Abstract
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.
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Abbreviations
- R ij :
-
Generalized resistance coefficients
- X i :
-
Thermodynamic forces in homogeneous conditions
- J i :
-
Thermodynamic fluxes in homogeneous conditions
- \({X_{i}^*}\) :
-
Thermodynamic forces in non-homogeneous conditions
- \({J_{i}^*}\) :
-
Thermodynamic fluxes in non-homogeneous conditions
- J v :
-
Volume flux in homogeneous conditions
- J vs :
-
Volume flux in non-homogeneous conditions
- J s :
-
Solute flux in homogeneous conditions
- J ss :
-
Solute flux in non-homogeneous conditions
- J sa :
-
Solute advective flux
- L p :
-
Hydraulic permeability coefficient
- σ :
-
Reflection coefficient
- ω :
-
Solute permeability coefficient
- ν :
-
Kinematic viscosity
- δ k :
-
Thickness of concentration boundary layers
- P h , P l :
-
Hydrostatic pressure (h higher and l lower value)
- π :
-
Osmotic pressure
- C h ,C l :
-
Solute concentrations in chambers of the membrane system
- \({\bar{C}}\) :
-
Mean solute concentration in the membrane
- R :
-
Gas constant
- R C :
-
Concentration Rayleigh number
- T :
-
Thermodynamic temperature
- D k :
-
Diffusion coefficient
- ζ p :
-
Hydraulic concentration polarization coefficient
- ζ v :
-
Osmotic concentration polarization coefficient
- ζ s :
-
Diffusive concentration polarization coefficient
- ζ a :
-
Advective concentration polarization coefficient
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Acknowledgments
This study was supported by the Ministry of Science and Higher Education under Grant No. BS/PB -622/3010/2011/P.
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Ślęzak, A., Grzegorczyn, S. & Batko, K.M. Resistance Coefficients of Polymer Membrane with Concentration Polarization. Transp Porous Med 95, 151–170 (2012). https://doi.org/10.1007/s11242-012-0038-5
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DOI: https://doi.org/10.1007/s11242-012-0038-5