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 (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.

Influencing factors of polarization coefficient of hollow fiber membrane

“…As shown in Figure 2, when there is no concentration polarization phenomenon, the partial pressure of oxygen on the hollow fiber membrane surface is equal to the partial pressure of oxygen in the gas phase, and the oxygen permeability driving force F is equal to the effective oxygen permeability driving force F eff . When there is concentration polarization phenomenon, the effective oxygen permeability driving force F eff is less than the oxygen permeability driving force F (Tong and Xiaofeng, 2017; Bryll and Ślęzak, 2017). Therefore, in this paper, the deviation degree of effective oxygen permeability driving force F eff compared to the oxygen permeability driving force F was used to define the concentration polarization coefficient (Yan and Guiping, 2015), and then a more intuitive oxygen permeability flux was used to express it, i.e.…”

Flow Rate Prediction for a Semi-permeable Membrane at Low Reynolds Number in a Circular Pipe

“…Instead of the direct measurement of the concentration on the membrane, the boundary film theory (Sablani et al 2001;Porter 1972), used for concentration polarization, with non-dimensional correlation formulae (Berg et al 1989;Lévêque 1928) or velocity variation method (Nakao and Kimura 1981) is used to predict the concentration value on the membrane surface. In the theoretical studies on the membrane transport, the Kedem-Katchalsky model has been modified to include the effect of the concentration boundary layer (Kargol 1996(Kargol , 2000Bryll and Ślȩzak 2017). However, the prediction method has not been established because it is difficult to obtain an accurate value of the mass transfer coefficient for the boundary layer thickness in the boundary film theory.…”