We investigate diffusive transport in a membrane system with a horizontally mounted membrane under concentration polarization conditions performed by a laser interferometry method. The data obtained from two different theoretical models are compared to the experimental results of the substance flux. In the first model, the membrane is considered as infinitely thin, while in the second one as a wall of finite thickness. The theoretical calculations show sufficient correspondence with the experimental results. On the basis of interferometric measurements, the relative permeability coefficient (ζs) for the system, consisting of the membrane and concentration boundary layers, was also obtained. This coefficient reflects the concentration polarization of the membrane system. The obtained results indicate that the coefficient ζs of the membrane-concentration boundary layer system decreases in time and seems to be independent of the initial concentration of the solute.
On the basis of the classic formula of the concentration Rayleigh number and the Kedem-Katchalsky equation for diffusive membrane transport, we derived the equations of sixteenth order which show the dependence of the thicknesses of the concentration boundary layers on the difference of the solution concentrations, the concentration Rayleigh number, the solute permeability coefficient of the membrane and the diffusion coefficients in the solution, the kinematic viscosity of the solution, the density of solutions, the temperature and gravitational acceleration. The obtained equation has numerical solutions in the first, third and fourth quadrant of a co-ordinate system. However, only two solutions from the first quadrant of the co-ordinate system have physical meaning. Confining ourselves to the set of solutions with physical meaning only, the thicknesses of concentration boundary layers for different parameters occurring in the obtained equation were calculated numerically.
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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