A note on the dissipation due to generalized diffusion with electro-chemo-mechanical couplings in heteroionic clays

Chemically active saturated clays are considered in a two-phase framework. The solid phase contains clay particles, absorbed water and dissolved ions, Na+, K+ and Cl−. The fluid phase, or pore water, contains free water and the same ionic species. Water and ions can transfer between the two phases. Emphasis is laid on the diffusion and electromigration of the species of the fluid phase through the porous medium. The generalized diffusion equations are motivated by a dissipation inequality written in two formats, in terms of two sets of conjugate pairs of fluxes and associated gradients. y point of the note is to address the dissipation inequality and to unveil the possible restrictions it might impose on the form of constitutive functions and on the range of parameters. Two generalized diffusion equations, that slightly differ in their algebraic structure, are analyzed. For the first classic structure, the osmotic efficiency ω∈[0,1] is shown to be bounded above, 0⩽ω⩽ω⩽1, by a bound ω that depends on the hydraulic conductivity, the effective diffusion coefficients and the cationic concentration. In contrast, the second structure of diffusion equations does not restrict the osmotic efficiency. alysis embodies the case where the solution contains a single undissociated salt, or an organic solute.