Direct comparison of simplified models of surface reacting flows in flow chambers

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 Peclet number. The small effects of the flow on the chemical reaction, which depend on the combination of the Damkohler and Peclet numbers, are highlighted. The results of these equations are favorably cross compared with the asymptotic (Leveque) 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.