Observable Quantities for Electrodiffusion Processes in Membranes

Abstract

Electrically driven ion transport processes in a membrane system are analyzed in terms of observable quantities, such as the apparent volume flow, the time dependence of the electrolyte concentration in one cell compartment, and the electrical potential difference between the electrodes. The relations between the fluxes and these observable quantities are rigorously deduced from balances for constituent mass and solution volume. These relations improve the results for the transport coefficients up to 25% with respect to those obtained using simplified expressions common in the literature. Given the practical importance of ionic transport numbers and the solvent transference number in the phenomenological description of electrically driven processes, the transport equations are presented using the electrolyte concentration difference and the electric current as the drivers of the different constituents. Because various electric potential differences can be used in this traditional irreversible thermodynamics approach, the advantages of the formulation of the transport equations in terms of concentration difference and electric current are emphasized.

Peltier’s and Thomson’s coefficients of thermoelectric phenomena in the observable formulation

“…The first can be expressed through the Seebeck coefficient of the probes, that is (d μe ) Z = eS Z dT , and the second is measured by a voltmeter, that is (d μe ) volt = −e dψ [12,13]. Then, we have…”