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Front propagation in cellular flows: scale dependence versus scale invariance
Published online by Cambridge University Press: 08 August 2023
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.
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- © The Author(s), 2023. Published by Cambridge University Press
References
Bodea et al. Supplementary Movie 1
Front propagation at $U/V_0 =22.2$ in an array of vortices of size $L=5$mm involving $20$ vortices in their width. The movie is accelerated 12 times.