%0 Journal Article
%T Front propagation in cellular flows for fast reaction and small diffusivity
%A Alexandra Tzella
%A Jacques Vanneste
%J Physics
%D 2014
%I arXiv
%R 10.1103/PhysRevE.90.011001
%X We investigate the influence of fluid flows on the propagation of chemical fronts arising in 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 P\'eclet ($Pe$) and Damk\"ohler ($Da$) 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 $(\log Pe)^{-1}\ll Da\ll Pe$ and for $Da\gg Pe$. Our theoretical predictions are compared with (i) numerical solutions of an eigenvalue problem and (ii) simulations of the advection--diffusion--reaction equation.
%U http://arxiv.org/abs/1404.1010v3