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 ) on a volume flux (J ), an osmotic force (Δπ) and a hydrostatic force (ΔP) of different values. Property ζ  = f(J ) for J  > 0 and for J  ≈ 0 and property ζ  = f(ΔC ) are calculated. Moreover, results of a simultaneous influence of ΔP and Δπ on a value of coefficient ζ when J  = 0 and J  ≠ 0 are investigated and a graphical representation of the dependences obtained in the research is provided. Also, mathematical relationships between the coefficient ζ and a concentration Rayleigh number (R ) were studied providing a relevant graphical representation. In an experimental test, aqueous solutions of glucose and ethanol were used.