Search Results (14)

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

One of the most important formalisms used to describe membrane transport is Onsager–Peusner thermodynamics (TOP). Within the TOP framework, a procedure has been developed for the transformation of the Kedem–Katchalsky (K–K) equations for the transport of binary electrolytic solutions across a membrane into the Kedem–Katchalsky–Peusner (K–K–P) equations. The membrane system with an Ultra Flo 145 Dialyser membrane used for hemodialysis and aqueous NaCl solutions was used as experimental setup. The H version of K–K–P formalism for binary electrolyte solutions was used to evaluate theoretical coefficients characterizing fluxes of energies and efficiencies for membrane transport processes. The coupling coefficients of membrane processes and the dissipative energy flux were calculated on the basis of the Peusner coefficients obtained from transformation of K–K coefficients. The knowledge of dissipative energy flux, which is a function of thermodynamic forces, allows for the determination of the energy conversions during transport processes in a membrane system. In addition, a frictional interpretation of the obtained coefficients is presented. 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

Electric potentials referred to as the gravielectric effect ($∆{\Psi }_S$) are generated in a double-membrane system containing identical polymer membranes set in horizontal planes and separating non-homogenous electrolyte solutions. The gravielectric effect depends on the concentration and composition of the solutions and is formed due to the gravitational field breaking the symmetry of membrane complexes/concentration boundary layers formed under concentration polarization conditions. As a part of the Kedem–Katchalsky formalism, a model of ion transport was developed, containing the transport parameters of membranes and solutions and taking into account hydrodynamic (convective) instabilities. The transition from non-convective to convective or vice versa can be controlled by a dimensionless concentration polarization factor or concentration Rayleigh number. Using the original measuring set, the time dependence of the membrane potentials was investigated. For steady states, the $∆{\Psi }_S$ was calculated and then the concentration characteristics of this effect were determined for aqueous solutions of NaCl and ethanol. The results obtained from the calculations based on the mathematical model of the gravitational effect are consistent with the experimental results within a 7% error range. It has been shown that a positive or negative gravielectric effect appeared when a density of the solution in the inter-membrane compartment was higher or lower than the density in the outer compartments. The values of the $∆{\Psi }_S$ were in a range from 0 to 27 mV. It was found that, the lower the concentration of solutions in the outer compartments of the two-membrane system ($C_0$), for the same values of $C_m/C_0$, the higher the $∆{\Psi }_S$, which indicates control properties of the double-membrane system. The considered two-membrane electrochemical system is a source of electromotive force and functions as an electrochemical gravireceptor. Full article

In this work, we analyse the influence of the parameters of a mathematical model, previously proposed by the authors, for reproducing atheroma plaque in arteries. The model uses Navier–Stokes equations to calculate the blood flow along the lumen in a transient mode. It also uses Darcy’s law, Kedem–Katchalsky equations, and the three-pore model to simulate plasma and substance flows across the endothelium. The behaviours of all substances in the arterial wall are modelled with convection–diffusion–reaction equations, and finally, plaque growth is calculated. We consider a 2D geometry of a carotid artery, but the model can be extrapolated to other geometries or arteries, such as the coronaries or the aorta. A mono-variant sensitivity analysis of the model parameters was performed, with values of $\pm 25\%$ and $\pm 10\%$, with respect to the values of the previous model. The results were analysed with respect to the volume in the plaque of foam cells (FC), synthetic smooth muscle cells (SSMC), and collagen fibre. It was observed that the volume in the plaque of the different substances (FC, SSMC, and collagen) has a strong influence on the results, so it could be used to analyse the vulnerability of plaque. The stenosis ratio of the plaque was also analysed, showing a strong influence on the results as well. Parameters that influence all the results considered when ranged $\pm 10\%$ are the rate of LDL degradation and the diffusion coefficients of LDL and monocytes in the arterial wall. Furthermore, it was observed that the change in the volume of foam cells in the plaque has a greater influence on the stenosis ratio than the change of synthetic smooth muscle cells or collagen fibre. 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

Tannic acid (TA)–Fe³⁺ membranes have received recent attention due to their sustainable method of fabrication, high water flux and organic solutes rejection performance. In this paper, we present a description of the transport of aqueous solutions of dyes through these membranes using the transport parameters of the Spiegler–Kedem–Katchalsky (SKK) model. The reflection coefficient (σ) and solute permeability ($P_S$) of the considered TA–Fe³⁺ membranes were estimated from the non-linear model equations to predict the retention of solutes. The coefficients σ and $P_S$ depended on the porous medium and dye molecular size as well as the charge. The simulated rejections were in good agreement with the experimental findings. The model was further validated at low permeate fluxes as well as at various feed concentrations. Discrepancies between the observed and simulated data were observed at low fluxes and diluted feed solutions due to limitations of the SKK model. This work provides insights into the mass transport mechanism of dye solutions and allows the prediction of dye rejection by the TFC membranes containing a TA–Fe³⁺ selective layer using an SKK model. 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

Based on Kedem–Katchalsky formalism, the model equation of the membrane potential ($\Delta {\psi }_s$) generated in a membrane system was derived for the conditions of concentration polarization. In this system, a horizontally oriented electro-neutral biomembrane separates solutions of the same electrolytes at different concentrations. The consequence of concentration polarization is the creation, on both sides of the membrane, of concentration boundary layers. The basic equation of this model includes the unknown ratio of solution concentrations ($C_i/C_e)$ at the membrane/concentration boundary layers. We present the calculation procedure ($C_i/C_e)$ based on novel equations derived in the paper containing the transport parameters of the membrane ($L_p$, $\sigma$, and $\omega$), solutions ($\rho$, $\nu$), concentration boundary layer thicknesses (${\delta }_l$, ${\delta }_h$), concentration Raileigh number ($R_C$), concentration polarization factor (${\zeta }_s$), volume flux ($J_v$), mechanical pressure difference ($\Delta P$), and ratio of known solution concentrations ($C_h/C_l$). From the resulting equation, $\Delta {\psi }_s$ was calculated for various combinations of the solution concentration ratio ($C_h/C_l$), the Rayleigh concentration number ($R_C$), the concentration polarization coefficient (${\zeta }_s$), and the hydrostatic pressure difference $(\Delta P$). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m⁻³ ($C_l$) was on one side of the membrane and on the other side an aqueous NaCl solution with a concentration between 1 and 15 mol m⁻³ ($C_h$). It is shown that ($\Delta {\psi }_s$) depends on the value of one of the factors (i.e., $\Delta P$, $C_h/C_l$, $R_C$ and ${\zeta }_s$) at a fixed value of the other three. Full article

The results of experimental studies of volume osmotic fluxes ($J_{vk}^r$) and fluxes of dissolved substances ($J_k^r$) in a system containing a synthetic Nephrophan^® membrane (Orwo VEB Filmfabrik, Wolfen, Germany) set in a horizontal plane are presented. The membrane separated water and aqueous HCl or ammonia solutions or aqueous ammonia and HCl solutions. It was found that for the homogeneity conditions of the solutions $J_{vk}$ and $J_k$ depend only on the concentration and composition of the solutions. For concentration polarization conditions (where concentration boundary layers are created on both sides), $J_{vk}^r$ and $J_k^r$ depend on both the concentration and composition of the solutions and the configuration of the membrane system. The obtained results of the $J_{vk}$ and $J_k$ flux studies were used to assess the global production of entropy for the conditions of homogeneity of solutions (${\Phi }_{Sk}$), while $J_{vk}^r$ and $J_k^r$—to assess the global production of entropy for concentration polarization conditions $({\Phi }_{Sk}^r$). In addition, the diffusion-convective effects and the convection effect in the global source of entropy were calculated. The concentration polarization coefficient ${\zeta }_i^r$ was related to modified concentration Rayleigh number, e.g., the parameter controlling the transition from non-convective (diffusive) to convective state. This number acts as a switch between two states of the concentration field: convective (with a higher entropy source value) and non-convective (with a lower entropy source value). The operation of this switch indicates the regulatory role of earthly gravity in relation to membrane transport. 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

The subject of the study was the osmotic volume transport of aqueous CuSO₄ and/or ethanol solutions through a selective cellulose acetate membrane (Nephrophan). The effect of concentration of solution components, concentration polarization of solutions and configuration of the membrane system on the value of the volume osmotic flux ( $J_{vi}^r)$ in a single-membrane system in which the polymer membrane located in the horizontal plane was examined. The investigations were carried out under mechanical stirring conditions of the solutions and after it was turned off. Based on the obtained measurement results $J_{vi}^r$ , the effects of concentration polarization, convection polarization, asymmetry and amplification of the volume osmotic flux and the thickness of the concentration boundary layers were calculated. Osmotic entropy production was also calculated for solution homogeneity and concentration polarization conditions. Using the thickness of the concentration boundary layers, critical values of the Rayleigh concentration number ( $R_C^r$ ), i.e., the switch, were estimated between two states: convective (with higher $J_{vi}^r$ ) and non-convective (with lower $J_{vi}^r$ ). The operation of this switch indicates the regulatory role of earthly gravity in relation to membrane transport. Full article

Using the classical Kedem–Katchalsky’ membrane transport theory, a mathematical model was developed and the original concentration volume flux (J_v), solute flux (J_s) characteristics, and S-entropy production by J_v, $\left({\left({\psi }_S\right)}_{J_v}\right)$ and by J_s $({\left({\psi }_S\right)}_{J_s})$ in a double-membrane system were simulated. In this system, M₁ and M_r membranes separated the l, m, and r compartments containing homogeneous solutions of one non-electrolytic substance. The compartment m consists of the infinitesimal layer of solution and its volume fulfills the condition V_m → 0. The volume of compartments l and r fulfills the condition V_l = V_r → ∞. At the initial moment, the concentrations of the solution in the cell satisfy the condition C_l < C_m < C_r. Based on this model, for fixed values of transport parameters of membranes (i.e., the reflection (σ_l, σ_r), hydraulic permeability (L_pl, L_pr), and solute permeability (ω_l, ω_r) coefficients), the original dependencies C_m = f(C_l − C_r), J_v = f(C_l − C_r), J_s = f(C_l − C_r), ${\left({\Psi }_S\right)}_{J_v}$ = f(C_l − C_r), ${\left({\Psi }_S\right)}_{J_s}$ = f(C_l − C_r), R_v = f(C_l − C_r), and R_s = f(C_l − C_r) were calculated. Each of the obtained features was specially arranged as a pair of parabola, hyperbola, or other complex curves. Full article

The inflammation and lipid accumulation in the arterial wall represents a progressive disease known as atherosclerosis. In this study, a numerical model of atherosclerosis progression was developed. The wall shear stress (WSS) and blood analysis data have a big influence on the development of this disease. The real geometry of patients, and the blood analysis data (cholesterol, HDL, LDL, and triglycerides), used in this paper, was obtained within the H2020 SMARTool project. Fluid domain (blood) was modeled using Navier-Stokes equations in conjunction with continuity equation, while the solid domain (arterial wall) was modeled using Darcy’s law. For the purpose of modeling low-density lipoprotein (LDL) and oxygen transport, convection-diffusion equations were used. Kedem-Katchalsky equations were used for coupling fluid and solid dynamics. Full article