Geometry-driven charge accumulation in electrokinetic flows between thin, closely spaced laminates (Q2884614)

The authors study flows in deformable porous media. The macro scale behavior of these systems depends on the microstructure, which may depend on local and global physical processes. A mathematical approach is developed to layered systems whose geometry depends on the macro scale and whose roughness is small. The approach removes two geometric restrictions. First the average is taken over a canonical laminate-galley pair whose overall spacing may be an unknown to be solved in the problem and which may vary spatially on the mesoscale. In order to close the homogenization portion of the analysis, a physical conservation principle is required to hold over the typical laminate-galley pair. Second the anisotropy of the material is considered from the beginning in the analysis, which simplifies the model significantly and allows for the inclusion of nonlinear effects in the flow direction which are comparable to the effective behavior on the macro scale. An effective set of equations is derived to describe the fluid pressure, the anion and cation concentrations in the fluid, and the electric potential. Anisotropic dispersion effects in the electric field are included, and electro neutrality in the fluid is not imposed. The gradients in the laminate spacing can lead to charge accumulation when the electro osmosis and the electrophoresis induced from the anisotropic dispersion effects balance.