Conclusion

We proposed simple relationships in the channel geometry to describe the passage from a fully transport-controlled process to an interface-controlled one when increasing convection (say wall shear rate y) for a study at some distance x from the entrance, as well as for the average value over the full or partial length of the channel (or wall). The experimental data of the initial experimental kinetic constant k(x, y) are plotted as a function of

(k/kLev)D2^3, where kLev is the Lévêque limit and D the diffusion coefficient. The adsorption kinetic constant ka and the protein diffusion coefficient to power 2/3 can be easily determined as the intercepts of the fit curve with the ordinate and abscissa axes, respectively. The normalizations of ordinates and abscissae to the intercepts provide directly the magnitude of the depletion in the liquid phase at the interface, and the relative evaluation to the transport-limited process. An example is given for the system a-chymotrypsin/mica at pH 8.6.

The variation of Ç potential as a function of surface coverage exhibits a change of regime, this suggests a new arrangement of adsorbed protein molecules above a threshold of surface occupation. The possibility of dipolar attractive interactions between the proteins is considered to create domains with an antiferroelectric order at high coverage.

Acknowledgements. We are grateful to R. Souard and P. Montels (EMI) for manufacturing the flow cell, and to D. Cot (EMI) for the photo. This work was supported by "Programme Ecologie Quantitative" of the French Ministry of Research, and performed within the framework of collaboration between Centre National de la Recherché Scientifique (France) and Kazan State University (Russia), project 12889.

We study the influence of the length of examination Ax around the average mean distance to the channel entrance x, through the parameter £ = Ax/x, on the numerical parameters a and b determined in Eq. 8. The two local limit expressions, valid near the control by the interfacial reaction (Eq. 6b) or by transport (Eq. 6a), can be written as k—1(x) = cak-x + cLk—1v(x), where ca and cL are numerical coefficients (Dejardin et al. 1994; Dejardin and Vasina 2004). In what follows, the average between xi = x — Ax/2 and x2 = x + Ax/2, is indicated by the use of brackets [].

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