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Background: The network forms of Kedem-Katchalsky (K-K) equations for ternary non-electrolyte solutions may contain one of the eight Peusner's coefficients: R(ij), L(ij), H(ij), W(ij), N(ij), K(ij), S(ij) or P(ij) (i, J ∈ {1, 2, 3}). These coefficients form the third degree matrixes ofPeusner's coefficients [R], [L], [H], [W], [N], [K], [S] or [P]., Objectives: Calculation of dependencies of the Peusner's coefficients W(ij) (i, j ∈ {1, 2, 3}) and det [W], on the average concentration of one component in the membrane solution (C1) for several different values of the second component set (C2)., Material and Methods: Glucose transport in aqueous ethanol solutions through Nephrophan membrane transport with known transport parameters (L(p), σ, Ω), using the network K-K equations for the ternary non-electrolytes solutions containing Peusner's coefficient W(ij) (i, j ∈ {1, 2, 3}) were analyzed., Results: Family dependencies of Peusner's coefficients W(ij) (i, j ∈ {1, 2, 3}) on the average concentration of one component in the membrane solution (C1) for several different values of a second set of component (C2) for the homogeneity of the solutions were calculated. Conclusions. Calculations showed that coefficients W12, W21, W22, W23, W32 and det [W] are sensitive to concentrations (C1) and (C2) of solutions separated by a polymeric membrane.

Background: A system of network forms of Kedem-Katchalsky (K-K) equations for ternary non-electrolyte solutions is made of eight matrix equations containing Peusner's coefficients R(ij), L(ij), H(ij), W(ij), K(ij), N(ij), S(ij) or P(ij) (i, j ∈ {1, 2, 3}). The equations are the result of symmetric or hybrid transformation of the classic form of K-K equations by the use of methods of Peusner's network thermodynamics (PNT)., Objectives: Calculating concentration dependences of the determinant of Peusner's coefficients matrixes R(ij), L(ij), H(ij), W(ij), S(ij), N(ij), K(ij) and P(ij) (i, j ∈ {1, 2, 3})., Material and Methods: The material used in the experiment was a hemodialysis Nephrophan membrane with specified transport properties (L(p), σ, Ω) in aqueous glucose and ethanol solution. The method involved equations for determinants of the matrixes coefficients R(ij), L(ij), H(ij), W(ij), S(ij), N(ij), K(ij) or P(ij) (i, j ∈ {1, 2, 3})., Results: The objective of calculations were dependences of determinants of Peusner's coeffcients matrixes R(ij), L(ij), H(ij), W(ij), S(ij), N(ij), K(ij) or P(ij) (i, j ∈ {1, 2, 3}) within the conditions of solution homogeneity upon an average concentration of one component of solution in the membrane (C1) with a determined value of the second component (C2)., Conclusions: The method of calculating the determinants of Peusner's coeffcients matrixes R(ij), L(ij), H(ij), W(ij), S(ij), N(ij), K(ij) or P(ij) (i, j ∈ {1, 2, 3}) is a new tool that may be applicable in studies on membrane transport. Calculations showed that the coefficients are sensitive to concentration and composition of solutions separated by a polymeric membrane.

In this paper the method of evaluation the value of osmotic vant't Hoff's coefficient (f) in membrane system, which is based on the original equation of third degree for the coefficient f was elaborated. This equation, obtained on the basis of Kedem-Katchalsky equation, contains the transport parameters of membrane (Lp, sigma, omega), solution concentration (C), volume flux (Jvm), thickness of concentration boundary layer (delta), etc. These parameters can be determined in a series of independent experiments. The calculation performed for the solution of ammonia in aqueous solution of KCl and polymer membranes show that, the value of coefficient f fulfill the condition 1 < or = f < or = 2 and that there is a range of concentrations of ammonia, in which the changes f occur nonmonitically

The method to determine of the concentration boundary layers thicknesses (delta) in a single-membrane system containing electrolytic ternary solutions was devised using the Kedem-Katchalsky formalism. A basis of this methods is a square equation, contains membrane transport (Lp, sigma, omega) and solution (D, C, gamma) parameters and volume flux (Jv). Calculated values delta for aqueous potassium chloride and ammonia solutions are nonlinearly dependent on the concentrations of investigated solutions. These nonlinearities are the effect of a competition between spontaneously occurring diffusion and natural convection.

Using Kedem-Katchalsky thermodynamic formalism the mathematical model describing relation between effective and real solute permeability coefficients through a membrane was elaborated. The relation is described by parameter 4, which is the quotient of these coefficients. Calculations performed on the basis of obtained quadratic equation show that for a polymeric membrane with fixed transport properties parameter zeta s is nonlinear function of solution concentration. The value of this parameter can express the distance between a system and stable diffusion state. Appearance of unstability related with breaking symmetry of concentration boundary layers towards the gravitation direction causes increase of the coefficient value. This is the sign of appearance of diffusion-convection of mass transport.

On the basis of transformed Kedem-Katchalsky equations the analysis of transport of aqueous glucose solutions through horizontally oriented polymeric membrane was occurred. Using experimentally determined membrane parameters, the resistance coefficients were calculated. Moreover, taking into account the resistance coefficients and experimentally determined volume and solute fluxes, the thermodynamic forces for homogeneous and nonhomogeneous solutions were calculated.

Using Kedem-Katchalsky thermodynamic formalism, the mathematical model describing concentration difference through a membrane (Ci-Ce) in concentration polarization conditions was elaborated. Concentration polarization is connected with concentration boundary layers (l(l), l(h)) creation on both sides of a polymeric membrane (M). These layers both with membrane are the complex l(1)/M/l(h). Obtaining expression, which is square equation considering volume flux (Jvm), contain the transport parameters of membrane (omega m), concentration boundary layers (omega l, omega h) and solution concentration in initial moment (Ch, Cl). Calculations performed on the basis of obtained square equation show that for a polymeric membrane with fixed transport properties, concentration difference (Ci-Ce) is nonlinear function of solution concentration (Ch-Cl). The nonlinearity is connected with appearance of the convection instability for (Ci-Ce) > 0.015 mol l(-1), breaking symmetry of complex l(h)/M/l(l) in relation to gravitational direction, what is the reason of increase (Ci-Ce) and volume and solute fluxes.

On a basis of the Kedem-Katchalsky formalism, the mathematical model enabling the calculation of mechanical pressure estimation characteristic of the concentration boundary layers thicknesses (delta) in a single-membrane system containing binary solutions was obtained. This model contains transport membrane, solution parameters and volume osmotic flux. These values were determined in a series of independent experiments. Calculated values delta are nonlinearly dependent on mechanical pressure difference for the same concentration of investigated solutions and membrane system configuration. These nonlinearities are an effect of a competition between spontaneously occurring diffusion, convection processes and modification of concentration field by mechanical pressure.

An expression for concentration polarization coefficient (chi) was derived from Kedem-Katchalsky equations. This expression contains the volume flux (Jvm), transport parameters of a membrane (omega m) and concentration boundary layers (omega 1, omega h). Calculations performed using the obtained expression showed that for a polymeric membrane with fixed transport properties, coefficient chi is a nonlinear function of concentration difference of solutions. This nonlinearity is related to the appearance of the convection instability that breaks symmetry of the l(h)/M/l(l) complex in relation to the gravitational direction.

Mathematical model of the volume flux through neutral polymeric membrane with concentration boundary layers on both sides of this membrane is presented. This model was based on the Kedem-Katchalsky equations for electrolyte solutions and describes the volume flux generated by osmotic and hydrostatic forces for dissociating substance non-homogeneous solutions. Nonlinear equation for volume flux was used for numerical calculations in linear regime of hydrodynamic stability. The validity of this model for binary solutions was confirmed by using a cell with a vertically mounted membrane. In the experimental set-up aqueous solution of KCl was placed on one side of the membrane. Whereas the ammonia in aqueous solution of KCl was placed at the other site of the membrane The good correlation between the experimental data o J(vm) and the results of calculation based on the model equations of J(vm) was observed.

The mathematical model of the thickness of concentration boundary layers controlling by concentration Rayleigh number and volume flows for ternary non-electrolyte solution was presented. The equations determining of this model can be used to numerical calculations.

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.

The influence of the concentration boundary layers on membrane potential (deltapsis) in a single-membrane system on basis of the Kedem-Katchalsky equations was described in cases of horizontally mounted neutral polymeric membrane separates non-homogeneous (mechanically unstirred) binary electrolytic solutions at different concentrations. Results of calculations of deltapsis as a function of ratio solution concentrations (Ch/Cl) at constant values of: concentration Rayleigh number (Rc), concentration polarization coefficient (zetas) and hydrostatic pressure (deltaP) were presented. Calculations were made for the case where on a one side of the membrane aqueous solution of NaCl at steady concentration 10(-3) mol x l(-1) (Cl) was placed and on the other aqueous solutions of NaCl at concentrations from 10(-3) mol x l(-1) to 2 x 10(-2) mol x l(-1) (Ch). Their densities were greater than NaCl solution's at 10(-3) mol x l(-1). It was shown that membrane potential depends on hydrodynamic state of a complex concentration boundary layer-membrane-concentration boundary layer, what is controlled by deltaP, Ch/Cl, Rc and zetas.

On the basis of model equation depending the membrane potential deltapsis, on mechanical pressure difference (deltaP), concentration polarization coefficient (zetas), concentration Rayleigh number (RC) and ratio concentration of solutions separated by membrane (Ch/Cl), the characteristics deltapsis = f(deltaP)zetas,RC,Ch/Cl for steady values of zetas, RC and Ch/Cl in single-membrane system were calculated. In this system neutral and isotropic polymeric membrane oriented in horizontal plane, the non-homogeneous binary electrolytic solutions of various concentrations were separated. Nonhomogeneity of solutions is results from creations of the concentration boundary layers on both sides of the membrane. Calculations were made for the case where on a one side of the membrane aqueous solution of NaCl at steady concentration 10(-3) mol x l(-1) (Cl) was placed and on the other aqueous solutions of NaCl at concentrations from 10(-3) mol x l(-1) to 2 x 10(-2) mol x l(-1) (Ch). Their densities were greater than NaCl solution's at 10(-3) mol x l(-1). It was shown that membrane potential depends on hydrodynamic state of a complex concentration boundary layer-membrane-concentration boundary layer, what is controlled by deltaP, Ch/Cl, RC and zetas.

In the paper, by applicating the classic definition of concentration Rayleigh number and the second Kedem-Katchalsky equation, there was deriven the equation of the fourth degree, which makes thicknesses (deltah and deltal) dependent on the concentration difference (Ch-Cl), concentration Rayleigh number (Rc), membrane permeability parameters (omega, xi s) and solutions (Dl, Dh), physico-chemical parameters of solutions (v(l), v(h), rho l, rho h, delta rho/deltaC), temperature (T) and gravitational acceleration (g). On the basis of the obtained formula for isothermal conditions (T = const) and constant gravitational field (g = const), there were calculated non-linear dependencies delta h = f(Ch-Cl)(Rc, zeta s), delta h = f (Rc)((Ch-Cl),zeta s) and delta h = f(delta s)((Ch-Cl),Rc).

Linear non-equilibrium thermodynamics (LNET) has been used to express the entropy production in single-membrane system representing the true forces (mechanical and osmotic pressures difference) and flows (volume and solute flows) in a homogeneous or non-homogeneous binary non-electrolyte solution. On the basis of Kedem-Katchalsky model equations of entropy production in single-membrane system in practical forms were described.

On the basis of model equation describing the membrane potential delta psi(s) on concentration Rayleigh number (R(C)), mechanical pressure difference (deltaP), concentration polarization coefficient (zeta s) and ratio concentration of solutions separated by membrane (Ch/Cl), the characteristics delta psi(s) = f(Rc)(delta P, zeta s, Ch/Cl) for steady values of zeta s, R(C) and Ch/Cl in single-membrane system were calculated. In this system neutral and isotropic polymeric membrane oriented in horizontal plane, the non-homogeneous binary electrolytic solutions of various concentrations were separated. Nonhomogeneity of solutions is results from creations of the concentration boundary layers on both sides of the membrane. Calculations were made for the case where on a one side of the membrane aqueous solution of NaCl at steady concentration 10(-3) mol x l(-1) (Cl) was placed and on the other aqueous solutions of NaCl at concentrations from 10(-3) mol x l(-1) to 2 x 10(-2) mol x l(-1) (Ch). Their densities were greater than NaCl solution's at 10(-3) mol x l(-1). It was shown that membrane potential depends on hydrodynamic state of a complex concentration boundary layer-membrane-concentration boundary layer, what is controlled by deltaP, Ch/Cl, Rc and Zeta(s).

Formalism leading to more general form of the Kedem-Katchalsky equation describing osmotic membrane transport, considering local unhomogenity of solutions called concentration boundary layers and influence of gravitational factor on membrane transport kinetics was presented. In order to test this formalism, osmotic volume flux was calculated, on the basis of experimental membrane transport parameters and aqueous glucose solutions in isothermal conditions. Obtained calculation's results are conformable to adequate experimental results presented in previous paper for flat polymeric membrane used in medicine (Biophys. Chem. 1986, 24, 173).

In the paper, review of papers devoted to biophysical properties of membrane dressing made of bacterial cellulose was done. These properties were determined on the basis of studies on osmotic and diffusive transport through pure (non modified) bacterial cellulose membrane form called Bio-Fill. The measures of these properties are values of membrane transport parameters resulted from Kedem-Katchalsky's theory and interferograms of near-membrane regions made laser interferometric method.

Review of papers devoted to medical properties of membrane dressing made of bacterial cellulose was done. These properties were determined on the basis of studies on application of this membrane to venous leg ulcer healing. Moreover, quantitative method of valuation of wound healing process efficiency which lies in calculating efficiency coefficient was described. Value of this coefficient is directly proportional to ulcer healing speed and indirectly proportional to product of initial surface and healing time.

The results of studies of influence of concentration boundary layers on passive diffusive transport in a double-membrane osmo-diffusive cell, containing a series of two (Ml and M(r)) vertically positioned, flat, microporous and symmetric polymer membranes (Nephrophane and Cellulose IMP-1) are presented in this paper. The membranes separated three compartments (l, m, r) containing binary, heterogeneous and non-ionic solutions (aqueous solutions of glucose or ethanol) or ternary non-electrolyte solutions (glucose solutions in 0.75 mol.l-1 solution of ethanol or ethanol solutions in 0.1 mol.l-1 aqueous solution of glucose). Solution concentrations fulfilled the condition C(k)l > C(k)m > C(k)r. The intermembrane compartment (m) was an infinitesimal solution layer. The volume of the m compartment and the volumes of the external (l and r) compartments fulfilled the condition Vl = Vr approximately 170 Vm. The tests were performed for configurations A and B of a double-membrane osmo-diffusive cell. In configuration A, the solution was located behind the M(r) membrane, and water was placed behind the Ml membrane, while in configuration B this sequence was reversed. The results obtained during experiment were interpreted in the categories of convective instability, which increased the value of diffusive permeability coefficient of the system: concentration boundary layer/membrane/concentration boundary layer.

The results of experiment of diffusive transmembrane transport in a single-membrane osmotic-diffusive electrochemical cell were presented. In all experiments one of the vessels was filed with pure water, and the second one--with aqueous potassium chloride solution in aqueous ammonia solutions of constant concentration. The flux of potassium chloride was assigned according to the following measure procedure. In a first step we assigned the time dependence of potassium chloride flux in conditions of uniform mechanically stirred solution with speed of 500 rpm. In a second step those characteristics were assigned in conditions of mechanically unstirred solution. Each experiment was made for two configurations of gravitational membrane system: (i) with the water in a vessel above the membrane and solution below it (configuration A) (ii) with the solution in a vessel above the membrane and water below it (configuration B). Taking under the consideration the values of potassium chloride flux in steady state for different solution concentration of the same substances and the same configurations of membrane system, the dependencies of potassium chloride flux from the solution concentration differences were made appropriately. On the base of those experiments the solute flux concentration boundary layers effects (jCBLE) were counted. Moreover it was shown that single-membrane osmotic-diffusive electrochemical cell has rectifier and amplifying of diffusive flow features. The coefficients, appropriately, of asymmetry and amplification of diffusive flux are the measurements of those features.

In this paper there were presented the results of studying accumulation and depletion in an inter-membrane compartment (m) of double-membrane osmotic-diffusive cell. This cell was contained two (Ml and M(r)), microporous and symmetrical flat polymeric membranes (Nephrophane and Cellulose IMP-1), separating three compartments (l, m, r) containing the heterogeneous binary and ternary nonelectrolytic solutions. The inter-membrane compartment (m) consists of the infinitesimal layer of solution. The volumes of compartment m and external compartment (l and r) fulfill the conditions Vm-->0 and Vl = Vr-->infinity respectively. As binary solutions were used the aqueous glucose, and as ternary--the glucose solutions in 0.75 mole.l-1 aqueous ethanol solution. In this system the solution concentrations fulfill the condition Cls > Co(ms) > Crs. In the initial moment Co(ms) = 0.5 (Cls + Crs). The calculations of a concentration in a steady-state Ci(ms) for configurations A and B of double-membrane osmotic-diffusive cell were elaborated. In configuration A solution with concentration Cls was placed in compartment above membrane Ml and water below membrane M(r). In configuration B--the sequence of solution was reversed. In case of the accumulation of substance in compartment m Ci(ms) > Co(ms), and a case of depletion--Ci(ms) < Co(ms).

In this paper the results of study flux gravidiffusive effect for a double-membrane osmotic-diffusive cell, in which series of two (Ml and M(r)), microporous and symmetrical flat polymeric membranes (Nephrophane and Cellulose IMP-1). These membranes separate three compartments (l, m, r) containing the heterogeneous and binary (aqueous glucose or ethanol solutions) or ternary (glucose solutions in 0.75 mole.l-1 aqueous ethanol solution or ethanol solutions in 0.1 mole.l-1 aqueous glucose solution) non-ionic solutions. The solution concentrations fulfil the condition Ckl > Ckm > Ckr. The inter-membrane compartment (m) consists of the infinitesimal layer of solution. The volume of compartment m and external compartment (l and r) fulfill the conditions Vm-->0 and Vl = Vr-->infinity respectively. The study of flux gravidiffusive effect for configurations A and B of the double-membrane osmotic-diffusive cell were elaborated. In configuration A solution was placed in compartment below membrane M(r) and water above membrane Ml. In configuration B solution was placed in compartment above membrane Ml and water below membrane Ml. These results are interpreted in terms of the convective instability that increases the diffusive permeability coefficients of complexes: concentration boundary layers/membrane Ml or M(r)/concentration boundary layer.

In this paper the results of study flux graviosmotic effect for a double-membrane system, in which two (Ml and M(r)), microporous and symmetrical flat polymeric membranes (Nephrophane and Cellulose IMP-1) separate three compartments (l, m, r) containing the heterogeneous and binary (aqueous glucose or ethanol solutions) or ternary (glucose solutions in 0.75 mole.l-1 aqueous ethanol solution or ethanol solutions in 0.1 mol.l-1 aqueous glucose solution) non-ionic solutions. In this system the solution concentrations fulfill the condition Ckl > Ckm > Ckr. The inter-membrane compartment (m) consists of the infinitesimal layer of solution. The volume of compartment m and external compartment (l and r) fulfill the conditions Vm-->0 and Vl = Vr-->infinity respectively. The calculations of flux graviosmotic effect for configurations A and B of the double-membrane osmotic-diffusive cell were elaborated. In configuration A solution was placed in compartment below membrane M(r) and water above membrane Ml. In configuration B solution was placed in compartment above membrane Ml and water below membrane Ml. These calculated results are interpreted in terms of the convective instability that increases the diffusive permeability coefficients of complexes: concentration boundary layers/membrane Ml or M(r)/concentration boundary layer.

In this paper the results of study pressure graviosmotic effect for a double-membrane osmotic-diffusive cell, in which series of two (Ml and M(r)), microporous and symmetrical flat polymeric membranes (Nephrophane and Cellulose IMP-1) separate three compartments (l, m, r) containing the heterogeneous and binary (aqueous glucose or ethanol solutions) or ternary (glucose solutions in 0.75 mole.l-1 aqueous ethanol solution or ethanol solutions in 0.1 mole.l-1 aqueous glucose solution) non-ionic solutions. In this system the solution concentrations fulfill the condition Ckl > Ckm > Ckr. The inter-membrane compartment (m) consists of the infinitesimal layer of solution. The volume of compartment m and external compartment (l and r) fulfill the conditions Vm-->0 and Vl = Vr-->infinity respectively. The calculations of pressure graviosmotic effect for configurations A and B of the double-membrane osmotic-diffusive cell were elaborated. In configuration A solution was placed in compartment below membrane M(r) and water above membrane Ml. In configuration B solution was placed in compartment above membrane Ml and water below membrane Ml. These calculated results are interpreted in terms of the convective instability that increases the diffusive permeability coefficients of complexes: concentration boundary layers (membrane Ml or M(r)) concentration boundary layer.

In this paper the pressure gravidiffusive model equation in a single-membrane osmotic-diffusive cell is elaborated. In this cell the flat, microporous and symmetric polymeric membrane so-called Nephrophane positioned horizontally separated water and binary (aqueous glucose or aqueous ethanol) or ternary (glucose in 0.2 mol.l-1 aqueous ethanol or ethanol in 0.05 mol.l-1 aqueous glucose) non-electrolyte solutions. The calculations of pressure gravidiffusive effects for the configurations A and B of the single-membrane osmotic-diffusive cell were elaborated. In configuration A solution was placed in compartment below membrane and in configuration B--above membrane. The calculated result are interpreted in terms of the convective instability that increases the diffusive permeability coefficient of complex: concentration boundary layer/membrane/concentration boundary layer.

Results of experimental study of volume flux in one-membrane system were presented. This system contains horizontal, microporous and symmetrical flat polymeric membrane (Nephrophan), which separate water and electrolyte solution. As binary solutions, aqueous ammonia solutions, which density is lower than water density, were used. As ternary solutions the ammonia with KC1 (0.1 or 0.2 mole.l-1) in aqueous solution were used. The density of ternary solutions was lower, higher or the same as water density. Two configurations of membrane system (A and B) in gravitational field were studied. In configuration A, water was in compartment over the membrane and the solution was under the membrane. In configuration B the succession was reverse. The thermodynamic model of flux graviosmotic effect was elaborated, and the calculations of this effect were performed for A and B configurations of one membrane system. The experimental results are interpreted in terms of gravitational instability that reduces concentration boundary layer dimensions and increases the diffusion permeability coefficient value of the complex: boundary layer/membrane/boundary layer.

In this paper the classification of the gravitational effects in a passive transmembrane transport is presented. Among these effects there are the flux (flux graviosmotic effect, flux gravidiffusive, current gravielectric effect) and force (pressure graviosmotic effect, pressure gravidiffusive effect, voltage gravielectric effect) gravitational effects. The pressure graviosmotic effect model equation in a single-membrane system is elaborated. In this system the flat, microporous and symmetric polymeric membrane (Nephrophan) positioned horizontally separated water and binary (aqueous glucose) or ternary (glucose-0.2 mole/l) aqueous ethanol) non-electrolyte solutions. The calculations of pressure graviosmotic effects for two (A and B) configurations of the single-membrane system were elaborated. In configuration A solution was placed in compartment below membrane and in configuration B--above membrane. These calculated results are interpreted in terms of the convective instability that increases the diffusive permeability coefficient of complex: boundary layer/membrane/boundary layer.