Emergence of a hexagonal pattern in shear-thickening suspensions under orbital oscillations

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 a novel dynamics of a non-Brownian suspension under horizontal circular 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 results from the competition between kinematic instability and particle migrations and symmetry argument. Our analysis shows that this instability is closely related to the onset of discontinuous shear thickening transition of the suspension. In addition, the density waves degenerate into random fluctuations when replacing the free surface with rigid confinement, however, they will long live under a constrained soft silicone oil layer. It indicates that the shear-thickened state is intrinsically heterogeneous, and the boundary conditions/deformability are crucial for developing local disturbance.