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2007 | 5 | 4 | 586-598

Article title

Practical Kedem-Katchalsky equations and their modification


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The research problem presented in this work concerns modification of the Kedem-Katchalsky (K-K) equation for volume flow (J
v) through system (h|M|l), consisting of a membrane M and boundary layers h and l. Such boundary layers appear in the vicinity of the membrane on both sides due to the lack of mixing of solutions. This paper also includes the derivation of the equation for volume flow (J
vr) dissipated on concentration boundary layers h and l. The derivation of these equations concerns the case in which the substance transport through the membrane is generated by the osmotic pressure gradient
$$\Delta \dot \prod $$
. On the basis of the equations for the volume flows (J
v) and (J
vr), some calculations for a nephrophane membrane, used in medicine, and for aqueous glucose solutions have been carried out. In order to test the equations for (J
v) and (J
vr), we have also carried out calculations for the volume flow (J′
v) that is transferred through the membrane in the case of mixed solutions on both sides of the membrane. This volume flux has been calculated on the basis of the original (K-K) equation. The results are presented in Fig. 2.










Physical description


1 - 12 - 2007
1 - 12 - 2007


  • Technical High School of Environment Developing, 97-300, Piotrkow Trybunalski, Poland


  • [1] O. Kedem and A. Katchalsky: “Termodynamics analysis of the permeability of biological membranes to non-electrolyyes”, Biochim. Biophys. Acta, Vol. 27, (1958), pp. 229–246. http://dx.doi.org/10.1016/0006-3002(58)90330-5[Crossref]
  • [2] A. Katchalsky and P.F. Curran: Non-equilibrium Thermodynamics in Biophysics, Harvard University Press, Cambridge, MA, 1965.
  • [3] O. Kedem and A. Katchalsky: “Permeability of composite membranes. Part 1. Electric current, volume flow and solute flow through membranes”, Trans. Faraday Soc., Vol. 59, (1963), pp. 1918–1930. http://dx.doi.org/10.1039/tf9635901918
  • [4] M. Kargol and A. Kargol: “Mechanistic equations for membrane substance transport and their identity with Kedem-Katchalsky equations”, Biophys. Chem., Vol. 103, (2003), pp. 117–127. http://dx.doi.org/10.1016/S0301-4622(02)00250-8[Crossref]
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  • [7] B.Z. Ginzburg and A. Katchalsky: “The frictional coefficients of the flows on non-electrolytes through artificial membranes”, J. Gen. Phisiol., Vol. 47, (1963), pp. 403–418. http://dx.doi.org/10.1085/jgp.47.2.403[Crossref]
  • [8] S. Koter: “The Kedem-Katchalsky equations and the sieve mechanism of membrane Transport”, J. Membrane Sci., Vol. 246, (2005), pp. 109–111. http://dx.doi.org/10.1016/j.memsci.2004.08.022[Crossref]
  • [9] G. Monticelli: “Some remarks about a mechanistic model of transport processes in porous membranes”, J. Membr. Sci., Vol. 214, (2003), pp. 331–333. http://dx.doi.org/10.1016/S0376-7388(02)00581-1[Crossref]
  • [10] M. Jarzyńska: “Mechanistic equations for membrane substance transport are consistent with Kedem-Katchalsky equations”, J. Membr. Sci., Vol. 263, (2005), pp. 162–163. http://dx.doi.org/10.1016/j.memsci.2005.07.016[Crossref]
  • [11] A. Kargol, M. Przestalski and M. Kargol: “A study of porous structure of cellular membranes in human erythrocytes”, Cryobiology, Vol. 50, (2005), pp. 332–337. http://dx.doi.org/10.1016/j.cryobiol.2005.04.003[Crossref]
  • [12] A.W. Mohammad and M.S. Takriff: “Predicting flux and rejection of multicomponent salts mixture in nanofiltration membranes”, Desalination, Vol. 157, (2003), pp. 105–111. http://dx.doi.org/10.1016/S0011-9164(03)00389-8[Crossref]
  • [13] A. Kargol: “Modified Kedem-Katchalsky equations and their applications”, J. Membr. Sci., Vol. 174, (2000), pp. 43–53. http://dx.doi.org/10.1016/S0376-7388(00)00367-7[Crossref]
  • [14] K. Dołowy, A. Szewczyk and S. Pikuła: Biological membranes, Scientific Publisher “Ślask”, Katowice-Warszawa, (2003) (in Polish), p. 109.
  • [15] M. Jarzyńska: “The application of practical Kedem-Katchalsky equations in membrane Transport”, Cent. Eur. J. Phys., Vol. 4, (2006) pp. 429–438. http://dx.doi.org/10.2478/s11534-006-0034-x[Crossref]
  • [16] A. Ślęzak, K. Dworecki, J. Jasik-Ślęzak and J. Wąsik: “Method to determine the critical concentration Rayleigh number in isothermal passive membrane transport processes”, Desalination, Vol. 168, (2004), pp. 397–412. http://dx.doi.org/10.1016/j.desal.2004.07.027[Crossref]

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