Invariant barriers to reactive front propagation in fluid flows

¹ School of Natural Sciences, University of California - Merced, CA 95344, USA
² Department of Physics and Astronomy, Bucknell University - Lewisburg, PA 17837, USA

^a jmahoney3@ucmerced.edu

Received: 7 March 2012
Accepted: 22 April 2012

Abstract

We present theory and experiments on the dynamics of reaction fronts in two-dimensional, vortex-dominated flows, for both time-independent and periodically driven cases. We find that the front propagation process is controlled by one-sided barriers that are either fixed in the laboratory frame (time-independent flows) or oscillate periodically (periodically driven flows). We call these barriers burning invariant manifolds (BIMs), since their role in front propagation is analogous to that of invariant manifolds in the transport and mixing of passive impurities under advection. Theoretically, the BIMs emerge from a dynamical systems approach when the advection-reaction-diffusion dynamics is recast as an ODE for front element dynamics. Experimentally, we measure the location of BIMs for several laboratory flows and confirm their role as barriers to front propagation.