An extended Teorell-Meyer-Sievers theory for membrane potential under non-isothermal conditions

Abstract

Membrane potential is one of the key performance parameters in reverse-electrodialysis based salinity gradient driven power generation. The Teorell-Meyer-Sievers (TMS) theory is widely used to describe the membrane potential under isothermal conditions. Here, we formulate an extended TMS theory that can be applicable to cases in which both salinity and temperature gradients are existent. The new theory shows a good quantitative agreement with the experimental data for purely salinity or temperature gradient induced membrane potential in the current literature. The activity coefficient correction, the temperature polarization (TP), the solute diffusion speed ratio between membrane and solution phases together with the unequal electrolyte heats of transport in membrane and solution phases can account for the experimental observations. Results also suggest that the membrane potential can be enhanced when the salinity gradient and the temperature gradient are in opposite directions, and can be enhanced or reduced when the directions of the two gradients are the same, depending on the extent of the TP effect. The enhancement can reach 43.7% for a temperature difference of 60 K when the gradients of salinity and temperature are in the opposite directions. The membrane potential can be enhanced by reducing the TP effect and increasing the membrane charge.