The [R.sup.r] Form of the Kedem-Katchalsky-Peusner Model Equations for Description of the Membrane Transport in Concentration Polarization Conditions

The paper presents the [R.sup.r] matrix form of Kedem-Katchalsky-Peusner equations for membrane transport of the non-homogeneous ternary non-electrolyte solutions. Peusner's coefficients [mathematical expression not reproducible] and det [[R.sup.r]] (i, j [member of] {1, 2, 3}, r = A, B) occurr...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2020-08, Vol.22 (8), p.1
Main Authors: Batko, Kornelia M, Slezak, Andrzej, Grzegorczyn, Slawomir, Bajdur, Wioletta M
Format: Article
Language:English
Subjects:
Chemical properties
Dextrose
Glucose
Mathematical models
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Summary:The paper presents the [R.sup.r] matrix form of Kedem-Katchalsky-Peusner equations for membrane transport of the non-homogeneous ternary non-electrolyte solutions. Peusner's coefficients [mathematical expression not reproducible] and det [[R.sup.r]] (i, j [member of] {1, 2, 3}, r = A, B) occurring in these equations, were calculated for Nephrophan biomembrane, glucose in aqueous ethanol solutions and two different settings of the solutions relative to the horizontally oriented membrane for concentration polarization conditions or homogeneity of solutions. Kedem-Katchalsky coefficients, measured for homogeneous and non-homogeneous solutions, were used for the calculations. The calculated Peusner's coefficients for homogeneous solutions depend linearly, and for non-homogeneous solutions non-linearly on the concentrations of solutes. The concentration dependences of the coefficients [R.sup.r]j and det [[R.sup.r]] indicate a characteristic glucose concentration of 9.24 mol/[m.sup.3] (at a fixed ethanol concentration) in which the obtained curves for Configurations A and B intersect. At this point, the density of solutions in the upper and lower membrane chamber are the same. Peusner's coefficients were used to assess the effect of concentration polarization and free convection on membrane transport (the [[xi].sub.ij] coefficient), determine the degree of coupling (the [mathematical expression not reproducible] coefficient) and coupling parameter (the [Q.sup.r]R coefficient) and energy conversion efficiency (the [mathematical expression not reproducible] coefficient).
ISSN:1099-4300
1099-4300
DOI:10.3390/e22080857