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Some remarks on the Kedem-Katchalsky equations for non-electrolytes

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Abstract

The Kedem-Katchalsky equation for the flow of a non-electrolyte through a homogeneous membrane is shown to be a first order expansion of an exact integral of the Spiegler-Bearman-Kirkwood frictional equations under the assumption that the partial frictional coefficients, ζ ij , are concentration independent. The equations are solved in terms of volume flow; there are no water-to-volume flow correction terms for the permeability, ω, or the reflection coefficient, σ. The precision of the expansion depends upon the magnitude of the water flow. The frictional coefficientsf sm andf sw are given as functions of the experimentally determined parameters ω and σ; the frictions, are shown to be independent ofL p .

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Abbreviations

(a)C m :

Concentrations in the membrane phase membrane matrix

(b)C w :

water

(c)C s =C s (x):

solute

(d)C′ s =C s (0):

at left solution-membrane interface

(e)C″ s =C s (Δx):

at right solution-membrane interface

(a)C Is :

to the left of the membrane

(b)C IIs :

to the right of the membrane

(c)C 0 w :

water in free solution

f ij :

Spiegler frictional coefficient

f 0 sw :

solute-water friction in free solution

F m :

force exerted by membrane support

J s ,J w ,J V :

solute (molar), water (molar) and volume flows relative to the membrane

J i :

absolute flows

J (n) i :

flows relative to thenth velocity

K :

partition coefficient

L p :

filtration coefficient

P :

hydrostatic pressure

L ij :

Onsager coefficient

R ij :

inverse Onsager coefficient

X i :

thermodynamic force

\(\overline V _s ,\overline V _w\) :

partial molar volumes

Δx :

membrane thickness

ω:

solute permeability

σ:

reflection coefficient

ζ ij :

Bearman-Kirkwood partial frictional coefficient

Δπ i :

osmotic pressure difference due to impermeable, species

μ s ,μ w :

chemical potentials

φ s :

water volume fraction in membrane phase

Literature

  • Bearman, R. J. and J. G. Kirkwood. 1958. “Statistical Mechanics of Transport Processes: XI. Equations of Transport in Multi-component Systems.”J. Chem. Phys.,28, 136–145.

    Article  MathSciNet  Google Scholar 

  • Ciani, S. and A. Gliozzi. 1966. “A Thermodynamic Analysis of Steady State Diffusion of Counterions and Water Through a Membrane with Immobile Sites.”Biophysik,3, 22–35.

    Article  Google Scholar 

  • —. 1967. “An Irreversible Thermodynamics Treatment of Electrodiffusion in Uniform Membranes.”Ibids.,3, 281–299.

    Article  Google Scholar 

  • Ginzberg, B. Z. and A. Katchalsky. 1963. “The Frictional Coefficients of the Flows of Non-electrolytes through Artificial Membranes.”J. Gen. Physiol.,47, 403–418.

    Article  Google Scholar 

  • Kedem, O. and A. Katchalsky. 1958. “Thermodynamic Analysis of the Permeability of Biological Membranes to Non-electrolytes.”Biochem. Biophys. Acta,27, 229–246.

    Article  Google Scholar 

  • ——. 1961. “A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability.”J. Gen. Physiol.,45, 143–179.

    Article  Google Scholar 

  • Kirkwood, J. G. 1954. “Transport of Ions Through Biological Membranes from the Standpoint of Irreversible Thermodynamics.” InIon Transport Across Membranes, ed. H. T. Clark. New York: Academic Press. 119–127.

    Google Scholar 

  • Laity, R. W. 1959. “An Application of Irreversible Thermodynamics to the Study of Diffusion.”J. Phys. Chem.,63, 80–83.

    Article  Google Scholar 

  • Mikulecky, D. C. 1967. “On the Relative Contribution of Viscous Flow vs. Diffusional (frictional) Flow to the Stationary State Flow of Water through a Tight Membrane.”Biophys. J.,7, 527–534.

    Article  Google Scholar 

  • Onsager, L. 1945. “Theories and Problems of Liquid Diffusion.”Ann. N.Y. Acad. Sci.,46, 241–265.

    Google Scholar 

  • Patlak, C. S., D. A. Goldstein and J. F. Hoffman. 1963. “Flow of Solute and Solvent Across a Two-membrane System.”J. Theoret. Biol.,5, 426–442.

    Article  Google Scholar 

  • Pringogine, I. 1961.Intro., to the Thermodynamics of Irreversible Processes, 2nd Edition, New York: Interscience.

    Google Scholar 

  • Solomon, A. K. 1968. “Characterization of Biological Membranes by Equivalent Proes.”J. Gen. Physiol.,51 (supplement), 335s–364s.

    Google Scholar 

  • Spiegler, K. S. 1958. “Transport Processes in Ionic Membranes.”Tr. Faraday Soc.,54, 1408–1428.

    Article  Google Scholar 

  • — and O. Kedem. 1966. “Thermodynamics of Hyper-filtration (Reverse Osmosis): Criteria for Efficient Membranes.”Desalination,1, 311–326.

    Article  Google Scholar 

  • Staverman, A. J. 1951. “The Theory of Measurement of Osmotic Pressure.”Rec. Trav. Chim.,70, 344–352.

    Google Scholar 

  • Vaidhyanathan, V. S. 1966. “Some Theoretical Aspects of Biological Transport.”Intracellular Transport, ed. K. B. Warren. New York: Academic Press. 153–165.

    Google Scholar 

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Author notes

  1. I. W. Richardson

    Present address: Institute of Physiology, Aarhus University, Aarhus, Denmark

Authors and Affiliations

  1. Department of Biochemistry and Biophysics, School of Medicine, University of California, 94122, San Francisco, California

    I. W. Richardson

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  1. I. W. Richardson
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Richardson, I.W. Some remarks on the Kedem-Katchalsky equations for non-electrolytes. Bulletin of Mathematical Biophysics 32, 237–247 (1970). https://doi.org/10.1007/BF02476888

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  • DOI: https://doi.org/10.1007/BF02476888

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