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Number of results


2006 | 4 | 4 | 429-438

Article title

The application of practical Kedem-Katchalsky equations in membrane transport


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Kedem-Katchalsky (K-K) equations, commonly used to describe the volume and solute flows of nonelectrolyte solutions across membranes, assume that the solutions on both sides are mixed. This paper presents a new contribution to the description of solute and solvent transfer through a membrane within the Kedem-Katchalsky formalism. The modified K-K equation obtained here, which expresses the volume flow (J
v), includes the effect of boundary layers of varied concentrations that form in the vicinity of the membrane in the case of poorly-mixed solutions. This equation is dependent on the following: membrane parameters (σ, L
p, ω), complex h/M/l parameters (σ
s-reflection, L
ps-hydraulic permeability, ω
s-solute permeability coefficients, δ
h, δ
l-thicknesses of concentration boundary layers), and solution parameters (c-concentration, ρ-density, v-kinematic viscosity, D-diffusion coefficient). In order to verify the elaborated equation concerning J
v, we calculated the following functions:
$$J_v = f(\Delta c)_{\Delta p,R_C = const} $$
$$J_v = f(R_C )_{\Delta p,\Delta c = const} $$
, and
$$J_v = f(\Delta p)_{\Delta c,R_C = const} $$
. The J
v equation was derived by means of two methods.










Physical description


1 - 12 - 2006
1 - 12 - 2006


  • Technical Schools, 97-300, Piotrkow Trybunalski, Poland


  • [1] O. Kedem and A. Katchalsky: “Termodynamics analysis of the permeability of biological membranes to nonelectrolyyes”, Biochim. Biophys. Acta, Vol. 27, (1958), pp. 229–246. http://dx.doi.org/10.1016/0006-3002(58)90330-5[Crossref]
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  • [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] 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, (2004), Vol. 168, pp. 397–412. http://dx.doi.org/10.1016/j.desal.2004.07.027[Crossref]
  • [10] 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]
  • [11] 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]
  • [12] A. Ślęzak and M. Jarzyńska: “Developing Kedem-Katchalsky equations of the transmembrane transport for binary nonhomogeneous non-electrolyte solutions”, Polymers in Medicine, T. XXXV(1), (2005), pp. 15–20.
  • [13] 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]
  • [14] M. Jarzyńska: “New method of derivation of practical Kedem-Katchalsky membrane transport equations”, Polymers in Medicine, T. XXXV(4), (2005), pp. 19–24.
  • [15] 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]
  • [16] K. Dołowy, A. Szewczyk and S. Pikuła: Biological membranes, Scientific Publisher “Śląsk”, Katowice-Warszawa, 2003 (in Polish), pp. 109.

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