[Concentration dependencies of W(ij) Peusner's coefficient for different composition and concentration of the non-electrolyte ternary solutions].

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).

[Evaluation of the vant'Hoff's osmotic coefficient in concentration polarization conditions of membrane system].

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.

Estimation of thickness of concentration boundary layers by osmotic volume flux determination.

The estimation method of the concentration boundary layers thicknesses (δ) in a single-membrane system containing non-electrolytic binary or ternary solutions was devised using the Kedem-Katchalsky formalism. A square equation used in this method contains membrane transport (L(p), σ, ω) and solution (D, C) parameters as well as a volume osmotic flux (J(v)). These values can be determined in a series of independent experiments.

[Evaluation of the concentration difference determining the membrane transport in concentration polarization conditions].

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).

[Analysis of the membrane transport using a transformed Kedem-Katchalsky equations].

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.

[Relation between effective and real solute permeability coefficients through polymeric membrane].

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.

[Mechanical pressure dependencies of the concentration boundary layers for polymeric membrane].

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.

[Mathematical model describing the transport of dissociating substances solutions through polymeric membrane with concentration polarization].

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.

[Thermodynamical description of the concentration polarization in a membrane transport of non-electrolyte solution].

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.

[Determination of thickness of concentration boundary layers for ternary electrolyte solutions and polymeric membrane].

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.

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.

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.

[Mathematical model of the membrane transport of ternary non-electrolyte solutions: the role of volume flows in creation of concentration boundary layers].

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.

Practical forms of entropy production for single-membrane system and binary non-electrolyte solutions.

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.

[Computer modeling the hydrostatic pressure characteristics of the membrane potential for polymeric membrane, separated non-homogeneous electrolyte solutions].

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.

[Computer modeling the concentration characteristics of the membrane potential for polymeric membrane, separated non-homogeneous electrolyte solutions].

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).

[Computer modeling the dependences of the membrane potential for polymeric membrane separated non-homogeneous electrolyte solutions on concentration Rayleigh number].

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.

Mathematical model describing thickness changes of concentration boundary layers controlled by polymeric membrane parameters and concentration Rayleigh number.

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).

Mathematical model equation of the volume flows through polymeric membrane of heterogeneous non-ionic solutions.

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.

[Medical properties of the membrane dressing made of bacterial cellulose].

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.

[Biophysical properties of membrane dressing made of bacterial cellulose].

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.

Effect of concentration boundary layers on passive solute flows in a system of two polymeric membranes positioned in vertical planes.

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.

Effects of concentration boundary layers in a transport of electrolyte solutions through horizontal mounted polymeric membrane.

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.

[Estimating accumulation and depletion of substances in a double osmotic-diffusive cell containing polymeric membranes].

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.