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.

最近的模拟和实验表明，致密颗粒悬浮液的剪切增稠对应于摩擦过渡。基于这种理解，提出了非单调流变定律并在流变仪中成功进行了测试。这些最新进展为超越流变学和定量处理增稠剪切悬浮液的流体动力学流动提供了独特的机会。在这里，我们研究了剪切增稠悬浮液在倾斜平面上的流动，并表明，在较大的体积分数下，表面运动波可以自发出现。奇怪的是，不稳定性在低雷诺数下发展，因此不适合经典的Kapitza框架或基于惯性的“侧倾波”不稳定性。我们证明了这种不稳定性，我们称之为“ Oobleck波”，