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 (zeta (s) ) on a volume flux (J (vm) ), an osmotic force (Delta pi) and a hydrostatic force (Delta P) of different values. Property zeta (s) = f(J (vm) ) for J (vm) > 0 and for J (vm) ae 0 and property zeta (s) = f(Delta C (1)) are calculated. Moreover, results of a simultaneous influence of Delta P and Delta pi on a value of coefficient zeta (s) when J (vm) = 0 and J (vm) not equal 0 are investigated and a graphical representation of the dependences obtained in the research is provided. Also, mathematical relationships between the coefficient zeta (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.