A dense particle suspension under shear may lose its uniform state to large local density and stress fluctuations, which challenge the mean-field description of the system. Here, we explore the novel dynamics of a non-Brownian suspension under orbital oscillations, where localized density waves along the flow direction appear beyond an excitation frequency threshold and self-organize into a hexagonal pattern across the system. The spontaneous occurrence of the inhomogeneity pattern arises from a coupling between particle advection and the shear-thickening nature of the suspension. Through linear stability analysis, we show that they overcome the stabilizing effects of particle pressure at sufficient particle volume fraction and oscillation frequency. In addition, the long-standing density waves degenerate into random fluctuations when replacing the free surface with rigid confinement. It indicates that the shear-thickened state is intrinsically heterogeneous, and the boundary conditions are crucial for developing local disturbance.

中文翻译：

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轨道振荡下剪切增稠悬浮液中六边形图案的出现

剪切下的致密颗粒悬浮液可能会因局部密度和应力波动而失去均匀状态，这对系统的平均场描述提出了挑战。在这里，我们探索了轨道振荡下非布朗悬浮液的新颖动力学，其中沿流动方向的局部密度波出现超出激发频率阈值，并在整个系统中自组织成六边形图案。不均匀模式的自发发生是由颗粒平流和悬浮液的剪切增稠性质之间的耦合引起的。通过线性稳定性分析，我们表明它们在足够的颗粒体积分数和振荡频率下克服了颗粒压力的稳定效应。此外，当用刚性约束代替自由表面时，长期存在的密度波会退化为随机涨落。这表明剪切增稠状态本质上是不均匀的，边界条件对于产生局部扰动至关重要。