Method of evaluation of the transport properties in polymeric membrane systems using the Nrhybrid form of Kedem–Katchalsky–Peusner formalism

In this paper, the Nrhybrid 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 (Nrij, i, j∈ {1, 2, 3}, r= A, B), which determine the transport properties of the membrane, the nrijcoefficients which determine the degree of coupling, and the energy conversion efficiency coefficient (erij). 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 Lr, Rr, Hr, Krversions of the Kedem–Katchalsky–Peusner formalism are presented. The formalism using the Nrform of the hybrid Kedem–Katchalsky–Peusner equations can be a useful tool to study the transport properties of artificial membranes for environmental engineering.