Ion size effects on the electrokinetic flow in nanoporous membranes caused by concentration gradients

The space charge model (SCM) relies on the Poisson-Boltzmann (PB) equation, and hence on the assumption of negligible ion size effects, to calculate the radial distribution of the electrical potential and ionic concentrations. The consideration of nanopores and/or high surface charge densities demands that we account for the finite ion size. In this work, the SCM has been extended by including the ion size effects in the modified PB equation, in the transport equations, and in the diffusion coefficients, through the Renkin function. The ion size effects on the electrokinetic flow through a nanoporous membrane caused by a concentration gradient under open circuit and no applied pressure gradient conditions have been analyzed. The conditions for the observation of the negative anomalous osmosis have also been studied. It has been concluded from the calculations that ion size effects decrease the average ionic concentrations in the pore solution, reduce the absolute values of the average solute flux density and the average solution velocity, and increase the absolute value of the membrane potential. Since the reduction in the solute flux density is quite significant, it is concluded that this extension of the SCM should be used, at least, when analyzing permeability measurements.