Simplifying concentration-polarization of trace-ions in pressure-driven membrane processes

TL;DR

This paper develops an analytical extension to classic film theory to accurately model concentration-polarization of trace ions in pressure-driven membrane processes, incorporating electromigration effects for better prediction and process optimization.

Contribution

It introduces a seamless extension to classic film theory that includes electromigration, enabling more accurate modeling of trace-ion CP in dominant salt solutions.

Findings

Electromigration significantly affects ion CP in membrane processes.

The new equations improve prediction accuracy over classic models.

Implications for membrane scaling and contaminant transport are quantified.

Abstract

Accounting for concentration-polarization (CP) is critical for modeling solute transport in membrane separation processes. In a mixed-electrolyte solution, ions CP is affected not only by diffusion and advection but also by electromigration. Yet, the classic film model, lacking an electromigration term, is frequently used for modeling ion CP. Often, ion CP is altogether neglected to reduce the computational load. Here, we study the CP of trace ions in a dominant salt solution, a case relevant for many reverse-osmosis and nanofiltration processes. First, we revisit the solution-diffusion-electromigration-film theory to obtain an analytical solution for the CP and membrane-transport of trace-ions in a dominant salt solution. Secondly, we consider limiting conditions relevant to reverse-osmosis and nanofiltration, from which we derive two compact equations that emerge as a seamless extension to the classic film theory. These equations can be used to account for the effect of electromigration on CP with minimal effort. Thirdly, we use our theory to quantify the effect of electromigration on ion CP in different dominant salt solutions. Finally, by analyzing two environmental membrane processes, we demonstrate how our theory deviates from the conventional one and quantify the implications on membrane scaling potential and the transport of ionic contaminants.