Coupled liquid and solute transport through semipermeable porous media: Dominant mechanism of membrane behavior and chemico-osmosis effect under high solute concentration

This study presents an analytical model for coupled liquid and solute transport considering membrane behavior based on a phenomenological framework of non-equilibrium thermodynamics. The model was validated, nondimensionalized, and applied to illustrate the effect of membrane behavior on solute transport through bentonite-based barriers, with a focus on the dominant mechanisms of membrane behavior and the chemico-osmosis effect under high solute concentrations. Results show that as the membrane efficiency coefficient ( ω ) increases, the time required to reach steady-state transport increases. In contrast, the steady-state concentration profile is independent of ω but decreases with increasing osmotic number ( N π ). When N π >0.3, assuming a linear pressure profile without considering coupled liquid transport may lead to a misinterpretation of the concentration profile. The effect of hyperfiltration (HY) on solute transport is negligible, with ≤4% error when HY is omitted for global Péclet number ( P eg ) ≤0.1 and ω ≤0.8. A threshold value ( ω th ) was identified: when ω > ω th , restricted diffusion (RD) is the dominant mechanism of membrane behavior; otherwise (i.e. ω ≤ ω th ), chemico-osmotic counteradvection (COC) becomes dominant. Moreover, COC significantly affects solute transport at lower but measurable ω and higher N π , as demonstrated in a sand-bentonite specimen subjected to a highly concentrated KCl solution, where neglecting chemico-osmosis led to significant errors (up to 93%) in steady-state flux predictions.