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

¹ Lab. de Modélisation en Mécanique, UMR CNRS 7607, Boîte 162, Université Paris 6, 4 place Jussieu, 75252 Paris, France
² Department of Mathematics, University of the West Timisoara, Bv. V. Parvan, nr. 4, 1900, Timisoara, Romania

Corresponding author: pyl@ccr.jussieu.fr

Received: 25 October 2001
Revised: 1 October 2003
Accepted: 6 February 2004
Published online: 7 April 2004

Abstract

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.