Chaotic mixing and front propagation in a three-dimensional flow

We present experiments on passive mixing and on the behavior of the excitable Belousov-Zhabotinsky (BZ) chemical reaction in a time-independent, three-dimensional (3D) flow. The flow is composed of nested horizontal and vertical chains of vortices, a flow that has been shown\footnote{M.A. Fogleman, M.J. Fawcett and T. H. Solomon, Phys. Rev. E {\bf 63}, 02101(R) (2001).} numerically to produce chaotic mixing with a complicated structure of ordered and chaotic regions. We study mixing experimentally by tracking neutrally-buoyant tracer particles in 3D and by imaging the evolution of a fluorescent dye with a scanning laser technique. The same scanning technique enables us to image fronts of the Ruthenium-catalyzed BZ reaction in the same flow. We analyze the behavior of these fronts with an extension of a theory of {\em burning invariant manifolds} \footnote{J. Mahoney, D. Bargteil, M. Kingsbury, K. Mitchell and T. Solomon, Europhys. Lett. {\bf 98}, 44005 (2012).} that has been shown to predict accurately the locations of barriers that impede reaction fronts in 2D flows.