Trace ion concentration polarization near water-permeable salt-rejecting membranes Oded Nir Ben Gurion University of the Negev, Israel When water is driven through a membrane that rejects solutes, partially or fully, a solute concentration gradient evolves at the water-membrane interface. This phenomenon, known as concentration-polarization, arises due to the advection of solutes towards the surface and their accumulation in a poorly mixed water layer near the interface. A steady state is reached once the diffusive flux of solutes in the opposite direction becomes equal to the advective flux towards the membrane. The extent of concentration-polarization depends on hydrodynamics, temperature, and solution composition. It can have severe effects on membrane processes such as desalination and water purification. For example, concentration-polarization may increase energy demand, reduce salt and contaminant removal, and induce the accumulation of solids on the membrane surface (fouling). Therefore, accounting for concentration-polarization is a cornerstone of modeling solute transport in membrane separation processes. In a mixed-electrolyte solution, ion concentration-polarization is not only affected by diffusion and advection but also by electromigration. An electric potential emerges at the interface due to the difference in diffusion rate between cations and anions. Yet, the classic film model, lacking an electromigration term, is still frequently used for modeling ion concentration-polarization, probably due to the lack of a simple mathematical description. Moreover, ion concentration-polarization tends to be altogether neglected in elaborated simulations to reduce the computational load. Herein, we present a compact concentration-polarization expression, accounting for electromigration, that emerges as a seamless extension of the classic film theory. This equation is an approximation based on the Nernst-Planck theory that can be used in the case of multicomponent mixtures with one dominant salt, which is relevant for nanofiltration applications such as removing trace ionic contaminants. To demonstrate the applicability and significance, we used the theory to quantify the effect of electromigration on ion concentration-polarization in different dominant salt solutions. Finally, by analyzing several membrane processes used in environmental applications, such as wastewater effluent treatment, we demonstrate how the new compact expression for concentration-polarization deviates from the conventional one and quantify the implications on membrane scaling potential and the transport of trace ionic contaminants. We found that in conditions promoting high concentration-polarization, the deviation is significant, which warrants the use of a more physical model, which accounts for ion electromigration at the interface.
P30
© The Author(s), 2023
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