Modelling of the Electrical Membrane Potential for Concentration Polarization Conditions

Based on Kedem–Katchalsky formalism, the model equation of the membrane potential ([Formula: see text]) generated in a membrane system was derived for the conditions of concentration polarization. In this system, a horizontally oriented electro-neutral biomembrane separates solutions of the same electrolytes at different concentrations. The consequence of concentration polarization is the creation, on both sides of the membrane, of concentration boundary layers. The basic equation of this model includes the unknown ratio of solution concentrations ([Formula: see text] at the membrane/concentration boundary layers. We present the calculation procedure ([Formula: see text] based on novel equations derived in the paper containing the transport parameters of the membrane ([Formula: see text] , [Formula: see text] , and [Formula: see text]), solutions ([Formula: see text] , [Formula: see text]), concentration boundary layer thicknesses ([Formula: see text] , [Formula: see text]), concentration Raileigh number ([Formula: see text]), concentration polarization factor ([Formula: see text]), volume flux ([Formula: see text]), mechanical pressure difference ([Formula: see text]), and ratio of known solution concentrations ([Formula: see text]). From the resulting equation, [Formula: see text] was calculated for various combinations of the solution concentration ratio ([Formula: see text]), the Rayleigh concentration number ([Formula: see text]), the concentration polarization coefficient ([Formula: see text]), and the hydrostatic pressure difference [Formula: see text]). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m(−3) ([Formula: see text]) was on one side of the membrane and on the other side an aqueous NaCl solution with a concentration between 1 and 15 mol m(−3) ([Formula: see text]). It is shown that ([Formula: see text]) depends on the value of one of the factors (i.e., [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text]) at a fixed value of the other three.