# Laboratoire de Mécanique des Fluides et d’Acoustique - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

## Nos partenaires

Article dans J. Fluid Mech. (2017)

## Primary instability of a shear-thinning film flow down an incline : experimental study

M. H. Allouche, V. Botton, S. Millet, D. Henry, S. Dagois-Bohy, B. Güzel, H. Ben Hadid

The main objective of this work is to study experimentally the primary instability of non-Newtonian film flows down an inclined plane. We focus on low-concentration shear-thinning aqueous solutions obeying the Carreau law. The experimental study essentially consists of measuring wavelengths in marginal conditions, which yields the primary stability threshold for a given slope. The experimental results for neutral curves presented in the $(Re,f_c)$ and $(Re,k)$ planes (where $f_c$ is the driving frequency, $k$ is the wavenumber and $Re$ is the Reynolds number) are in good agreement with the numerical results obtained by a resolution of the generalized Orr–Sommerfeld equation. The long-wave asymptotic extension of our results is consistent with former theoretical predictions of the critical Reynolds number. This is the first experimental evidence of the destabilizing effect of the shear-thinning behaviour in comparison with the Newtonian case : the critical Reynolds number is smaller, and the ratio between the critical wave celerity and the flow velocity at the free surface is larger.