title: Front propagation in cellular flows for fast reaction and small diffusivity.
abstract: We investigate the influence of fluid flows on the propagation of chemical fronts arising in Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type models. We develop an asymptotic theory for the front speed in a cellular flow in the limit of small molecular diffusivity and fast reaction, i.e., large Péclet (Pe) and Damköhler (Da) numbers. The front speed is expressed in terms of a periodic path--an instanton--that minimizes a certain functional. This leads to an efficient procedure to calculate the front speed, and to closed-form expressions for (logPe)(-1) ≪ Da ≪ Pe and for Da ≫ Pe. Our theoretical predictions are compared with (i) numerical solutions of an eigenvalue problem and (ii) simulations of the advection-diffusion-reaction equation.
authors.affiliation: School of Mathematics, University of Birmingham, Birmingham, United Kingdom.
authors.forename: Alexandra
authors.initials: A
authors.lastname: Tzella
authors.affiliation: School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, United Kingdom.
authors.forename: Jacques
authors.initials: J
authors.lastname: Vanneste
mesh_terms: D004058:Diffusion; D057446:Hydrodynamics; D007700:Kinetics; D008962:Models, Theoretical