Coupled electrohydrodynamic transport in rough fractures: a generalized lubrication theory

Fractures provide pathways for fluids and solutes through crystalline rocks low permeability materials, thus playing a key role in many subsurface processes applications. In small aperture fractures, solute transport is strongly impacted by the coupling of electrical double layers at mineral–fluid interfaces to bulk ion transport. Yet, most models flow fractures ignore these effects. Solving such coupled electrohydrodynamics realistic three-dimensional (3-D) fracture geometries poses computational challenges which have so far limited our understanding those electro-osmotic effects’ impact. Starting from Poisson–Nernst–Planck–Navier–Stokes (PNPNS) equations using combination rescaling, asymptotic analysis Leibniz rule, we derive set nonlinearly conservation local fluxes fluid mass, mass charges. Their solution yields pressure, concentration potential fields. The model validated comparing its predictions solutions PNPNS 3-D rough fractures. Application evidences several phenomena hitherto not reported literature, including: (i) dependence conductivity on walls’ charge density, (ii) (sometimes global) reversal, (iii) spatial heterogeneities field without any imposed gradient. This new theoretical framework will allow systematically addressing large statistics geometry realizations given stochastic parameters, infer impact various hydrodynamic parameters ions