Theoretical calculation of reflection coefficients of single salt solutions through charged porous membranes

Abstract

Normal rejections of salt solutions through charged membranes have been studied a lot in theories and experiments, but few works touched upon negative anomalous rejection. In this paper, the negative rejection behaviors were investigated based on the reflection coefficients (σ). The space-charge (SC) model and the Teorell–Meyer–Sievers (TMS) model were adopted to calculate σ for single salt solutions with different ionic valences and diffusion coefficients. The results indicated that equivalent concentration is beneficial to describe σ. σ would be negative in a certain intermediate concentration region if the diffusion coefficient ratio of co-ion and counter-ion is more than 1.0. The negative osmosis phenomena can be explained utilizing the ionic transport numbers. Concerning the comparison of the two models, TMS model would overestimate the σ when the radius is larger than 5.0 nm, and the dimensionless charge density in the pore wall is more than 1.0. Otherwise, the TMS model is comparable to the SC model when σ is positive, or else, it would underrate σ. These findings are helpful to explain the nature of negative osmosis phenomena.