[Evaluation of the vant'Hoff's osmotic coefficient in concentration polarization conditions of membrane system]. / Ocena wartosci wspólczynnika osmotycznego van't Hoffa w warunkach polaryzacji stezeniowej ukladu membranowego.

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

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. Calculated values δ are nonlinearly dependent on the concentrations of investigated solutions and the membrane system configuration. These nonlinearities are the effect of a competition between spontaneously occurring diffusion and natural convection. The mathematical model based on Kedem-Katchalsky equations and a concentration Rayleigh number (R(C)) was presented. On the basis of this model we introduce the dimensionless parameter, called by us a Katchalsky number (Ka), modifies R(C) of membrane transport. The critical value of this number well describes a moment of transition from the state of diffusion into convective diffusion membrane transport.

[Analysis of the membrane transport using a transformed Kedem-Katchalsky equations]. / Analiza transportu membranowego przy pomocy transformowanych równan Kedem-Katchalskyego.

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.

[Evaluation of the concentration difference determining the membrane transport in concentration polarization conditions]. / Ocena wartosci róznicy stezen determinujacej transport membranowy w warunkach polaryzacji stezeniowej.

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.