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.

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.

The Role of the Gravitational Field in Generating Electric Potentials in a Double-Membrane System for Concentration Polarization Conditions.

Electric potentials referred to as the gravielectric effect (∆ΨS) 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 ∆ΨS 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 ∆ΨS 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 (C0), for the same values of Cm/C0, the higher the ∆ΨS, 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.

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.

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.

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.

The use of Big Data Analytics in healthcare.

The introduction of Big Data Analytics (BDA) in healthcare will allow to use new technologies both in treatment of patients and health management. The paper aims at analyzing the possibilities of using Big Data Analytics in healthcare. The research is based on a critical analysis of the literature, as well as the presentation of selected results of direct research on the use of Big Data Analytics in medical facilities. The direct research was carried out based on research questionnaire and conducted on a sample of 217 medical facilities in Poland. Literature studies have shown that the use of Big Data Analytics can bring many benefits to medical facilities, while direct research has shown that medical facilities in Poland are moving towards data-based healthcare because they use structured and unstructured data, reach for analytics in the administrative, business and clinical area. The research positively confirmed that medical facilities are working on both structural data and unstructured data. The following kinds and sources of data can be distinguished: from databases, transaction data, unstructured content of emails and documents, data from devices and sensors. However, the use of data from social media is lower as in their activity they reach for analytics, not only in the administrative and business but also in the clinical area. It clearly shows that the decisions made in medical facilities are highly data-driven. The results of the study confirm what has been analyzed in the literature that medical facilities are moving towards data-based healthcare, together with its benefits.

Modelling of the Electrical Membrane Potential for Concentration Polarization Conditions.

Based on Kedem-Katchalsky formalism, the model equation of the membrane potential (Δψs) 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 (Ci/Ce) at the membrane/concentration boundary layers. We present the calculation procedure (Ci/Ce) based on novel equations derived in the paper containing the transport parameters of the membrane (Lp, σ, and ω), solutions (ρ, ν), concentration boundary layer thicknesses (δl, δh), concentration Raileigh number (RC), concentration polarization factor (ζs), volume flux (Jv), mechanical pressure difference (ΔP), and ratio of known solution concentrations (Ch/Cl). From the resulting equation, Δψs was calculated for various combinations of the solution concentration ratio (Ch/Cl), the Rayleigh concentration number (RC), the concentration polarization coefficient (ζs), and the hydrostatic pressure difference (ΔP). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m-3 (Cl) 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 (Ch). It is shown that (Δψs) depends on the value of one of the factors (i.e., ΔP, Ch/Cl, RC and ζs) at a fixed value of the other three.

Evaluation of Transport Properties and Energy Conversion of Bacterial Cellulose Membrane Using Peusner Network Thermodynamics.

We evaluated the transport properties of a bacterial cellulose (BC) membrane for aqueous ethanol solutions. Using the Rr 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 (Lp), reflection (σ), and solute permeability (ω). We used these parameters and the Peusner (Rijr) 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 R11r, R22r, and Rdetr were positive and higher, and the R12r 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.

Evaluation of transport properties of biomembranes by means of Peusner network thermodynamics.

PURPOSE: The R version of the Kedem-Katchalsky-Peusner (KKP) network equations is one of the basic research tools for membrane transport. For binary solutions of non-electrolytes containing a solvent and one solute, these equations include the Peusner resistance coefficients. The aim of the study was to assess the transport properties of biomembranes on the basis of the concentration characteristics of the coefficients: resistance, coupling, energy conversion efficiency and degraded and free energy fluxes. METHODS: The subject of the study were polymer biomembranes used as a membrane dressing (Bioprocess) and used in hemodialysis (Nephrophan, Ultra-flo) with the coefficients of hydraulic permeability (Lp), reflection () and diffusion permeability () for aqueous glucose solutions. The research method was the R version of the KKP network equations for binary solutions of non-electrolytes. RESULTS: We developed a procedure for evaluation the transport properties of membranes. This procedure requires the calculation of the dependence of the following coefficients: Peusner resistance, Kedem-Caplan-Peusner coupling, Caplan-Peusner energy conversion efficiency, Peusner coupling, and the dissipated energy and free energy fluxes on the mean glucose concentration. Results show that the values of the Peusner resistance coefficients, the Kedem-Caplan-Peusner coupling, the Caplan-Peusner energy conversion efficiency, and the Peusner coupling depend on the mutual relationship between the coefficients Lp, ,  and C. In turn, the value of the dissipated energy and free energy fluxes it is also determined by the values of the volume and diffusion fluxes. CONCLUSIONS: The presented procedure for evaluation transport properties of membranes can be helpful in explaining the mechanisms of membrane transport and conducting energy analyzes of membrane processes. Therefore, this procedure can be used for selection of a suitable membrane for practical (eg., industrial or medical) applications.

Simulation of S-Entropy Production during the Transport of Non-Electrolyte Solutions in the Double-Membrane System.

Using the classical Kedem-Katchalsky' membrane transport theory, a mathematical model was developed and the original concentration volume flux (Jv), solute flux (Js) characteristics, and S-entropy production by Jv, ( ( ψ S ) J v ) and by Js ( ( ψ S ) J s ) in a double-membrane system were simulated. In this system, M1 and Mr 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 Vm → 0. The volume of compartments l and r fulfills the condition Vl = Vr → ∞. At the initial moment, the concentrations of the solution in the cell satisfy the condition Cl < Cm < Cr. Based on this model, for fixed values of transport parameters of membranes (i.e., the reflection (σl, σr), hydraulic permeability (Lpl, Lpr), and solute permeability (ωl, ωr) coefficients), the original dependencies Cm = f(Cl - Cr), Jv = f(Cl - Cr), Js = f(Cl - Cr), ( Ψ S ) J v = f(Cl - Cr), ( Ψ S ) J s = f(Cl - Cr), Rv = f(Cl - Cr), and Rs = f(Cl - Cr) were calculated. Each of the obtained features was specially arranged as a pair of parabola, hyperbola, or other complex curves.

The Role of Gravity in the Evolution of the Concentration Field in the Electrochemical Membrane Cell.

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 v i 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 v i 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 v i r ) and non-convective (with lower J v i r ). The operation of this switch indicates the regulatory role of earthly gravity in relation to membrane transport.

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).

Evaluation of the Global S-Entropy Production in Membrane Transport of Aqueous Solutions of Hydrochloric Acid and Ammonia.

The results of experimental studies of volume osmotic fluxes (Jvkr) and fluxes of dissolved substances (Jkr) 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 Jvk and Jk depend only on the concentration and composition of the solutions. For concentration polarization conditions (where concentration boundary layers are created on both sides), Jvkr and Jkr depend on both the concentration and composition of the solutions and the configuration of the membrane system. The obtained results of the Jvk and Jk flux studies were used to assess the global production of entropy for the conditions of homogeneity of solutions (ΦSk), while Jvkr and Jkr-to assess the global production of entropy for concentration polarization conditions (ΦSkr). In addition, the diffusion-convective effects and the convection effect in the global source of entropy were calculated. The concentration polarization coefficient ζir 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.

Eight Days of Water-Only Fasting Promotes Favorable Changes in the Functioning of the Urogenital System of Middle-Aged Healthy Men.

The aim of this study was to determine whether, after 8 days of water-only fasting, there are changes in the efficiency of the lower urinary tract, the concentration of sex hormones, and the symptoms of prostate diseases in a group of middle-aged men (n = 14). For this purpose, before and after 8 days of water-only fasting (subjects drank ad libitum moderately mineralized water), and the following somatic and blood concentration measurements were made: total prostate specific antigen (PSA-T), free prostate specific antigen (PSA-F), follicle stimulating hormone (FSH), luteotropic hormone (LH), prolactin (Pr), total testosterone (T-T), free testosterone (T-F), dehydroepiandrosterone (DHEA), sex hormone globulin binding (SHGB), total cholesterol (Ch-T), ß-hydroxybutyrate (ß-HB). In addition, prostate volume (PV), volume of each testis (TV), total volume of both testes (TTV), maximal urinary flow rate (Qmax), and International Prostate Symptom Score (IPSS) values were determined. The results showed that after 8 days of water-only fasting, Qmax and IPSS improved but PV and TTV decreased significantly. There was also a decrease in blood levels of PSA-T, FSH, P, T-T, T-F, and DHEA, but SHGB concentration increased significantly. These results indicate that 8 days of water-only fasting improved lower urinary tract functions without negative health effects.

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 mathematical model of concentration polarization coefficient in membrane transport and volume flows.

In this paper, the authors investigate the membrane transport of aqueous non-electrolyte solutions in a single-membrane system with the membrane mounted horizontally. The purpose of the research is to analyze the influence of volume flows on the process of forming concentration boundary layers (CBLs). A mathematical model is provided to calculate dependences of a concentration polarization coefficient (ζ s ) on a volume flux (J vm ), an osmotic force (Δπ) and a hydrostatic force (ΔP) of different values. Property ζ s = f(J vm ) for J vm > 0 and for J vm ≈ 0 and property ζ s = f(ΔC 1) are calculated. Moreover, results of a simultaneous influence of ΔP and Δπ on a value of coefficient ζ s when J vm = 0 and J vm ≠ 0 are investigated and a graphical representation of the dependences obtained in the research is provided. Also, mathematical relationships between the coefficient ζ s and a concentration Rayleigh number (R C ) were studied providing a relevant graphical representation. In an experimental test, aqueous solutions of glucose and ethanol were used.

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.

Laser interferometric investigation of solute transport through membrane-concentration boundary layer system.

We investigate diffusive transport in a membrane system with a horizontally mounted membrane under concentration polarization conditions performed by a laser interferometry method. The data obtained from two different theoretical models are compared to the experimental results of the substance flux. In the first model, the membrane is considered as infinitely thin, while in the second one as a wall of finite thickness. The theoretical calculations show sufficient correspondence with the experimental results. On the basis of interferometric measurements, the relative permeability coefficient (ζ(s)) for the system, consisting of the membrane and concentration boundary layers, was also obtained. This coefficient reflects the concentration polarization of the membrane system. The obtained results indicate that the coefficient ζ(s) of the membrane-concentration boundary layer system decreases in time and seems to be independent of the initial concentration of the solute.