Fluid Mechanics and Acoustics Laboratory - UMR 5509

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

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Coupled convective phenomena Team

Stability analysis of multi-layer liquid film flows

Séverine Millet, Valéry Botton, Hamda Ben Hadid, Daniel Henry, J. Hu

We study the instabilities which develop in multi-layer liquid film flows. We want to determine their characteristics, their domain of existence, and their critical threshold. This problem has a practical interest for some environmental flows (rock glaciers, sediment transport, estuary flows), and for industrial processes, such as the coating processes and the manufacture of multi-layer solid films.

As a first step, within the frame of the post-doctoral position of J. Hu (Beijing, China), we considered Newtonian fluids. We first considered a two-layer film down an incline and showed the effects of the density and viscosity ratios on the instabilities. Two approaches were used: an asymptotic approximation for small inertia to study the interface instabilities which are triggered even without inertia [A75], and a more general analysis taking into account inertia to study both interface and free surface instabilities [A84]. The density stratification was shown to favour the long-wave interface instability (with even a possible disappearance of the short-wave interface instability) for any viscosity ratio. We then considered the Poiseuille-Rayleigh-Bénard instability including a solutal influence through the Soret effect [A76]. We finally considered a single layer of a mixture flowing down a heated inclined plate, taking into account the Soret effect [A83]. [All these results were obtained by stability analyses combining temporal, spatial and spatio-temporal approaches.

Then, within the frame of the thesis of S. Millet, we studied non-Newtonian fluid flows using a Careau model implemented in a linear stability code. We characterized the influence of the non-Newtonian model on the instabilities, surface instabilities for a single layer film flow and surface and interface instabilities for a two-layer film flow. For two layers, it has been shown that it is the rheology of the lower layer which mainly influences the onset of instabilities [B17, B18, B19, B21].

An experimental set-up concerned with single or double layer film flows down an incline for fluids with variable rheology is currently developed in our team by V. Botton.