Front propagation in cellular flows: scale dependence versus scale invariance

Abstract

We experimentally study front propagation in a vortex lattice providing closed steady cellular flows and no mean flow. To this end, we trigger an autocatalytic reaction in a solution stirred by magnetohydrodynamic flows in a Hele-Shaw cell. We evidence a scale-invariant regime below some flow magnitude and a scale-dependent regime above, the scales referring here to the vortex scale and the front thickness. The transition between these regimes corresponds to a unitary Damköhler number$Da$:$Da=1$. The enhancement of the mean front velocity with the flow magnitude nicely agrees with the literature on numerical simulations and theoretical analyses in the scale-invariant regime$Da>1$, but displays noticeable discrepancies in the scale-dependent one$Da<1$. This shows that the transition between regimes is qualitatively sharp but quantitatively smooth.