Search Results (5)

Peusner’s network thermodynamics (PNT) is an important way of describing processes in nonequilibrium thermodynamics. PNT allows energy transport and conversion processes in membrane systems to be described. This conversion concerns internal energy transformation into free and dissipated energies linked with the membrane transport of solutes. A transformation of the Kedem–Katchalsky (K-K) equations into the R variant of Kedem–Katchalsky–Peusner (K-K-P) equations was developed for the transport of binary electrolytic solutions through a membrane. The procedure was verified for a system in which a membrane Ultra Flo 145 Dialyser separated aqueous NaCl solutions. Peusner coefficients were calculated by the transformation of the K-K coefficients. Next, the coupling coefficients of the membrane processes and energy fluxes for electrolyte solutions transported through the membrane were calculated based on the Peusner coefficients. The efficiency of energy conversion in the membrane transport processes was estimated, and this coefficient increased nonlinearly with the increase in the solute concentration in the membrane. In addition, the energy fluxes as functions of ionic current density for constant solute fluxes were also investigated for membrane transport processes in the Ultra Flo 145 Dialyser membrane. Full article

Peusner’s network thermodynamics (PNT) is one of the more important formalisms of nonequilibrium thermodynamics used to describe membrane transport and the conversion of the internal energy of the system into energy dissipated in the environment and free energy used for the work involved in the transport of solution components in membrane processes. A procedure of transformation the Kedem–Katchalsky (K-K) equations for the transport of binary electrolytic solutions through a membrane to the Kedem–Katchalsky–Peusner (K-K-P) equations based on the PNT formalism for liquid junction potentials was developed. The subject of the study was a membrane used for hemodialysis (Ultra Flo 145 Dialyser) and aqueous NaCl solutions. The research method was the L version of the K-K-P formalism for binary electrolyte solutions. The Peusner coefficients obtained from the transformations of the K-K formalism coefficients for the transport of electrolyte solutions through the artificial polymer membrane were used to calculate the coupling coefficients of the membrane processes and to calculate the dissipative energy flux. In addition, the dissipative energy flux, as a function of thermodynamic forces, made it possible to investigate the energy conversion of transport processes in the membrane system. Full article

We evaluated the transport properties of a bacterial cellulose (BC) membrane for aqueous ethanol solutions. Using the R^r version of the Kedem–Katchalsky–Peusner formalism (KKP) for the concentration polarization (CP) conditions of solutions, the osmotic and diffusion fluxes as well as the membrane transport parameters were determined, such as the hydraulic permeability (L_p), reflection (σ), and solute permeability (ω). We used these parameters and the Peusner ($R_{ij}^r$) coefficients resulting from the KKP equations to assess the transport properties of the membrane based on the calculated dependence of the concentration coefficients: the resistance, coupling, and energy conversion efficiency for aqueous ethanol solutions. The transport properties of the membrane depended on the hydrodynamic conditions of the osmotic diffusion transport. The resistance coefficients $R_{11}^r$, $R_{22}^r$, and $R_{det}^r$ were positive and higher, and the $R_{12}^r$ coefficient was negative and lower under CP conditions (higher in convective than nonconvective states). The energy conversion was evaluated and fluxes were calculated for the U-, F-, and S-energy. It was found that the energy conversion was greater and the S-energy and F-energy were lower under CP conditions. The convection effect was negative, which means that convection movements were directed vertically upwards. Understanding the membrane transport properties and mechanisms could help to develop and improve the membrane technologies and techniques used in medicine and in water and wastewater treatment processes. Full article

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 $K^r$ 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 $K_{ij}^r$ and $K_{det}^r$ (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 $K^r$ form of the Kedem–Katchalsky–Peusner model equations, containing the Peusner coefficients $K_{ij}^r$ and $K_{det}^r$, 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. Full article

The paper presents the $R^r$ matrix form of Kedem–Katchalsky–Peusner equations for membrane transport of the non-homogeneous ternary non-electrolyte solutions. Peusner’s coefficients $R_{ij}^r$ and det [$R^r$] (i, j ∈ {1, 2, 3}, r = A, B) occurring in these equations, were calculated for Nephrophan biomembrane, glucose in aqueous ethanol solutions and two different settings of the solutions relative to the horizontally oriented membrane for concentration polarization conditions or homogeneity of solutions. Kedem–Katchalsky coefficients, measured for homogeneous and non-homogeneous solutions, were used for the calculations. The calculated Peusner’s coefficients for homogeneous solutions depend linearly, and for non-homogeneous solutions non-linearly on the concentrations of solutes. The concentration dependences of the coefficients $R_{ij}^r$ and det [$R^r$] indicate a characteristic glucose concentration of 9.24 mol/m³ (at a fixed ethanol concentration) in which the obtained curves for Configurations A and B intersect. At this point, the density of solutions in the upper and lower membrane chamber are the same. Peusner’s coefficients were used to assess the effect of concentration polarization and free convection on membrane transport (the ξ_ij coefficient), determine the degree of coupling (the $r_{ij}^r$ coefficient) and coupling parameter (the $Q_R^r$ coefficient) and energy conversion efficiency (the ${\left(e_{ij}^r\right)}_r$ coefficient). Full article