L version of the transformed Kedem-Katchalsky equations for membrane transport of electrolyte solutions and internal energy conversion

Abstract

Background: One of the important formalisms of non-equilibrium thermodynamics is Peusner network thermodynamics. The description of the energy conversion in membrane processes, i.e., the conversion of the internal energy of the system into the dissipated energy and the free energy used for the work associated with the transport of solution components, allows us to describe the relationship between these energies and the thermodynamic forces acting in the membrane system.

Objectives: The aim of this study was to develop a procedure to transform the Kedem-Katchalsky equations for the transport of binary electrolytic solutions across a membrane into the Kedem-Katchalsky-Peusner equations based on Peusner network thermodynamics. The conversion of electrochemical energy to free energy in the membrane system was also determined.

Material and methods: The nanobiocellulose biomembranes (Biofill) were the subject of the study with experimentally determined transport parameters for aqueous NaCl solutions. The research method is the Kedem-Katchalsky-Peusner formalism for binary electrolyte solutions with introduced Peusner coefficients.

Results: The coefficients of the L version of the membrane transport equations and the Peusner coupling coefficients were derived as functions of NaCl concentration in the membrane. Based on these coefficients, the fluxes of internal energy of the system, energy dissipated to the surroundings and free energy related to the transport of electrolyte across the membrane were calculated and presented as functions of the osmotic and electric forces on the membrane.

Conclusions: The Peusner coefficients obtained from the transformations of the coefficients of the Kedem-Katchalsky formalism for the transport of electrolyte solutions through the Biofill membrane were used to calculate the coupling coefficients of the membrane processes and the dissipative energy flux. The dissipative energy flux takes the form of a quadratic form due to the thermodynamic forces on the membrane - second degree curves are obtained. Moreover, the dissipative energy flux as a function of thermodynamic forces allowed us to examine the energy conversion in transport processes in the membrane system.

Keywords: Kedem–Katchalsky–Peusner equations; Peusner transport coefficients; bacterial cellulose membrane; internal energy conversion; membrane transport.