The ionic separation efficiency of a novel membrane module comprising an array of microchannel units is analyzed. Under the Debye–Hückel approximation, we derive a semianalytical expression for the ionic separation efficiency. Analyses reveal that the effects of the size of the microchannel, the fixed charge density in the membrane layer, and the permittivity of the membrane layer on ionic separation efficiency depend strongly on the valence type of electrolyte in treated water. Under the condition of a symmetric electrolyte, the ionic separation efficiency is found to be about unity and unresponsive to variation of system parameters. If the valence of the cation is higher than that of the anion, the ionic separation efficiency is larger than unity, and decreases to unity as the size of the microchannel increases. In contrast, if the valence of the cation is lower than that of the anion, the ionic separation efficiency is smaller than unity and increases to unity as the size of the microchannel increases. Under the latter two conditions, the effects of both fixed charge density in the membrane layer and permittivity of the membrane layer on the ionic separation efficiency are found to be reversed.
Journal of Colloid and Interface Science 307(2), pp.516-523