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

Abstract

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 Lévêque 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)/( 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 α-chymotrypsin onto mica plates is provided.