Surface-wave instability without inertia in shear-thickening suspensions

Abstract

Recent simulations and experiments have shown that shear-thickening of dense particle suspensions corresponds to a frictional transition. Based on this understanding, non-monotonic rheological laws have been proposed and successfully tested in rheometers. These recent advances offer a unique opportunity for moving beyond rheometry and tackling quantitatively hydrodynamic flows of shear-thickening suspensions. Here, we investigate the flow of a shear-thickening suspension down an inclined plane and show that, at large volume fractions, surface kinematic waves can spontaneously emerge. Curiously, the instability develops at low Reynolds numbers, and therefore does not fit into the classical framework of Kapitza or ‘roll-waves’ instabilities based on inertia. We show that this instability, that we call ‘Oobleck waves’, arises from the sole coupling between the non-monotonic (S-shape) rheological laws of shear-thickening suspensions and the flow free surface.