In this paper a steady laminar 2D Poiseuille flow between two
plates with chemical reactions on the upper wall is considered. This
is a typical configuration in flow chambers (like the BIACORE one),
which are used for the determination of the rate constants of reversible
reactions between biological macromolecules. As the chamber thickness
is small compared to its length, simplifications are possible, so,
some asymptotic limits of mass conservation equation coupled with the
wall chemistry are presented. We obtain a system with a large
Péclet number.
The small effects of the flow on the
chemical reaction, which depend on the combination of the
Damköhler and Péclet numbers, are highlighted. The results of these equations
are favorably cross compared with the asymptotic (Lévêque)
solution or with the simplified solutions (integral methods) found in
the literature. The final result is that, due to the fact that the
exchange coefficient is shown to be nearly constant, the simplified
integral method is derived in a more rigorous way and its area of use
is improved.