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

  • M. H. Allouche (a1) (a2), V. Botton (a1) (a2), S. Millet (a1), D. Henry (a1), S. Dagois-Bohy (a1), B. Güzel (a1) (a3) and H. Ben Hadid (a1)...

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.

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Journal of Fluid Mechanics
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