Theoretical study of electrolyte transport in nanofiltration membranes with constant surface potential/charge density

Abstract

Abstract. The pressure-driven ion transport through nanofiltration membrane pores with constant surface potential or charge density is investigated theoretically. Two approaches are employed in the study. The first one is based on one-dimensional Nernst-Planck equation coupled with electroneutrality, zero current, and Donnan equilibrium conditions. This model is extended to account for interfacial effects by using a smooth approximation of step function for the volume charge density. A simplified model for the case of constant surface potential is also proposed. The second approach is based on two-dimensional Nernst-Planck, Poisson, and Navier-Stokes equations, which are solved in a high aspect ratio nanopore connecting two reservoirs with much larger diameter. The modification of equations on the basis of Slotboom transformation is employed to speed up the convergence rate. The distributions of potential, pressure, ion concentrations and fluxes due to convection, diffusion, and migration in the nanopore and reservoirs are discussed and analyzed. It is found that for constant surface charge density, the convective flux of counter-ions in the nanopore is almost completely balanced by the opposite migration flux, while for constant surface potential, the convective flux is balanced by the opposite diffusion and migration fluxes. The co-ions in the nanopore are mainly transported by diffusion. A particular attention is focused on describing the interfacial effects at the nanopore entrance/exit. Detailed comparison between one-and two-dimensional models is performed in terms of rejection, pressure drop, and membrane potential dependence on the surface potential/charge density, volume flux, electrolyte concentration, and pore radius. A good agreement between these models is found when the Debye length is smaller than the pore radius and the surface potential or charge density are sufficiently low.

Carbon Coated Alumina Nanofiber Membranes for Selective Ion Transport

“…The two–parameter fit for C–Nafen membrane provides unphysical results, so we do not present them here. More precise description of membrane potential can be obtained with the help of Space‐charge model, but we do not use it here due to computational complexity.…”

Finite Ion Size Effects on Electrolyte Transport in Nanofiltration Membranes

“…Otherwise, a strong overestimation of rejection by the TMS model in comparison with the SC model was found. These conclusions were later confirmed by comparing the results from Uniform potential model with full 2D numerical modelling [15]. Different contributions of diffusion and migration fluxes to ion rejection were observed for cases of constant surface potential / charge density.…”

“…The mechanism of rejection for constant wall potential is related to balancing of counter-ions convective flux by the opposite migration and diffusion fluxes. In this case, the total flux of counter-ions becomes equal to that of co-ions, which is very small and mainly governed by diffusion [15].…”

“…The stationary flow and ion transport are described by the Navier-Stokes, Nernst-Plank, and Poisson equations [15,16,21]. We introduce dimensionless variables by taking the characteristic scales of length L (to be specified later), velocity J V , pressure ρJ 2 V , concentration C L , and potential RT /F .…”

Modelling Ion Transport in an Amine Solution Through a Nanofiltration Membrane

“…NF is a pressure-driven membrane process that has characteristics between ultrafiltration (UF) and reverse osmosis (RO) (Roy et al, 2017;Ryzhkov and Minakov, 2016;Wei et al, 2016;Zhao et al, 2016). NF has important advantages including lower pressure, higher permeate flux, low rejection for monovalent ions, high rejection for multivalent ions, and low energy consumption (Wei et al, 2016).…”