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Updated: Mar 12, 2026

Merging Ion Concentration Polarization between Juxtaposed Ion Exchange Membranes to Block the Propagation of the Polarization Zone
Published on: February 23, 2017
The mathematical model of concentration polarization coefficient in membrane transport and volume flows
Arkadiusz Bryll1, Andrzej Ślęzak2
1Department of Public Health, Częstochowa University of Technology, 36b Armia Krajowa Al., 42200, Częstochowa, Poland. tex@op.pl.
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 (ζ s ) on a volume flux (J vm ), an osmotic force (Δπ) and a hydrostatic force (ΔP) of different values. Property ζ s = f(J vm ) for J vm > 0 and for J vm ≈ 0 and property ζ s = f(ΔC 1) are calculated. Moreover, results of a simultaneous influence of ΔP and Δπ on a value of coefficient ζ s when J vm = 0 and J vm ≠ 0 are investigated and a graphical representation of the dependences obtained in the research is provided. Also, mathematical relationships between the coefficient ζ s and a concentration Rayleigh number (R C ) were studied providing a relevant graphical representation. In an experimental test, aqueous solutions of glucose and ethanol were used.
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