This study investigates the multiscale coupling of electro-diffusive ion transport, osmosis, and fluid flow between two Stokes-flow regions separated by a thin porous membrane that can contain fixed charges. To bypass the numerical challenges posed by thin Debye layers, we employ matched asymptotic expansions to derive effective boundary conditions that reduce the system to a macroscale model where concentration, potential, and fluid motion on either side of the membrane are fully coupled. Our analysis reveals that electrokinetic effects are significantly weaker than a simple scaling argument suggests, remaining negligible for biological and traditional synthetic membranes where osmotic effects dominate. By solving the steady-state equations, we identify a critical stability limit governed by a dimensionless osmotic parameter. Exceeding this limit triggers a localized pressure drop and flow reversal at the channel inlets. This represents a catastrophic failure for applications like micro-dialysis or renal filtration, as it leads to the ingestion of unfiltered fluid. We show that osmotic fluxes can be further enhanced by membrane fixed charges and external electric fields. We also consider the possibility of utilizing modern high-permittivity synthetic membranes to obtain non-negligible electrokinetic effects. We show that these effects can enhance transmembrane ion fluxes with a much lower risk of triggering flow reversal compared to osmotic enhancement. Our asymptotic reduced model serves as a computationally efficient design tool for optimizing microfluidic devices by establishing links between membrane properties, external potentials, and transport efficiency.
He et al. (2026) studied this question.