University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Effective diffusion for nonlinear reactive flows in strong convection regime

Effective diffusion for nonlinear reactive flows in strong convection regime

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If you have a question about this talk, please contact Prof. Clément Mouhot.

We study the transport of a tracer in a periodic porous medium in large Peclet regime. Tracers are assumed to undergo nonlinear adsorption/desorption reaction, modeled via Langmuir isotherm, on the fluid-pore interfaces. We work with a coupled system of convection-diffusion equations. Expression for effective diffusion is derived by Homogenization. We have introduced a new notion of compactness called “Two-scale convergence with drift on periodic surfaces” which happens to be the right tool for the Homogenization problems posed in strong convection regime. This talk concerns the mathematical modeling of reactive flows and the techniques of Homogenization. The main result states that the homogenized limit of the coupled model is a scalar nonlinear monotone diffusion equation posed in the full domain $\mathbb{R}^d$. The homogenization result is proved under a technical assumption of equal drifts for the fluid velocity in the bulk and its slip velocity on the pore surfaces. This emphasizes the need for the developments of new techniques in the theory of Homogenization. This is a joint work with Gregoire Allaire.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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