Effective models for reactive flow under a dominant Péclet number and order one Damköhler number: Numerical simulations

Catherine Choquet (1) , Carole Rosier (2)

1 MIA - Mathématiques, Image et Applications - EA 3165
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

The paper is devoted to the longitudinal dispersion of a soluble substance released in a steady laminar flow through a slit channel with heterogeneous reaction at the outer wall. The reactive transport happens in the presence of a dominant Péclet number and order one Damköhler number. In particular, these Péclet numbers correspond to Taylor's dispersion regime. An effective model for the enhanced diffusion in this context was derived recently. It contains memory effects and contributions to the effective diffusion and effective advection velocity, due to the flow and chemistry reaction regime. In the present paper, we show through numerical simulations the efficiency of this new model. In particular, using Taylor's 'historical' parameters, we illustrate that our derived contributions are important and that using them is necessary in order to simulate correctly the reactive flows. We emphasize three main points. First, we show how the effective diffusion is enhanced by chemical effects at dispersive times. Second, our model captures an intermediate regime where the diffusion is anomalous and the distribution is asymmetric. Third, we show how the chemical effects also slow down the average speed of the front.

Mots clés: Numerical simulations; Effective models; Dispersion

Domaines: Equations aux dérivées partielles [math.AP]

Catherine Choquet, Carole Rosier. Effective models for reactive flow under a dominant Péclet number and order one Damköhler number: Numerical simulations. Nonlinear Analysis: Real World Applications, 2012, pp.10.1016/j.nonrwa.2012.02.008. ⟨10.1016/j.nonrwa.2012.02.008⟩. ⟨hal-00823357⟩