Link Search Menu Expand Document
Theory Manual Version 3.6
 Subsection 2.9.3: Donnan Equilibrium Swelling Up Chapter 2: Continuum Mechanics Subsection 2.10.1: Solid Matrix and Solid-Bound Molecular Constituents 

2.10 Chemical Reactions

Chemical reactions may be incorportated into a multiphasic mixture by adding a mass supply term to the equation of mass balance, Where is the volume density of mass supply to resulting from chemical reactions with all other mixture constitutents. Since mass must be conserved over all constituents, mass supply terms are constrained by In a mixture containing a solid constituent (denoted by ), it is conveniemt to define the mixture domain (and thus the finite element mesh) on the solid and evaluate mass fluxes of constituents relative to the solid, Substituting eq.(2.10-3) into eq.(2.10-1), the differential form of the mass balance may be rewritten as Where represents the material time derivative in the spatial frame, following the solid, , where is the deformation gradient of the solid matrix; is the apparent density and is the volume density of mass supply to normalized to the mixture volume in the reference configuration, Since is the mass of in the current configuration per volume of the mixture in the reference configuration (an invariant quantity), this parameter represents a direct measure of the mass content of in the mixture, which may thus be used as a state variable in a framework that accounts for chemical reactions. A distinction is now made between solid and solute species in the mixture, since they are often treated differential in an analysis.
 Subsection 2.9.3: Donnan Equilibrium Swelling Up Chapter 2: Continuum Mechanics Subsection 2.10.1: Solid Matrix and Solid-Bound Molecular Constituents 

Table of contents