  Particle suspensions, present in many natural and industrial settings,
typically contain aggregates or other microstructures that can complicate
macroscopic flow behaviors and damage processing equipment. Recent work found
that applying uniform periodic shear near a critical transition can reduce
fluctuations in the 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 scaling automatically occurs. Our
simulations and theoretical arguments show that the homogenization extends up
to a finite lengthscale that diverges as the sedimentation speed approaches
zero.
