Modelling of the Electrical Membrane Potential for Concentration Polarization Conditions

Abstract

Based on Kedem–Katchalsky formalism, the model equation of the membrane potential (∆ψs) 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 (CiCe) at the membrane/concentration boundary layers. We present the calculation procedure (CiCe) based on novel equations derived in the paper containing the transport parameters of the membrane (Lp, σ, and ω), solutions (ρ, ν), concentration boundary layer thicknesses (δl, δh), concentration Raileigh number (RC), concentration polarization factor (ζs), volume flux (Jv), mechanical pressure difference (∆P), and ratio of known solution concentrations (ChCl). From the resulting equation, ∆ψs was calculated for various combinations of the solution concentration ratio (ChCl), the Rayleigh concentration number (RC), the concentration polarization coefficient (ζs), and the hydrostatic pressure difference (∆P). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m−3 (Cl) 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 (Ch). It is shown that (∆ψs) depends on the value of one of the factors (i.e., ∆P, ChCl, RC and ζs) at a fixed value of the other three.

The Role of the Gravitational Field in Generating Electric Potentials in a Double-Membrane System for Concentration Polarization Conditions

“…The term concentration polarization (CP) refers to the effects of creating additional concentration gradients of ionic or non-ionic components in the solution areas of an electrolyte and/or non-electrolyte adjacent to the surface of any selective membrane, separating solutions of different concentrations [10][11][12][13]. These areas, called concentration boundary layers (CBLs), are created on both sides of the membrane in both single-and multi-membrane systems [12,[14][15][16][17]. CBLs formation is a result of molecular diffusion and leads to a significant reduction in the concentration gradient (osmotic pressure) and, consequently, in membrane transport [11,12].…”

“…CBLs formation is a result of molecular diffusion and leads to a significant reduction in the concentration gradient (osmotic pressure) and, consequently, in membrane transport [11,12]. These processes are reflected in nonlinear concentration characteristics of volume flux, solute flux and membrane potentials [16,17]. When the concentration (density) gradient is antiparallel to the gravity vector, CBLs undergo natural destruction due to the appearance of natural (gravitational) convection [15][16][17][18][19][20][21][22].…”

“…These processes are reflected in nonlinear concentration characteristics of volume flux, solute flux and membrane potentials [16,17]. When the concentration (density) gradient is antiparallel to the gravity vector, CBLs undergo natural destruction due to the appearance of natural (gravitational) convection [15][16][17][18][19][20][21][22].…”

“…The membrane potential that is a consequence of convective destruction of CBLs in a single-membrane electrochemical cell is called the gravielectric effect [16,17,23,24]. This effect is a consequence of diffusion, concentration polarization and the action of gravity [16,17,23].…”

“…The membrane potential that is a consequence of convective destruction of CBLs in a single-membrane electrochemical cell is called the gravielectric effect [16,17,23,24]. This effect is a consequence of diffusion, concentration polarization and the action of gravity [16,17,23]. For the electrochemical cell design, a system was used in which two solutions with different NaCl or KCl solutions were separated by a synthetic polymer membrane.…”