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

## TL;DR

This paper investigates how orbital oscillations induce a hexagonal pattern in shear-thickening suspensions, revealing the intrinsic heterogeneity of the state and the influence of boundary conditions on pattern formation.

## Contribution

It demonstrates the emergence of hexagonal density patterns driven by orbital oscillations and provides a linear stability analysis explaining the conditions for pattern formation.

## Key findings

- Localized density waves appear beyond a frequency threshold.
- Hexagonal patterns form due to coupling between advection and shear-thickening.
- Rigid confinement suppresses density wave formation.

## Abstract

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.