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

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.

A method for evaluating the transport and energy conversion properties of polymer biomembranes using the Kedem-Katchalsky-Peusner equations.

BACKGROUND: A basic parameter in non-equilibrium thermodynamics is the production of entropy (S-entropy), which is a consequence of the irreversible processes of mass, charge, energy, and momentum transport in various systems. The product of S-entropy production and absolute temperature (T) is called the dissipation function and is a measure of energy dissipation in non-equilibrium processes. OBJECTIVES: This study aimed to estimate energy conversion in membrane transport processes of homogeneous non-electrolyte solutions. The stimulus version of the R, L, H, and P equations for the intensity of the entropy source achieved this purpose. MATERIAL AND METHODS: The transport parameters for aqueous glucose solutions through Nephrophan® and Ultra-Flo 145 dialyser® synthetic polymer biomembranes were experimentally determined. Kedem-Katchalsky-Peusner (KKP) formalism was used for binary solutions of non-electrolytes, with Peusner coefficients introduced. RESULTS: The R, L, H, and P versions of the equations for the S-energy dissipation were derived for the membrane systems based on the linear non-equilibrium Onsager and Peusner network thermodynamics. Using the equations for the S-energy and the energy conversion efficiency factor, equations for F-energy and U-energy were derived. The S-energy, F-energy and U-energy were calculated as functions of osmotic pressure difference using the equations obtained and presented as suitable graphs. CONCLUSIONS: The R, L, H, and P versions of the equations describing the dissipation function had the form of second-degree equations. Meanwhile, the S-energy characteristics had the form of second-degree curves located in the 1st and 2nd quadrants of the coordinate system. These findings indicate that the R, L, H, and P versions of S-energy, F-energy and U-energy are not equivalent for the Nephrophan® and Ultra-Flo 145 dialyser® membranes.

Energy conversion in Textus Bioactiv Ag membrane dressings using Peusner's network thermodynamic descriptions.

BACKGROUND: The Textus Bioactiv Ag membrane is an active dressing for the treatment of chronic wounds such as venous stasis ulcers and burns. OBJECTIVES: Determination of the transport and internal energy conversion properties of the Textus Bioactiv Ag membrane using the Kedem-Katchalsky-Peusner model. This model introduces the coefficients Lij necessary to calculate the degree of coupling (lij, QL), energy conversion efficiency (eij), dissipated energy (S-energy), free energy (F-energy), and internal energy (U-energy). MATERIAL AND METHODS: The research material was the Textus Bioactiv Ag membrane that is used as an active dressing in the treatment of difficult-to-heal wounds, and KCl aqueous solutions. The research methods employed Peusner's formalism of network thermodynamics and Kedem and Katchalsky's thermodynamics of membrane processes. To calculate the Lij coefficients, we used hydraulic conductivity (Lp), diffusion conductivity (u) and reflection (ó) coefficients to perform experimental measurements in different conditions. RESULTS: The Lp coefficient for the Textus Bioactiv Ag membrane is nonlinearly dependent on the average concentrations of the solutions. In turn, the u and ó coefficients are nonlinearly dependent on the differences in osmotic pressures (Äd). An increase in the Äd causes the Textus Bioactiv Ag membrane to become more permeable and less selective for KCl solutions. The coefficients of Peusner (Lij), couplings (lij, QL), energy conversion efficiency (eij), S-energy, F-energy, and U-energy also depend nonlinearly on Äd. Our results showed that for higher concentrations of KCl solutions transported through the Textus Bioactiv Ag membrane, the coupling and energy conversion coefficients were greater for larger Äd up to their maximum values for large Äd. Coupling of the membrane structure with the electrolyte flux through the membrane is observed for Äd greater than 10 kPa. CONCLUSIONS: Textus Bioactiv Ag membrane dressings possess the properties of a solution component separator as well as an internal energy converter.

The Rr Form of the Kedem-Katchalsky-Peusner Model Equations for Description of the Membrane Transport in Concentration Polarization Conditions.

The paper presents the Rr matrix form of Kedem-Katchalsky-Peusner equations for membrane transport of the non-homogeneous ternary non-electrolyte solutions. Peusner's coefficients Rijr and det [Rr] (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 Rijr and det [Rr] 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 ξij coefficient), determine the degree of coupling (the rijr coefficient) and coupling parameter (the QRr coefficient) and energy conversion efficiency (the (eijr)r coefficient).

Chemokines and Growth Factors Produced by Lymphocytes in the Incompetent Great Saphenous Vein.

The role of cytokines in the pathogenesis of chronic venous disease (CVD) remains obscure. It has been postulated that oscillatory flow present in incompetent veins causes proinflammatory changes. Our earlier study confirmed this hypothesis. This study is aimed at assessing chemokines and growth factors (GFs) released by lymphocytes in patients with great saphenous vein (GSV) incompetence. In 34 patients exhibiting reflux in GSV, blood was derived from the cubital vein and from the incompetent saphenofemoral junction. In 12 healthy controls, blood was derived from the cubital vein. Lymphocyte culture with and without stimulation by phytohemagglutinin (PHA) was performed. Eotaxin, interleukin 8 (IL-8), macrophage inflammatory protein 1 A and 1B (MIP-1A and MIP-1B), interferon gamma-induced protein (IP-10), monocyte chemoattractant protein-1 (MCP-1), interleukin 5 (IL-5), fibroblast growth factor (FGF), granulocyte colony-stimulating factor (G-CSF), granulocyte-macrophage colony-stimulating factor (GM-CSF), platelet-derived growth factor-BB (PDGF-BB), and vascular endothelial growth factor (VEGF) were assessed in culture supernatants by a Bio-Plex assay. Higher concentrations of eotaxin and G-CSF were revealed in the incompetent GSV, compared with the concentrations in the patients' upper limbs. The concentrations of MIP-1A and MIP-1B were higher in the CVD group while the concentration of VEGF was lower. In the stimulated cultures, the concentration of G-CSF proved higher in the incompetent GSV, as compared with the patients' upper limbs. Between the groups, the concentration of eotaxin was higher in the CVD group, while the IL-5 and MCP-1 concentrations were lower. IL-8, IP-10, FGF, GM-CSF, and PDGF-BB did not reveal any significant differences in concentrations between the samples. These observations suggest that the concentrations of chemokines and GFs are different in the blood of CVD patients. The oscillatory flow present in incompetent veins may play a role in these changes. However, the role of cytokines in CVD requires further study.

Concentration polarization phenomenon in the case of mechanical pressure difference on the membrane.

We analyzed the transport of KCl solutions through the bacterial cellulose membrane and concentration boundary layers (CBLs) near membrane with pressure differences on the membrane. The membrane was located in horizontal-plane between two chambers with different KCL solutions. The membrane was located in horizontal-plane between two chambers with different KCL solutions. As results from the elaborated model, gradient of KCL concentration in CBLs is maximal at membrane surfaces in the case when pressure difference on the membrane equals zero. The amplitude of this maximum decreases with time of CBLs buildup. Application of mechanical pressure gradient in the direction of gradient of osmotic pressure on the membrane causes a shift of this maximum into the chamber with lower concentration. In turn, application of mechanical pressure gradient directed opposite to the gradient of osmotic pressure causes the appearance of maximum of concentration gradient in chamber with higher concentration. Besides, the increase of time of CBLs buildup entails a decrease of peak height and shift of this peak further from the membrane. Similar behavior is observed for distribution of energy dissipation in CBLs but for pressure difference on the membrane equal to zero the maximum of energy dissipation is observed in the chamber with lower concentration. We also measured time characteristics of voltage in the membrane system with greater KCl concentrations over the membrane. We can state that mechanical pressure difference on the membrane can suppress or strengthen hydrodynamic instabilities visible as pulsations of measured voltage. Additionally, time of appearance of voltage pulsations, its amplitude, and frequency depend on mechanical pressure differences on the membrane and initial quotient of KCl concentrations in chambers.

The role of mechanical pressure difference in the generation of membrane voltage under conditions of concentration polarization.

The mechanical pressure difference across the bacterial cellulose membrane located in a horizontal plane causes asymmetry of voltage measured between electrodes immersed in KCl solutions symmetrically on both sides of the membrane. For all measurements, KCl solution with lower concentration was above the membrane. In configuration of the analyzed membrane system, the concentration boundary layers (CBLs) are created only by molecular diffusion. The voltages measured in the membrane system in concentration polarization conditions were compared with suitable voltages obtained from the model of diffusion through CBLs and ion transport through the membrane. An increase of difference of mechanical pressure across the membrane directed as a difference of osmotic pressure always causes a decrease of voltage between the electrodes in the membrane system. In turn, for mechanical pressure difference across the membrane directed in an opposite direction to the difference of osmotic pressure, a peak in the voltage as a function of mechanical pressure difference is observed. An increase of osmotic pressure difference across the membrane at the initial moment causes an increase of the maximal value of the observed peak and a shift of this peak position in the direction of higher values of the mechanical pressure differences across the membrane.

Network Derivation of Liquid Junction Potentials in Single-Membrane System.

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.

The Efficacy of Extracorporeal Shockwave Therapy Compared with Compression Therapy in Healing Venous Leg Ulcers.

Background: Innovative methods of physical therapy delivered via modern medical devices have significantly extended the possibility of applying conservative treatments in healing venous leg ulcers. The primary objective of this study was to compare the therapeutic efficacy of selected mechanical physical therapies (intermittent pneumatic compression vs. radial extracorporeal shockwave vs. focal extracorporeal shockwave) vs. standard care in the treatment of venous leg ulcers over a 4-week period. Materials: This study included 69 patients, comprising 45 females (65%) and 24 males (35%), with a mean age of 67.1 ± 8.6 years (range: from 52.0 to 80.0 years). Methods: The patients were allocated into four groups: the IPC group was treated with intermittent pneumatic compression therapy, the R-ESWT group was treated with radial extracorporeal shockwave therapy, the F-ESWT group was treated with focal extracorporeal shockwave therapy, and the SC group was treated with standard care. Results: After one month of therapy, the median percentage decrease in wound total surface area after treatment was as follows: in the IPC group, there was a 52.9% decrease (range: 3.3-100%); in the R-ESWT group, there was a 31.6% decrease (range: 2.4-95.8%); in the F-ESWT group, there was an 18.0% decrease (range: 1.9-76.1%); and in the SC group, there was a 16.0% decrease (range: 1.5-45.8%). Conclusions: All the studied therapies caused a statistically significant reduction in the surface area of venous leg ulcers. The best results were observed with the intermittent pneumatic compression, while the radial and focal extracorporeal shockwave therapies appeared less effective. The standard care alone turned out to be the least effective. Our results did not show statistically significant changes in the values of RBC deformability at the investigated shear rates.

Influence of Method of Treatment of Mandibular Condylar Fractures on Range of Articular Path Measured by Cadiax Device.

Background/Objectives: The aim of this study was to evaluate the function of the treated temporomandibular joint based on the analysis of the image of the articular path using the Cadiax device depending on the choice of treatment method for unilateral condylar fracture of the mandible. Methods: Sixty patients who were treated for condylar fractures of the mandible at the Maxil-lofacial Surgery Department in Katowice were qualified for the analysis of the range of movements of the mandibular heads using the Cadiax device. From the group of patients who suffered fractures of the mandible, including condylar processes, patients were finally qualified for the measurement of the articular path of the injured and healthy joint according to strict criteria. Results: The condylar examination was performed in 20 patients who had conservative condylar fracture treatment and 40 patients who underwent various surgeries in the course of a single condylar fracture. The control group consisted of 20 patients whose mean values for the articular pathway measured for both sides were 12.73 and 12.69 and fell within the standard developed for healthy joints tested with the Cadiax device. Conclusions: We have achieved an almost ideal treatment for condylar fractures. We are also beginning to notice the need for rehabilitation of patients after this type of surgery.

In Vitro Comparison of Several Thrombus Removal Tools.

BACKGROUND: Although the routine use of thrombus aspiration is not recommended, the thrombectomy technique still might be considered for a selected population of patients. Therefore, the assessment of the effectiveness of commercially available thrombectomy devices is still clinically relevant. AIM: Here, we present an in vitro comparison of several different types of catheters that can be used for thrombus aspiration or removal. METHODS: Through the removal of 6 h and 24 h human blood clots in an in vitro model, four catheters were compared: the Launcher, Pronto V4, Vasco+ and the stent-retriever Catchview. The aspiration efficacy was expressed as a percentage of the initial thrombus weight. The effectiveness of the patient's aspiration was dependent on the time of thrombus formation and was significantly higher for a thrombus formed over 24 h (58.5 ± 26.5%) than for one formed over 6 h (48.0 ± 22.5%; p < 0.001). In the presented in vitro model, Pronto V4 and Launcher showed the highest efficiency. CONCLUSIONS: Large-bore aspiration catheters were found to be more effective than narrow-bore catheters or stent-retrievers in an in vitro model of thrombus removal. The thrombus aspiration efficacy increases with longer thrombus formation times.

Study of thin layer film evolution near bacterial cellulose membrane by Ag|AgCl electrodes in chamber with lower concentration.

We used the method of measuring potential difference between two Ag|AgCl electrodes immersed directly into electrolyte solution with lower concentration and at different distances from membrane. The bacterial cellulose membrane was placed in horizontal plane in the membrane system with configurations with higher NaCl concentration and density under (A) and over the membrane (B). In both configurations at the initial moment the voltage between electrodes amounted to zero. After turning off mechanical stirring of solutions, in configuration A we observed the monotonic increase and next stabilization of voltage while in configuration B after short time dependent on the initial quotient of NaCl concentrations on the membrane we observed appearance of pulsations of measured voltage and gradual decrease of mean voltage over time. Smooth changes of voltage are connected with diffusional reconstruction of Concentration Boundary Layers (CBLs) while fast increase and subsequent pulsations of voltage are connected with the appearance of hydrodynamic instabilities (gravitational convection) near membrane imposed on diffusive reconstruction of thin layer. The time needed for the appearance of hydrodynamic instabilities in CBL depended nonlinearly on the initial ratio of electrolyte concentrations on the membrane.

Analgesic and Functional Efficiency of High-Voltage Electrical Stimulation in Patients with Lateral Epicondylitis-A Report with a 180-Day Follow-Up.

The available publications describing the beneficial effects of electrostimulation does not unequivocally confirm the clinical utility of high-voltage electrical stimulation (HVES) in the treatment of the lateral epicondylitis (LE). The aim of this study was the estimation of the effect of HVES on pain intensity and functional efficiency, both in the short and long term in patients with LE. The trial was registered by the Australian and New Zealand Clinical Trials Registry (ACTRN12621001389897). There were 58 patients allocated into two groups: the HVES group (n = 29, mean age 49.9 ± 11.0 years), treated with HVES (pulse duration: 200µs, frequency: 100 Hz, current amplitude in the range of 18-25 mA, voltage amplitude: 100 V), and the NORM group (n = 29, mean age 48.0 ± 12.6 years), who were healthy and untreated patients. The treatments were performed 5 days a week (from Monday to Friday) for two weeks. Treatment progress was measured by the visual analogue scale (VAS) for rest pain, night pain, and pain during activity; the Laitinen Pain Scale (LPS); and hand grip strength (HGS) before and after the treatment, as well as after 3, 6, 12, and 24 weeks. The reduction of pain (according to the VAS and LPS) and increase in the functional condition (according to the HGS) were observed in all HVES patients in the short- and long-term observation. Therefore, the HVES in treatment of LE was found to be effective and safe.

A Comparative Study of Pigmented and Non-pigmented Basal Cell Carcinoma in Reflectance Confocal Microscopy.

BACKGROUND/AIM: Basal cell carcinoma (BCC) is a common skin cancer, especially in the elderly population. The probability of BCC development increases past the age of 55. Dermoscopy and reflectance confocal microscopy (RCM) are two modern tools useful in the diagnosis of BCC. PATIENTS AND METHODS: This is a retrospective study conducted on a group of 21 patients with a confirmed diagnosis of BCC. All patients were examined by dermoscopy and RCM. Dermoscopic images were taken using a videodermoscope. RCM was performed in three layers: epidermal, dermoepidermal junction (DEJ), and superficial dermal layer. In each layer, a few RCM criteria of basal cell carcinoma diagnosis were taken into consideration. RESULTS: Dermoscopy of pigmented BCCs revealed blue globules of pigment (p<0.05), gray and blue ovoid nests, which were absent in the entire non-pigmented carcinomas group. In RCM, the epidermis showed no differences between pigmented and non-pigmented carcinomas, however, significant differences were observed at the DEJ. In pigmented BCCs, cordlike structures and plump atypical cells were observed (p<0.05), while in non-pigmented carcinomas, dark silhouettes were present (p<0.05). CONCLUSION: To our knowledge, that is the first study comparing features between pigmented and non-pigmented BCC by RCM. Pigmented and non-pigmented BCCs presented different features in both dermoscopy and RCM. Furthermore, RCM revealed more discriminating features at the DEJ than dermoscopy, thus can be more efficient in the differential diagnosis of difficult BCC.

Type of Physical Training and Selected Aspects of Psychological Functioning of Women with Obesity: A Randomised Trial.

OBJECTIVE: We conducted a prospective randomised trial to assess whether a specific type of regular physical training performed by women with obesity is related to obtaining specific psychological benefits. METHODS: Forty-four women qualified for the study and were divided into two groups. The applied intervention consisted of regular three-month physical exercises in the form of endurance training (group A) or endurance strength training (group B). Initially, and after the completed intervention, we examined anthropometric measurements and the level of: stress (PSS-10), general self-esteem (SES), body self-report (BSQ-34, FRS), and behaviours associated with diet (TFEQ-18). RESULTS: As a result of the intervention, both groups had significantly lower anthropometric parameters and FRS scores with regard to the current figure (gr. A:δ FRS CS -0.90 ± 0.83, p < 0.001; gr. B:δ FRS CS -0.41 ± 0.50, p = 0.01) and BSQ-34 results (gr. A:δ BSQ-34 -14.90 ± 13.5, p = 0.001; gr. B:δ BSQ-34 - 18.64 ± 25.4, p = 0.01). Additionally, an increase in cognitive restraint (δ TFEQ-18 CR1.65 ± 2.06, p = 0.01) and a decrease in emotional eating (δ TFEQ-18 EE -0.82 ± 1.28, p = 0.01) were observed in group B. There were no between-group differences in terms of the magnitude of changes achieved due to the intervention, except for asignificant improvement in the perception of their current figure (FRS) (δ FRSCS -0.90 ± 0.83, p = 0.03) in group A. CONCLUSIONS: Regular physical activity over a three-month period by women with obesity promotes the perception of their own body as slimmer and lowers body shape concerns. The change in body shape perception was more pronounced under the influence of endurance training than endurance strength training. TRIAL REGISTRATION: ClinicalTrials.gov ID NCT04793451.

Efficacy of intra-arterial lidocaine infusion in the treatment of cerulein-induced acute pancreatitis.

BACKGROUND: Disturbances in pancreatic microcirculation, beginning with vasoconstriction, are crucial in early pancreatitis and progression to necrotizing pancreatitis. Thus, vascular-targeted treatment aiming to restore a sufficient level of microcirculation through vasodilation would possibly reduce the severity of pancreatitis. Lidocaine is an anti-arrhythmic and local anesthetic drug, which also acts as a vasodilator at higher concentrations. OBJECTIVES: To evaluate the efficacy of intra-arterial infusion of lidocaine into the celiac trunk in treatment of cerulein-induced acute pancreatitis. MATERIAL AND METHODS: Wistar rats (n = 20) were randomly divided into 2 equal groups: the control group (NaCl group, n = 10) and the study group (lidocaine group, n = 10). All subjects underwent surgical intervention with intra-arterial infusion of 0.9% NaCl (control group) or 1% lidocaine hydrochloride (study group) into the celiac trunk. Blood samples were collected 5 times at regular intervals from each rat for amylase and lipase measurements. Histopathological analysis of the pancreas was performed. RESULTS: A total number of 16 rats (control group n = 7, study group n = 9) were included. In the postoperative course, the study group (lidocaine group) revealed lower values of serum amylase and lipase levels compared to the control group (NaCl group), except the values at the 1st treatment point, which appeared 1 h after intraoperative drug injection. Significantly lower treatment endpoint levels of pancreatic enzymes were seen in the lidocaine group. Moreover, no differences were observed between the 1st and the last treatment point in the control group; however, these differences were significant for both enzymes in the study group. Histopathology revealed reduced pancreatitis severity in the study group compared to the controls. CONCLUSIONS: Intra-arterial lidocaine infusion into the celiac trunk decreases pancreatitis severity. What is more, this study demonstrates the relevance of early vasodilation in the therapy of acute pancreatitis.

Transport of non-electrolyte solutions through membrane with concentration polarization.

Mathematical model of the volume fluxes through neutral membrane with concentration boundary layers on both sides of this membrane is presented. This model, based on the Kedem-Katchalsky equations, describes the volume flux generated by osmotic and hydrostatic forces for non-homogeneous and non-electrolyte solutions. Nonlinear equation for volume flux was used for numerical calculation in linear regime of hydrodynamic stability. In the steady state of non-homogeneous solutions the dependence of volume flux on pressure difference is shifted with regard to this dependence for homogeneous solution, while the volume flux as a function of osmotic pressure between chambers is characterized by different angle of inclination for homogeneous and non-homogeneous solutions.

Time evolution of NaCl flux through the microbial cellulose membrane with concentration polarization.

The method of solute permeability coefficient and solute fluxes appointment for the membrane, based on monitoring of changes of conductivity of electrolyte solutions was presented. It was stated that during mechanical stirring of solutions the coefficient of NaCl permeability for microbial cellulose membrane (Biofill) did not depend on configuration of the membrane system and concentrations of solutions. Time characteristics of NaCl flux through the membrane Biofill oriented in horizontal plane were measured and modeled. The changes of NaCl fluxes through the membrane Biofill caused by concentration boundary layers build up on both sides of the membrane depended on NaCl concentrations and configuration of the membrane system. The differences between fluxes in different configurations of the membrane system were observed after time depended on initial concentrations in chambers. After that time, for configuration with solution with higher density over the membrane (configuration B) the NaCl flux through the membrane was greater than for configuration with solution with lower density over the membrane (configuration A). Besides it was stated that the coefficient of concentration polarization for configuration B was higher than for configuration A for all studied NaCl concentrations. Increase of mean concentration in the membrane at the initial moment caused increase (for configuration B) and lack of changes (for configuration A) of concentration polarization coefficient in the steady state of the membrane system. The interpretation of experimental results was made on the basis of Kedem-Katchalsky equations for the membrane system.

[Theoretical analysis of the membrane transport non-homogeneous non-electrolyte solutions: influence of thermodynamic forces on thickness of concentration boundary layers for binary solutions]. / Teoretyczna analiza transportu membranowego niejednorodnych roztworów nieelektrolitów: wplyw bodzców termodynamicznych na grubosc stezeniowych warstw granicznych w roztworach binarnych.

The nonlinear mathematical model equations for membrane transport of binary non-electrolyte solutions was presented. This model, the influence of the volume flows caused by simultaneous action of osmotic and hydraulic forces in concentration boundary layers creation, controlled by concentration Rayleigh number is taken into account. In a basis of obtained fourth order equations, the numerical calculations of concentration boundary layers thicknesses (delta(l) and delta(h)) for five variables: concentration (C(h)), hydrostatic pressure difference (deltaP), hydraulic permeability (L(p)), reflection (sigma), solute permeability (omega) coefficients and concentration Rayleigh number (R(c)) were performed. Characteristics obtained in the study show that external forces cause nonlinear increase or decrease of the concentration boundary layers thicknesses.

Osmotic, diffusive and convective volume and solute flows of ionic solutions through a horizontally mounted polymeric membrane.

On the basis of Kedem-Katchalsky's equations in classical and modified versions, the model equations of volume and solute fluxes were presented. In this model the osmotic volume flux is a sum of: simple osmotic, osmotic connected with natural convection and osmotic connected with forced convection fluxes. The solute flux is a sum of: simple diffusion, diffusion connected with natural convection and diffusion connected with forced convection fluxes. On the basis of this model, the respective definitions of the reflection and permeability coefficients were presented. In order to verification of this model, the volume and solute flows in a single-membrane osmotic-diffusive cell, which contains a flat polymer membrane separating water and electrolyte solutions has been studied. In the experimental set-up, water was placed on one side of horizontally mounted membrane. The opposite side of the membrane was exposed to aqueous solution of KCl or NH3. Each experiment was performed for configurations A and B of the single-membrane system. In configuration A water was placed in the compartment above the membrane and solution below it. In configuration B the arrangement of water and solution was reversed. The measurements of stationary volume and solute fluxes were performed in conditions of mechanical stirring and after stopping of mechanical stirring of solutions. On the basis of experimental data of volume and solute fluxes, calculations of reflections and solute permeability coefficients for aqueous solutions of KCl and NH3 were presented.