Abstract
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.
[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)90330-510.1016/0006-3002(58)90330-5Search in Google Scholar
[2] A. Katchalsky and P.F. Curran: Non-equilibrium Thermodynamics in Biophysics, Harvard University Press, Cambridge, MA, 1965. 10.4159/harvard.9780674494121Search in Google Scholar
[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/tf963590191810.1039/TF9635901918Search in Google Scholar
[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)00250-810.1016/S0301-4622(02)00250-8Search in Google Scholar
[5] P.H. Barry and J.M. Diamond: “Effects of unstirred layers on membrane phenomena”, Physiol. Rev., Vol. 64, (1984), pp. 763–872. Search in Google Scholar
[6] A. Narębska, W. Kujawski and S. Koter: “Irreversible thermodynamics of transport across charged membranes”, J. Membr. Sci., Vol. 25, (1985), pp. 153–170. http://dx.doi.org/10.1016/S0376-7388(00)80248-310.1016/S0376-7388(00)80248-3Search in Google Scholar
[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.47.2.40310.1085/jgp.47.2.403Search in Google Scholar
[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.2004.08.02210.1016/j.memsci.2004.08.022Search in Google Scholar
[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.2004.07.02710.1016/j.desal.2004.07.027Search in Google Scholar
[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)00389-810.1016/S0011-9164(03)00389-8Search in Google Scholar
[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.2005.07.01610.1016/j.memsci.2005.07.016Search in Google Scholar
[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. Search in Google Scholar
[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.2005.04.00310.1016/j.cryobiol.2005.04.003Search in Google Scholar
[14] M. Jarzyńska: “New method of derivation of practical Kedem-Katchalsky membrane transport equations”, Polymers in Medicine, T. XXXV(4), (2005), pp. 19–24. Search in Google Scholar
[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)00367-710.1016/S0376-7388(00)00367-7Search in Google Scholar
[16] K. Dołowy, A. Szewczyk and S. Pikuła: Biological membranes, Scientific Publisher “Śląsk”, Katowice-Warszawa, 2003 (in Polish), pp. 109. Search in Google Scholar
© 2006 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
