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

摘要

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 ∈{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 ∈ {1, 2}) for non-homogenous (P_(ij)~*) and homogenous (P_(ij)) solutions upon the average concentration of glucose in the membrane (C-bar) were calculated. The transport properties of membrane are characterized by coefficients determined experimentally: the coefficient of reflection (σ), hydraulic permeability (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-bar 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.