  In ion-exchange membrane processes, ions and water flow under the influence
of gradients in hydrostatic pressure, ion chemical potential, and electrical
potential (voltage), leading to solvent flow, ionic fluxes and ionic current.
At the outer surfaces of the membranes, electrical double layers (EDLs) are
formed (Donnan layers). When a current flows through the membrane, we argue
that besides Joule heating in the bulk of the membrane and in the electrolyte
outside the membrane, there is also electrostatic heating and cooling in the
EDLs. In addition, when fluid flows through a charged membrane, at the outsides
of the membrane there is pressure-related heating or cooling due to the osmotic
and hydrostatic pressure differences across the EDLs.
