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2.10.1 Solid Matrix and Solid-Bound Molecular Constituents
For constituents constrained to move with the solid (denoted generically by and satisfying , , the statement of mass balance in (2.10-4) reduces to the special form This representation makes it easy to see that alterations in can occur only as a result of chemical reactions (such as synthesis, degradation, or binding). In contrast, as seen in (2.10-4), alterations in for solutes or solvent ( may also occur as a result of mass transport into or out of the pore space of the solid matrix. Therefore, is the natural choice of state variable for describing the content of solid constituents in a reactive mixture.
When multiple solid species are present, the net solid mass content may be given by whereas the net mass supply of solid is such that . The referential solid volume fraction, , may be evaluated from where is the true density of solid constituent (mass of per volume of and is the referential solid volume fraction of solid constituents not explicitly modeled by solid-bound molecules (a user-defined parameter). According to (2.10-5), it follows that the solid volume fraction in the current configuration is given by . Note that under all circumstances, while , implying that may exceed unity when solid growth occurs. In this study, it is assumed that all mixture constituents are intrinsically incompressible, implying that their true density is invariant.
The various constituents of the solid matrix may be electrically charged. Let be the charge number (equivalent charge per mole) of solid constituent , then the net referential fixed charge density of the solid matrix (equivalent charge per fluid volume in the referential configuration) is given by where is the molar mass of (an invariant quantity) and represents the referential volume fraction of all fluid constituents (solvent solutes) in a saturated mixture. Based on the kinematics of the continuum, the fixed charge density in the current configuration is