Influence of the Exclusion-Enrichment Effect on Ion Transport in Two-Dimensional Molybdenum Disulfide Membranes

Two-dimensional (2D) nanosheet membranes have been widely studied for water and wastewater treatment. However, mass transport inside 2D nanosheet membranes is far from being fully understood, and suitable applications of these membranes are yet to be identified. In this study, we investigate ion transport inside a 2D molybdenum disulfide (MoS₂) membrane by combining experimental results with numerical modeling. Specifically, we analyze the influence of the electrical double layer (EDL) extension on ion diffusion in the MoS₂ membrane, and a parameter called the exclusion-enrichment coefficient (β) is introduced to quantify how the electrostatic interaction between the coions and the EDL can affect the ion diffusion. Using the model developed in this study, the β values under different experimental conditions (feed solution concentration and applied hydraulic pressure) are calculated. The results show that coion diffusion inside the membrane can be retarded since β is smaller than one. Furthermore, the underlying mechanism is explored by theoretically estimating the radial ion concentration and electrical potential distributions across the membrane nanochannel. In addition, we find that convective mass transport can weaken the exclusion-enrichment effect by increasing β. Based on the results in this study, the potential applications and feasible membrane design strategies of 2D nanosheet membranes are discussed.