Abstract
The applicability of the classical version of Kedem and Katchalsky's practical equations is reduced to membrane systems with sufficiently diluted and well mixed solutions. In biophysical practice (and not only), we usually have to deal with systems whose solutions are poorly mixed. In such systems are generated the so-called near-membrane diffusion layers. Their existence significantly reduces the stream of diluted substance (j s ) and the volume stream (J v ). In order to describe mathematically these streams generated in the conditions of poor mixing of solutions, it was necessary to transform the Kedem and Katchalsky classical equations into a more general form. This has been done in the present work. The more general equations obtained here are applicable to the description of streams j s and J v generated in the conditions of both good and poor mixing of solutes.
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DworeckiK.: Interferometric investigation of near-membrane diffusion layers. J. Biol. Phys. 21 (1995), 37–49.
Dworecki, K. and Kargol, M.: Interferometric investigations of graviosmotic polarization of membrane system, Int. Symp. Membrane and Membrane Separation Processes, 11–15 Sep. 1989, Toruń (in Polish).
DworeckiK., KargolM. and PrzestalskiS.: Investigation of the diffusion layers in one-membrane systems, Stud. Biophys. 122 (1987), 83–85.
ForgacsC., LebovitzJ., O'BrienR.N. and SpieglerK.S.: Interferometric study of concentration profiles in solutions near membrane surfaces, Electrochim. Acta, 20 (1975), 555–562.
HoogervorstC.I.P., GoedeI., VersluijsC.W. and SmitI.A.M.: Transient diffusion through a membrane separating two semiinfinite volumes of unstirred solutions. J. Phys. Chem. 82 (1979) 1318–1324.
IbanezJ.A., HernándezA. and TejerinaA.F.: Effect of the diffusion boundary layers on the surface charge density in passive membranes. J. Non-Equilib. Thermodyn. 7 (1982), 363–370.
KargolM.: The graviosmotic hypothesis of xylem transport of water in plants. Gen. Physiol. Biophys., 11 (1992), 469–487.
KargolM.: Full analytical description of graviosmotic volume flows, Gen. Physiol. Biophys., 13 (1994), 109–126.
KargolM. and DworeckiK.: Interferometric studies of diffusive unstirred layers generated in graviosmotic systems, Curr. Top. Biophys. 18 (1994), 99–104.
KargolM., OrnalB. and KosztołowiczT.: A study on gravielectric polarization in 1-membrane systems, Curr. Top. Biophys. 18 (1994), 105–111.
KargolM., DworeckiK. and PrzestalskiS.: Interferometric investigation of diffusive boundary layers in a graviosmotic systems. Stud. Biophys. 113 (1986), 31–37.
KargolM. and ŚlęzakA.: Modification of Kedem-Katchalsky practical equations, Probl. Nauk Podstawowych, Wyd. Polit. Świet., Kielce, 16 (1985), 5–12 (in Polish).
KatchalskyA. and CurranP.F., Nonequilibrium Thermodynamics in Biophysics, Harvard Univ. Press, Cambridge, Ma. 1965, pp. 113–132.
KedemO. and KatchalskyA.: Thermodynamics analysis of the permeability of biological membranes to non-electrolytes. Biochim. Biophys. Acta, 27 (1958), 229–246.
KedemO. and KatchalskyA.: Permeability of composite membranes (Part 3), Trans. Faraday Soc. 59 (1963), 1941–1953.
KumamotoE.: Effect of unstirred layers on the membrane potential in a concentration cell, J. Membr. Sci. 9 (1981), 43–51.
PatlakC.S., GoldsteinD.A. and HoffmannI.F.: The flow of solute and solvent across a two-membrane system, J. Theoret. Biol. 5 (1963), 426–442.
ŚlęzakA. and TurczyńskiB.: Modification of Kedem-Katchalsky equations, Biophys. Chem. 24 (1986), 173–178.
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Kargol, M. A more general form of Kedem and Katchalsky's practical equations. J Biol Phys 22, 15–26 (1996). https://doi.org/10.1007/BF00383819
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DOI: https://doi.org/10.1007/BF00383819