The Rr Form of the Kedem–Katchalsky–Peusner Model Equations for Description of the Membrane Transport in Concentration Polarization Conditions

Kornelia M Batko,Sławomir Grzegorczyn,Wioletta M Bajdur,Andrzej Ślęzak

doi:10.3390/e22080857

Abstract

The paper presents the matrix form of Kedem–Katchalsky–Peusner equations for membrane transport of the non-homogeneous ternary non-electrolyte solutions. Peusner’s coefficients and det [] (i, j ∈ {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 and det [] indicate a characteristic glucose concentration of 9.24 mol/m3 (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 ξij coefficient), determine the degree of coupling (the coefficient) and coupling parameter (the coefficient) and energy conversion efficiency (the coefficient).

Highlights

Membrane transport belongs to the group of processes described by thermodynamics of irreversible processes, called modern thermodynamics
This theory was created and described by Lars Onsager, Theophile De Donder, Ilya Prigogine and others [1]. This field of knowledge has provided many research tools for transport mechanisms, including membrane transport, which is used in many areas of science and technology [2,3,4,5,6,7,8,9]
Nephrophan is a microporous, highly hydrophilic membrane made of cellulose acetate (cello- triacetate (OCO-CH3 )n )

Summary

Introduction

Membrane transport belongs to the group of processes described by thermodynamics of irreversible processes, called modern thermodynamics. This theory was created and described by Lars Onsager, Theophile De Donder, Ilya Prigogine and others [1]. This field of knowledge has provided many research tools for transport mechanisms, including membrane transport, which is used in many areas of science (physics, biology, chemistry) and technology (biotechnology, biomedical engineering, water and sewage engineering, bioenergetics) [2,3,4,5,6,7,8,9]. Several versions of these equations classical form [12] and forms presented by Kargol and Kargol [13,14], Peusner [15], Elmoazzen et al [16], Cheng and Pinsky [17] and Cardoso and Cartwright [18]

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Conclusion