Calculation of ion rejection by extended Nernst-Planck equation with charged reverse osmosis membranes for single and mixed electrolyte solutions.

Abstract

The extended Nernst–Planck equation, which takes account of the effective charge densities, was used to calculate rejection of single- and mixed-electrolyte solutions. Ion rejections with negatively charged membranes were calculated for single electrolytes of various valences (sodium chloride, hydrochloric acid, magnesium chloride, sodium hydroxide, magnesium chloride, sodium sulfate), mixed electrolytes having common cations (sodium chloride/sodium sulfate, sodium hydroxide/sodium sulfate) and mixed electrolytes having common anions (sodium chloride/magnesium chloride, hydrochloric acid/magnesium chloride). Mono- and divalent coions in mixtures were found to be separated effectively, and monovalent ions in particular showed negative rejections in a certain condition. Mono- and divalent counter ions in mixtures were not separated as efficiently as coions in mixtures. Rejections were found to be strongly dependent upon volume flux, mole fraction of the mixture and ratio of fixed charge density to feed concentration. For the single solution of mono-monovalent electrolyte, rejection obtained from the extended Nernst–Planck equation was compared with that from the previous model based on the irreversible thermodynamics.