An accurate simplified data treatment for the initial adsorption kinetics in conditions of laminar convection in a slit:: application to protein adsorption

We present the derivation of a simple approximation for the original expression of the adsorption rate [Langmuir 10 (1994) 3898] in conditions of laminar flow in a slit, to relate the measured initial kinetic constant k with the interfacial kinetic constant k(a) and the transport-limited Leveque constant k(Lev). The same method of derivation is applied here to get a simple approximation of the average kinetic constant (k) [Biomaterials 20 (1999) 1621]. For the local value, at distance x from the entrance of the slit, we propose k(x)/k(a) = (u - 1)(au - 1)1(bu + 1), where u = k(x)/k(Lev), a = 0.452, b = -0.625, with a maximal error of 1% in comparison with the exact solution. For the average value over the length of the slit, we propose <k>/k(a) = (U - 1)(AU - 1)/(BU + 1), where U = <k>/<k(Lev)>, A = 0.203, B = -0.273, with a maximal error of 0.03%. These approximations lead to an easy determination of the adsorption constant and diffusion coefficient D of the solute, as appropriate plots of experimental data provide k(a) and D-2/3 as the intercepts of the curve with the ordinate and abscissa axes, respectively. It is pointed out that the linear approximation k(-1) = k(a)(-1) + k(Lev)(-1) would lead to the overestimation of both the diffusion coefficient and adsorption kinetic constant. As an example, the application to the analysis of experimental data for adsorption of alpha-chymotrypsin onto mica plates is provided. (C) 2003 Elsevier B.V. All rights reserved.