Derivation of film theory coupled Spiegler-Kedem-Katchalsky model for membrane separation and purification

TL;DR

This paper derives a coupled film theory and Spiegler-Kedem-Katchalsky model to analyze concentration polarization in membrane separation, providing analytical solutions to predict flux and rejection rates.

Contribution

It introduces a coupled differential equation model integrating film theory with SKK for membrane processes, offering analytical solutions for concentration polarization effects.

Findings

Analytical solutions for concentration polarization differential equations.

Model can evaluate polarization degree and predict flux and rejection.

Provides a framework for improved membrane separation analysis.

Abstract

In this article, we will derive the differential equations considering the concentration polarization (\textsc{cp}) in membrane separations and purifications, which involve convective-diffusive equations of the concentration polarization layer and the Spiegler-Kedem-Katchalsky (\textsc{skk}) model of the membrane layer. Analytical solutions of these differential equations are straightforward and given. The film theory coupled \textsc{skk} model can be used to evaluate the degree of concentration polarization, and predict flux and rejection rates.