Network Hybrid Form of the Kedem-Katchalsky Equations for Non-homogenous Binary Non-electrolyte Solutions: Evaluation of \(P_{ij}}\) Peusner's Tensor Coefficients

• Published in: Transport in porous media Vol. 106; no. 1; pp. 1 - 20
• Main Authors: Batko, Kornelia M, Slezak-Prochazka, Izabella, Slezak, Andrzej
• Format: Journal Article
• Language: English
• Published: 01.01.2015
• Subjects: Ethyl alcohol; Glucose; Hydraulics; Mathematical analysis; Membranes; Networks; Permeability; Transport
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-014-0352-1

Methods of Peusner's network of thermodynamics enable the symmetric or hybrid transformation of classic Kedem-Katchalsky (K-K) equations into a network form. In the case of binary non-electrolyte solutions (homogenous and non-homogenous ones), two symmetric and two hybrid forms of the K-K equations may be obtained, containing relatively symmetric ( \(R_{ij}*},\,R_{ij},\,L_{ij}*}\) or \(L_{ij}),\) or hybrid ( \(P_{ij}*},\,P_{ij},\,H_{ij}*}\) or \(H_{ij})\) Peusner's coefficients. In the following paper, the network form of the K-K equations was obtained, containing the Peusner's coefficients \(P_{ij}*}\,(i,\, j\in \{1,\,2\}),\) and creating matrix of the second row of the Peusner's coefficients \([P*}].\) The equations were used to study transport of aqueous glucose solutions through a Nephrophan membrane oriented horizontally as well as configurations A and B of a membrane system. The configuration A involves a solution with a higher concentration placed under the membrane, whereas a solution with a lower concentration is placed above the membrane. In the configuration B, the solutions are swapped with places. Dependences of the Peusner's coefficients \(P_{ij}*}\) and \(P_{ij}\,(i,\, j \in \{1,\,2\})\) for non-homogenous ( \(P_{ij}*})\) and homogenous ( \(P_{ij})\) solutions upon the average concentration of glucose in the membrane ( \(\overline{{C}})\) were calculated. The transport properties of membrane are characterized by coefficients determined experimentally: the coefficient of reflection ( \(\sigma \) ), hydraulic permeability ( \(L_\mathrm{p})\) , and solution permeability ( \(\omega \) ) for aqueous glucose or ethanol solutions. The calculations show that values of coefficients \(P_{11}*},\,P_{12}*},\,P_{21}*}\) , and \(P_{22}*}\) depend non-linearly on both the membrane \(\overline{{C}}\) and the configuration of the membrane system. The values of the coefficients are different from the values of the coefficients \(P_{11},\,P_{12},\,P_{21}\) and \(P_{22}.\) Moreover, the coefficients \(P_{11},\,P_{12},\,P_{21}\) and \(P_{22}\) do not depend on the configuration of the membrane system. It was shown that there is a threshold value of concentration above which relations \(P_{11}*}/P_{11},\,P_{12}*}/P_{12}\) and \(P_{22}*}/P_{22}\) depend on the configuration of the membrane system.