Evaluation of S-Entropy Production in a Single-Membrane System in Concentration Polarization Conditions

Transport in Porous Media - S-entropy source of membrane system was described based on linear non-equilibrium thermodynamics. The volume and diffusive fluxes of non-electrolyte solutions and...     

Nonlinear Effects in Osmotic Volume Flows of Electrolyte Solutions through Double-Membrane System

The results of experimental study of volume osmotic flows in a double-membrane system are presented in this article. The double-membrane system consists of two membranes (M _u, M _d) oriented in horizontal planes and three identical compartments (u, m, d), containing unstirred binary or ternary ionic solutions. In this system concentrations of the solutions fulfil the following conditions C _us  = C _ds  < C _ms (s = 1 or 2). Solutions of aqueous potassium chloride or ammonia were used as binary solutions, whereas potassium chloride dissolved in aqueous ammonia solution or ammonia dissolved in aqueous potassium chloride solution were used as ternary solutions. For binary solutions, the dependencies of a volume flux (J _v) on potassium chloride or ammonia concentration (C _ms ) are linear, whereas for ternary solutions these dependencies are nonlinear. The volume flux amplification and the osmotic conductivity coefficients were calculated on the basis of experimental data. The coefficient of the volume flux amplification for ternary solutions in comparison to binary ones depends on solutes concentrations and has maximum values dependent on solutes concentrations. Similarly, the osmotic conductivity coefficient has maximal values dependent on solutes concentrations. Moreover, the thermodynamic model of the osmotic volume flux was developed and the results were interpreted within the gravitational instability category.     

Time characteristics of electromotive force in single-membrane cell for stable and unstable conditions of reconstructing of concentration boundary layers

The stability of concentration boundary layers near membrane (CBLs), arising after turning off mechanical stirring of KCl solutions in single-membrane cell with polymer membrane placed in horizontal plane, was studied by measurement of time changes of electromotive force of single-membrane cell (EMF). In the case when solution with low concentration and low density (C_l) was over the membrane and the solution with higher concentration and higher density (C_h) was under the membrane (configuration A) the stable recreation of CBLs by diffusion was observed, which was manifested by gradual and monotonous decrease of EMF after turning off mechanical stirring. The results of the carried out experiment show that character of time changes of EMF for A configuration depends on the quotient of concentrations on the membrane C_h/C_l at the initial moment. Besides, for configuration A the pulsations of EMF were not observed in the whole studied range of concentrations. In the case of opposite location of solutions in relation to the membrane (configuration B) it was stated that for C_h/C_l ≤ 10 time changes of EMF were similar to time changes of EMF in configuration A. For C_h/C_l > 10 time characteristics of EMF for A and B configurations were different. For B configuration and C_h/C_l ≥ 100 the pulsations of EMF, arising in a short time after turning off mechanical stirring, were observed. The pulsations of EMF can be connected with hydrodynamic instability in CBLs. Increase of C_h/C_l caused increase of amplitude and decrease of period of EMF pulsations. Besides, for C_h/C_l > 1000 damping of EMF pulsation was observed, greater for higher C_h/C_l. The interpretation of experimental data was made by means of the Kedem–Katchalsky model, diffusion equation and concentration Rayleigh number.     

Natural Convection as an Asymmetrical Factor of the Transport Through Porous Membrane

For nonionic substances, which density of solution depends on its concentration, concentration polarization of the membrane in horizontal plane depends not only on diffusion but on the hydrodynamic instabilities at the membrane surfaces also. Such instabilities are the cause of asymmetry of membrane transport in gravitational field. On the basis of results of glucose transport through the Nephrophan membrane in horizontal plane we can state that this asymmetry was observed for the cases with concentration Rayleigh number greater than critical value (R _C )_crit = 1709.3. The mathematical model based on Kedem–Katchalsky equations and Rayleigh number was presented. On the basis of this model and the dependence of volume flux through the Nephrophan membrane as a function of glucose concentration in the upper (configuration B) and lower (configuration A) chamber of the membrane system, the dependencies of thickness of concentration boundary layer, Rayleigh number, and introduced coefficient of asymmetry as a function of glucose concentration were presented for both configurations. These dependencies show that asymmetry of the membrane transport is observed for glucose concentration higher than 0.015 mol l^?1.     

Resistance Coefficients of Polymer Membrane with Concentration Polarization

The Kedem-Katchalsky equations, modified by means of symmetric transformations of Peusner thermodynamic networks, were applied to interpret the membrane transport in concentration polarization conditions. The results from the study demonstrate that the resistance coefficients counted for membrane transport of aqueous solutions of glucose through Nephrophan membrane in horizontal plane are nonlinearly dependent on mean concentration of glucose in the membrane ${(\bar{C})}$ . It was also shown that the threshold value of concentration ${(\bar{C}_{cr})}$ existed, and for ${\bar{C} > \bar{C}_{cr}}$ , the resistance coefficients depend, while for ${\bar{C} < \bar{C}_{cr}}$ , they do not depend on the membrane system configuration. Increase of mean glucose concentration in the membrane (in the range ${\bar{C} > \bar{C}_{cr})}$ causes decrease of difference between resistance coefficients of the membrane system in homogeneous conditions (solutions mechanically stirred) and in conditions with hydrodynamic instabilities (configuration B). Besides increase of mean glucose concentration in the membrane (in the range ${\bar{C} > \bar{C}_{cr})}$ causes increase of the difference between resistance coefficients for membrane system with concentration polarization without hydrodynamic instabilities (configuration A) and membrane system in homogeneous conditions.