Sedimentation of random suspensions and the effect of hyperuniformity

This work is concerned with the mathematical analysis of bulk rheology random suspensions rigid particles settling under gravity in viscous fluids. Each particle generates a fluid flow that turn acts on other and hinders their settling. In an equilibrium perspective, for given ensemble positions, we analyze both associated mean speed velocity fluctuations individual particles. 1970s, Batchelor gave proper definition speed, 60-year-old open problem physics, based appropriate renormalization long-range contributions. 1980s, celebrated formal calculation by Caflisch Luke suggested dimension $$d=3$$ should diverge size sedimentation tank, contradicting intuition experimental observations. The role self-organization suspended form hyperuniformity was later put forward to explain additional screening this divergence steady-state present contribution, develop first rigorous theory allows justify all these calculations physics literature.