Force and flux relations for flows of ionic solutions between parallel plates with porous and charged layers

We derive coefficients of the electrokinetic coupling matrix (χ(11), χ(12), and χ(21)) for the flow of an ionic solution through a parallel-plate geometry having porous and charged layers grafted onto a solid surface with a known potential and demonstrate Onsager reciprocity for the cross terms (i.e., χ(12)=χ(21)). Our results enable the prediction of system outputs in the solid-porous-fluid system from parameters that are either known or may be measured and inferred. These electrokinetic coupling coefficients are in terms of the potential, ϕ, and fixed charge, ρ(f), only, removing dependence on field gradients and fluid velocity. Additionally, we present simplified expressions of these coupling coefficients in limiting regions of the parameter space. Away from these limits, we present numerical results demonstrating the facility of our functional form for facile numerical approximation and report the utility and accuracy of our analytical approximations.