Transp Porous Med (2015) 106:1–20 DOI 10.1007/s11242-014-0352-1 Network Hybrid Form of the Kedem–Katchalsky Equations for Non-homogenous Binary Non-electrolyte Solutions: Evaluation of P ∗ ij Peusner’s Tensor Coefficients Kornelia M. Batko · Izabella ´ Sle ˛ zak-Prochazka · Andrzej ´ Sle ˛ zak Received: 31 March 2014 / Accepted: 17 June 2014 / Published online: 29 October 2014 © The Author(s) 2014. This article is published with open access at Springerlink.com Abstract 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 sym- metric 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 ∈{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 con- centration 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 ∈{1, 2}) for non-homogenous ( P ∗ ij ) and homogenous ( P ij ) solutions upon the average concentration of glucose in the membrane ( C ) were calculated. The transport properties of membrane are characterized by coefficients determined experimentally: the coefficient of reflection (σ ), hydraulic perme- ability ( L p ), and solution permeability (ω) 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 C and the configuration of the membrane system. The values of the coef- ficients 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 K. M. Batko (B ) Membrane Science Group, Department of Informatics for Economics, University of Economics in Katowice, 2B Bogucicka Str., 40287 Katowice, Poland e-mail: kornelia.batko@ue.katowice.pl I. ´ Sle ˛zak-Prochazka · A. ´ Sle ˛zak Membrane Science Group, Department ofPublic Health, Cze˛stochowa University ofTechnology, 36b Armia Krajowa Al., 42200 Czestochowa, Poland e-mail: aslezak52@gmail.com 123