Effective dispersion equations for reactive flows with dominant Péclet and Damkohler numbers

In this chapter we study a reactive flow through a capillary tube. The solute particles are transported and diffused by the fluid. At the tube lateral boundary they undergo an adsorption–desorption process. The transport and reaction parameters are such that we have large, dominant Péclet and Damkohler numbers with respect to the ratio of characteristic transversal and longitudinal lengths (the small parameter e). Using the anisotropic singular perturbation technique we derive the effective equations. In the absence of the chemical reactions they coincide with Taylor's dispersion model. The result is compared with the turbulence closure modeling and with the center manifold approach. Furthermore, we present a numerical justification of the model by a direct simulation.