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Article Dans Une Revue Journal of Fluid Mechanics Année : 2023

Shear-thickening suspensions down inclines: from Kapitza to Oobleck waves

Résumé

We investigate experimentally and theoretically the stability of a shear-thickening suspension flowing down an inclined plane. In a recent work, we have shown that above the discontinuous shear-thickening volume fraction φ DST , long surface waves, called 'Oobleck waves', can spontaneously emerge although the flow Reynolds numbers becomes vanishingly small. The analysis we proposed, based on the coupling between the negatively-sloped rheology of shear-thickening suspensions and the free surface deformation, can very well capture the instability onset and the wave speed for φ > φDST (Darbois Texier et al. 2020). However, this analysis which did not take into account the effect of inertia, could not describe the inertial Kapitza waves observed for φ < φ DST , nor could we distinguish the 'Oobleck wave' instability from other inertial instabilities expected above φ DST in the presence of inertia. Here, we address these questions by extending the lubrication approach based on Wyart-Cates constitutive flow rules performed in Darbois Texier et al. (2020) to include the effect of inertia. Overall, our analysis enables to quantitatively predict the instability onset over the whole range of volume fraction investigated, capturing the transition between Kapitza waves below φ DST to Oobleck waves above φ DST. By providing additional measurements of the growth rate of the instability and investigating the effect of a strain delay in the rheology, we confirm that in the discontinuous shear-thickening regime, Oobleck waves arise from a non-inertial mechanism specific to free-surface flows which dominates other inertial unstable modes. Our results opens the route to the study of other free surface flows in complex fluids presenting velocity-weakening rheology where similar instability mechanisms could be unveiled.
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Dates et versions

hal-03763665 , version 1 (29-08-2022)
hal-03763665 , version 2 (21-11-2023)

Identifiants

Citer

Baptiste Darbois Texier, Henri Lhuissier, Bloen Metzger, Yoel Forterre. Shear-thickening suspensions down inclines: from Kapitza to Oobleck waves. Journal of Fluid Mechanics, 2023, 959, pp.A27. ⟨10.1017/jfm.2023.162⟩. ⟨hal-03763665v2⟩
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