The mathematical model of concentration polarization coefficient in membrane transport and volume flows

Abstract

In this paper, the authors investigate the membrane transport of aqueous non-electrolyte solutions in a single-membrane system with the membrane mounted horizontally. The purpose of the research is to analyze the influence of volume flows on the process of forming concentration boundary layers (CBLs). A mathematical model is provided to calculate dependences of a concentration polarization coefficient (ζs) on a volume flux (Jvm), an osmotic force (Δπ) and a hydrostatic force (ΔP) of different values. Property ζs = f(Jvm) for Jvm > 0 and for Jvm ≈ 0 and property ζs = f(ΔC1) are calculated. Moreover, results of a simultaneous influence of ΔP and Δπ on a value of coefficient ζs when Jvm = 0 and Jvm ≠ 0 are investigated and a graphical representation of the dependences obtained in the research is provided. Also, mathematical relationships between the coefficient ζs and a concentration Rayleigh number (RC) were studied providing a relevant graphical representation. In an experimental test, aqueous solutions of glucose and ethanol were used.