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We experimentally revisite the flow down an inclined plane of dense granular suspensions, with particles of sizes in the micron range, for which thermal fluctuations cannot be ignored. Using confocal microscopy on a miniaturized set-up, we observe that, in contrast with standard granular rheology, the flow profiles strongly depend on the particles size. Also, suspensions composed of small enough particles flow at infinitesimal inclinations. From the velocity measurements, an effective rheology is extracted in terms of a friction coefficient as a fonction of the dimensionless shear rate (the viscous number), and of the particle pressure normalized by the thermal pressure. Inspired by a previous work [1], a phenomenological model based on the sum of a thermal contribution describing the glass transition and an athermal contribution capturing the jamming transition is developed, which reproduces well the experimental observations. The model predicts the existence of a glassy friction angle lower than the granular athermal friction angle, a signature of the glass transition in the framework of a pressure imposed rheology.

We investigate experimentally and theoretically the stability of a shear-thickening suspension flowing down an inclined plane. In a previous paper (Darbois Texier et al., Commun. Phys., vol. 3, 2020), we have shown that for particle volume fractions $\phi$ above the discontinuous shear-thickening fraction $\phi _{DST}$ , long surface waves grow spontaneously at a flow Reynolds number much below 1. This motivated a simplified analysis based on a purely inertialess mechanism, called the ‘Oobleck waves’ mechanism, which couples the negatively sloped rheology of the suspension with the free-surface deflection and captures well the experimental instability threshold and the wave speed, for $\phi >\phi _{DST}$ . However, neglecting inertia does not allow us to describe the inertial Kapitza regime observed for $\phi , nor does it allow us to discriminate between Oobleck waves and other inertial instabilities expected above $\phi _{DST}$ . This paper fills this gap by extending our previous analysis, based on a depth-averaged approach and the Wyart–Cates constitutive shear-thickening rheology, to account for inertia. The extended analysis recovers quantitatively the experimental instability threshold in the Kapitza regime, below $\phi _{DST}$ , and in the Oobleck waves regime, above $\phi _{DST}$ . By providing additional measurements of the wave growth rate and investigating theoretically the effect of a strain delay in the rheology, it also confirms that the instability observed above $\phi _{DST}$ stems from the non-inertial Oobleck wave mechanism, which is specific to free-surface flows and dominates modes of inertial origin. These results emphasize the variety of instability mechanisms for shear-thickening suspensions and might be relevant to free-surface flows of other complex fluids displaying velocity-weakening rheology.