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Front propagation in cellular flows: scale dependence versus scale invariance

Published online by Cambridge University Press:  08 August 2023

S. Bodea Open the ORCID record for S. Bodea [Opens in a new window] ,
E. Beauvier  and
A. Pocheau Open the ORCID record for A. Pocheau [Opens in a new window]
S. Bodea
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, 13384 Marseille, France
E. Beauvier
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, 13384 Marseille, France
A. Pocheau*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, 13384 Marseille, France
*
†Email address for correspondence: alain.pocheau@univ-amu.fr
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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.

JFM classification

Reacting Flows: Laminar reacting flows Low-Reynolds-number flows: Hele-Shaw flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 968 , 10 August 2023 , A29
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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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.

Download Bodea et al. Supplementary Movie 1(Video)
Video 3 MB

Bodea et al. Supplementary Movie 2

Front propagation at $U/V_0 = 50.8$ in an array of vortices of size $L=20$mm involving $5$ vortices in their width. The movie is accelerated 12 times.

Download Bodea et al. Supplementary Movie 2(Video)
Video 2.1 MB

Bodea et al. Supplementary Movie 3

Front propagation at $U/V_0 = 63.4$ in an array of vortices of size $L=40$mm involving $3$ vortices in their width. The movie is accelerated 12 times.

Download Bodea et al. Supplementary Movie 3(Video)
Video 2.4 MB