This thesis explores how the average sedimentation velocity u0 of a monodisperse suspension of spheres depends on the volume fraction of solids c and on the application of shear to the suspension and considers how changes in the sedimentation velocity reflect changes in the microscale distribution of particles in the suspension. For dilute, quiescent, monodisperse suspensions of spheres with radius a greater than 2µm, previous experimental measurements of u0 are well-correlated by the result
u0 = us(1 - c1/3)
where us is the Stokes settling velocity of the spheres (cf. Barnea, E. and Mizrahi, J., Chem. Eng. J. 5, 171-189 (1973)). Although none of the previous theoretical predictions are in even rough accord with this result, this type of behavior is shown to be consistent with that of a suspension having a pair-probability function changing over a length scale of O(ac-1/3), which is comparable to the average interparticle spacing. A molecular-dynamics-type simulation is employed to show that multiparticle hydrodynamic interactions can create this type of microscale "structure" in a sedimenting suspension. This thesis also presents the first results for the influence of bulk flow on non-flocculating sedimenting suspensions. In a uniaxial extensional flow, a dilute suspension which is being sheared sufficiently rapidly for the effect of the shear to dominate the effect of multiparticle hydrodynamic interactions is shown to settle with velocity
u0 = us(1 - 4.52c) + o(c).
This increase in u0 results because the pair-probability function now changes over a length scale of O(a), not of O(ac-1/3). Experimental measurements presented here of the sedimentation velocity as a function of particle volume fraction and dimensionless shear rate in the simple shear flow created by a Couette device agree remarkably well with this result.
