Hyperuniformity with no fine tuning in sheared sedimenting suspensions*

Particle suspensions, present in many natural and industrial settings, typically contain aggregates and other microstructures that can complicate flow behaviors and damage processing equipment. Recent work found that applying uniform periodic shear near a critical transition can reduce fluctuations in the local particle concentration across all length scales, leading to a hyperuniform state. However, this strategy for homogenization requires fine tuning of the strain amplitude. Here we show that in a model of sedimenting particles under periodic shear, there is a well-defined regime at low sedimentation speed where hyperuniform density fluctuations automatically occur. Our simulations and theoretical arguments show that hyperuniformity is lost beyond a finite lengthscale that is set by vertical density gradients. Nonetheless, this lengthscale can be made arbitrarily large simply by slowing the sedimentation rate.