibbsian chemical potential.