Abstract
The internal energy (U-energy) conversion to free energy (F-energy) and energy dissipation (S-energy) is a basic process that enables the continuity of life on Earth. Here, we present a novel method of evaluating F-energy in a membrane system containing ternary solutions of non-electrolytes based on the Kr version of the Kedem–Katchalsky–Peusner (K–K–P) formalism for concentration polarization conditions. The use of this formalism allows the determination of F-energy based on the production of S-energy and coefficient of the energy conversion efficiency. The K–K–P formalism requires the calculation of the Peusner coefficients Kijr and Kdetr (i, j ∈ {1, 2, 3}, r = A, B), which are necessary to calculate S-energy, the degree of coupling and coefficients of energy conversion efficiency. In turn, the equations for S-energy and coefficients of energy conversion efficiency are used in the F-energy calculations. The Kr form of the Kedem–Katchalsky–Peusner model equations, containing the Peusner coefficients Kijr and Kdetr, enables the analysis of energy conversion in membrane systems and is a useful tool for studying the transport properties of membranes. We showed that osmotic pressure dependences of indicated Peusner coefficients, energy conversion efficiency coefficient, entropy and energy production are nonlinear. These nonlinearities were caused by pseudophase transitions from non-convective to convective states or vice versa. The method presented in the paper can be used to assess F-energy resources. The results can be adapted to various membrane systems used in chemical engineering, environmental engineering or medical applications. It can be used in designing new technologies as a part of process management.
Highlights
We propose a novel form of network K–K–P equations, K r, that contain the Peusner coefficients Kijr (i, j ∈ {1, 2, 3}, r = A, B) and the equation for the global source of entropy (( φrS )Kr )
The method of F-energy determination that we proposed in this paper for cellulose membranes can be used to characterize other membrane systems, in which a solution is transported through the membrane in osmotic-diffusive transport
The coefficients Kijr are dependent on the concentration of the solutions separated by the membrane and the configuration of the membrane system
Summary
Energy conversion is one of the basic phenomena that ensure the continuity of life on Earth. It occurs in various types of micro- and macrosystems including membrane systems. The study of membrane transport processes is both cognitive and applicable [1,2]. Cognitive studies include molecular mechanisms of the exchange of fluids and dissolved substances by biological and/or synthetic membranes [3]. Membranes in living systems act as regulators of the transport of substances necessary for living organisms to maintain their metabolic activity, regulate the pressure balance and for structural integrity.
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