Department of Mathematics
Massachusetts Institute of Technology
This work was done in collaboration with Michael P. Brenner, Dept. of Mathematics, MIT; and Boris I. Shraiman, Bell Labs, Lucent Technologies.
Particulate suspension flows arise in a number of industrial, environmental, and biological contexts. In the creeping flow (Re=0) limit, the particles in these dynamically-evolving heterogeneous flows interact via a long-range advection, decaying as small inverse powers of particle separation. We consider the dilute, creeping flow limit of a noncolloidal suspension of monodisperse rigid spheres sedimenting under gravity in an otherwise Newtonian incompressible liquid. Nonintegrability of the microstructural Green's functions makes macroscopic averaging difficult, and leads to the troublesome possibility that velocity fluctuations diverge with increasing system size as proposed by Caflisch and Luke. Simulations indicate the presence of coherent "blobs," which control the velocity fluctuations and particle diffusivity. Non-trivial scaling of density correlation times is explained in terms of particle displacements, and conditional density correlations demonstrate that the blobs are long-lived structures. Results are compared with recent experiments.