ISSN 打印: 1091-028X
ISSN 在线: 1934-0508

# 多孔介质期刊

DOI: 10.1615/JPorMedia.v17.i7.20
pages 573-586

## MEMBRANE TRANSPORT IN CONCENTRATION POLARIZATION CONDITIONS: NETWORK THERMODYNAMICS MODEL EQUATIONS

Kornelia M. Batko
Department of Informatics for Economics, Membrane Science Group, University of Economics, Bogucicka 3B, 40287 Katowice, Poland
Izabella Slezak-Prochazka
Institute of Marteting, Membrane Science Group, Czestochowa University of Technology, 36b Armia Krajowa al., 42200 Czestochowa, Poland
Slawomir Grzegorczyn
Department of Biophysics, Membrane Science Group, Silesian Medical University, 19 Henryk Jordan Str., 41808 Zabrze, Poland
Andrzej Slezak
Chair of Public Health, Membrane Science Group, Czestochowa University of Technology, 36b Armia Krajowa al., 42200 Czestochowa, Poland

### ABSTRACT

The Kedem−Katchalsky equations in matrix version for homogeneous and nonhomogeneous solutions were applied for the interpretation of membrane transport. Coefficients L*ij (for unstirred solutions), Lij (for mechanically stirred solutions) (ij = 1, 2), and L*ij/Lij were calculated, on the basis of experimentally determined coefficients (Lp, σ, ω), for an aqueous glucose solution and configurations A and B of the membrane system, in which a cellulose membrane was mounted in a horizontal plane. In configuration A, the upper chamber contained aqueous glucose solution at concentration Cl, and the lower chamber contained aqueous glucose solution at concentration Ch. In configuration B, the position of solutions with concentrations Cl. and Ch. was reversed. From the calculations, it results that the values of coefficients L*11 = L11 are constant, but the values of coefficients L*12, L12, L21, L*21, and L22 depend linearly on solution concentration in the membrane ( C). However, the value of coefficient L*22 depends nonlinearly on C as well as on a membrane system configuration. A concentration Rayleigh number (RC) was used in a thermodynamic model based on Kedem−Katchalsky equations for counting L*ij/Lij . It can be also stated that for RC greater than threshold value ((RC)crit), conductance coefficients L*12/L12, L*22/L22, and det[L*]/det[L] depend on a configuration of the membrane system.

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