Method of evaluation of the transport properties in polymeric membrane systems using the N^r hybrid form of Kedem–Katchalsky–Peusner formalism

In this paper, the N^r hybrid version of the Kedem–Katchalsky–Peusner (K-K-P) formalism for concentration polarization conditions is developed. For ternary non-electrolyte solutions, this formalism includes the hybrid Peusner coefficients (N^r_ij, i, j ∈ {1, 2, 3}, r = A, B), which determine the transport properties of the membrane, the n^r_ij coefficients which determine the degree of coupling, and the energy conversion efficiency coefficient (e^r_ij). Besides, K-K-P formalism is the basis for a method to evaluate the conversion of internal energy (U-energy) into free energy (F-energy) and dissipated energy (S-energy) in a membrane system containing ternary non-electrolyte solutions separated by a polymer membrane. Moreover, it is shown that the Peusner coefficients are proposed as a flux-induced version of the modified Péclet number for concentration polarization conditions. The present paper is a continuation of several previous papers, of which the L^r, R^r, H^r, K^r versions of the Kedem–Katchalsky–Peusner formalism are presented. The formalism using the N^r form of the hybrid Kedem–Katchalsky–Peusner equations can be a useful tool to study the transport properties of artificial membranes for environmental engineering.