Resistance Coefficients of Polymer Membrane with Concentration Polarization

Andrzej Ślęzak,Kornelia M Batko,Sławomir Grzegorczyn

doi:10.1007/s11242-012-0038-5

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.

Highlights

Ri j Xi Ji XJi∗i∗ Jv Jvs Js Jss Jsa Lp σ ω ν δk Ph, Pl π Ch, Cl C
Network Thermodynamics (NT) is the synthesis of non-equilibrium thermodynamics, theory of electric circuits, theory of graphs and differential geometry
The first characteristic was obtained in homogeneous conditions and the second, in conditions of concentration polarization of the membrane

Summary

Introduction

Ri j Xi Ji XJi∗i∗ Jv Jvs Js Jss Jsa Lp σ ω ν δk Ph , Pl π Ch, Cl C. Biophysical systems, because of its complex structure, organization and numerous couplings, show nonlinear properties implying their unique behaviour, especially in living organisms (Oster et al 1971; Nicolis and Prigogine 1977; Peusner 1970). For this reason, the analysis of biophysical systems cannot be reduced to investigations of linear thermodynamic systems (Demirel 2002; Newman and Forgacs 2005; Grzegorczyn et al 2008). NT allows us to describe topology of the system and enables us to analyse dynamics of non-equilibrium processes of mass, charge, energy and information transport (Oster et al 1971; Perelson 1975; Peusner 1986a; Mikulecky 2005)

Methods

Results

Conclusion