Irreversible thermodynamic model equations of the transport across a horizontally mounted membrane

Ślęzak, Andrzej

doi:10.1016/0301-4622(89)80047-x

Cited by 46 publications

(77 citation statements)

References 30 publications

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“…Therefore, membrane permeability can be controlled by changes in pH, concentration, and/or density of outside solutions, or by external fields [8,15,17]. For a membrane oriented in a horizontal plane and solution with density dependent on concentration, transport through the membrane depends on configurations of a membrane system [6,12,19,21]. Diffusion and hydrodynamic instabilities appearing near membrane surfaces influence a degree of the concentration polarization of the membrane.…”

Section: Introductionmentioning

confidence: 99%

“…These processes lead to creation of local and/or global non-homogeneities in the membrane system by time and space evolution of concentration profiles near the membrane [5][6][7]. For transport of electrolytes or nonelectrolytes through neutral membranes, concentration polarization manifests itself by building up concentration boundary layers (CBLs) at both surfaces of the membrane [1, 10,19]. Concentration boundary layers modify membrane transport [12,19,21] by changes in thermodynamic forces and fluxes [19,21].…”

Section: Introductionmentioning

confidence: 99%

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Conditions of hydrodynamic instability appearance in fluid thin layers with changes in time thickness and density gradient

Grzegorczyn

Ślęzak

Michalska-Małecka

et al. 2012

Journal of Non-Equilibrium Thermodynamics

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The transport of NaCl and ethanol through the microbial cellulose membrane was used as a generator of layers with density gradients, parallel to gravity vector. Changes in NaCl concentrations connected with density gradients in these layers were monitored by means of Ag|AgCl electrodes dipped directly into aqueous NaCl solutions with or without ethanol. The parameters used in this article and characterizing diffusive or diffusiveconvective processes in layers are the ratio of NaCl concentrations at electrode surfaces (C i =C e ) calculated for voltage which was measured 6 h after rebuilding of layers with density gradients, and time of appearance of hydrodynamic instabilities in the membrane system. The C i =C e is the nonlinear function of initial ratio of NaCl on the membrane (C h =C l ), with maximum concentration at initial moment dependent on ethanol and configuration of the membrane system. The time of appearance of hydrodynamic instabilities in layers with density gradients parallel and directed opposite to the gravity vector depends on C h =C l , ethanol concentration, and configuration of the membrane system. Besides, for aqueous NaCl solutions, critical values of density gradients and thicknesses of layers needed This work was supported by KNW-1-086/10. 78 S. Grzegorczyn et al. for the appearance of hydrodynamic instabilities were calculated and presented as functions of C h =C l .

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Conditions of hydrodynamic instability appearance in fluid thin layers with changes in time thickness and density gradient

Grzegorczyn

Ślęzak

Michalska-Małecka

et al. 2012

Journal of Non-Equilibrium Thermodynamics

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“…For the concentration Rayleigh number greater than its critical value, the hydrodynamic instability occurs to lead to natural convection which reduces the thickness of CBL and increases the value of concentration gradient of the membrane and consequently osmotic stimulus (Ślęzak 1989;. The existence of such a regulatory mechanism at the presence of an external field enables to explain an aim of the osmotic effects, such as the osmotic volume flux amplification (Kargol et al 1979;Ślęzak 1989;Ślęzak et al 2002).…”

Section: Introductionmentioning

confidence: 99%

“…The existence of such a regulatory mechanism at the presence of an external field enables to explain an aim of the osmotic effects, such as the osmotic volume flux amplification (Kargol et al 1979;Ślęzak 1989;Ślęzak et al 2002). This effect occurs in the single-membrane system containing ternary solutions in conditions of concentration polarization (Ślęzak 1989), and occurs when the density gradient in CBL in surroundings of horizontally mounted membrane is anti-parallel to the vector of gravity.…”

Section: Introductionmentioning

confidence: 99%

“…These layers serve as additional kinetic barriers to the fast penetrating substances, both through natural and artificial membranes (Winne 1973;Ślęzak 1989;Dionne et al 1996;Pohl et al 1998;Peppenheimer 2001;Baumgartner and Montrose 2004;Loftsson et al 2006;Knipfer and Steudle 2008). CBL are formed spontaneously on both sides of a membrane separating two solutions of different concentrations.…”

Section: Introductionmentioning

confidence: 99%

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

Jasik-Slezak¹,

Olszówka²,

Ślęzak³

2011

gpb

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Abstract. The estimation method of the concentration boundary layers thicknesses (δ) in a singlemembrane 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.

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Diffusion Characteristics in Ethyl Alcohol and Glucose Solutions Using Kedem‐Katchalsky Equations

Jarzyńska¹,

Staryga

Kluza

et al. 2019

Chem Eng & Technol

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Formulas for calculating the viscosity and diffusion coefficients for two-component aqueous non-electrolyte solutions as a function of the solution concentration under isothermal conditions were derived. The dependence of diffusion coefficient, filtration coefficient, and dynamic viscosity coefficient for these solutions on the solution concentration was estimated and evaluated. Based on the obtained formulas, the results of diffusion coefficient, membrane filtration coefficient, and dynamic viscosity calculations for aqueous solutions of ethanol and glucose are presented and compared with literature data.

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Irreversible thermodynamic model equations of the transport across a horizontally mounted membrane

Cited by 46 publications

References 30 publications

Conditions of hydrodynamic instability appearance in fluid thin layers with changes in time thickness and density gradient

Conditions of hydrodynamic instability appearance in fluid thin layers with changes in time thickness and density gradient

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

Diffusion Characteristics in Ethyl Alcohol and Glucose Solutions Using Kedem‐Katchalsky Equations

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