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

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.