Fluid Mechanics and Acoustics Laboratory - UMR 5509

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Stability analysis of liquid film flows

Stability analysis of liquid film flows

Simon Dagois-Bohy, Séverine Millet, Valéry Botton, Hamda Ben Hadid, Daniel Henry, R. Usha, J. Hu.

This research topic concerns the study of the instabilities which develop in non-Newtonian liquid film flows. This problem has a practical interest for some environmental flows (mud flows, rock glaciers, sediment transport) and for industrial processes, such as the coating processes and the manufacture of multi-layer solid films.
We are interested by the characterization of the instabilities which affect the non-Newtonian liquid film flows on inclines. An experimental set-up with a transparent incline plane has been developed in our team. It allows to obtain the linear instability thresholds corresponding to the amplification of the applied perturbations.
The recent PhD work of M.H. Allouche considered the shear-thinning fluids (Carreau model). It was shown a very good agreement between the experimental results and the theoretical predictions obtained by Orr-Sommerfeld type approaches [A125].
A first step of this work was to give a good characterization of the fluid rheology: a new method was proposed allowing the measurement of the rheological parameters at low shear rate by attenuation of surface waves (electrocapillarity) [A114].
A theoretical study following a Squire approach was also performed: it showed that, in certain parameter ranges, the three-dimensional instabilities (i.e. oblique waves) could be dominant. This fact was taken into account in the choice of our experimental configuration [A117].
More recently, we considered viscoplastic fluids (yield stress fluids) more representative of real fluids (mud, paints,...). The theoretical and experimental study of the instabilities developing in the film flows for these types of fluids is the PhD work of D. Mounkaila Noma, which started at the end of 2017.
Numerical stability studies were also developed in collaboration with the team of Pr R. Usha at IIT of Madras in India: it concerned different configurations of film flows or canal flows, with the presence of non-homogeneous and/or anisotrop porous substrates [B27, Millet et al. (AM 2019)].

Older work: numerical stability studies.

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].