Hydrodynamic Dispersion in Concentrated Sedimenting Suspensions

Citation

Lester, Julia Catherine (1988) Hydrodynamic Dispersion in Concentrated Sedimenting Suspensions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/hv2d-rx78. https://resolver.caltech.edu/CaltechETD:etd-08012006-113003

Abstract

The hydrodynamic dispersion in concentrated sedimenting suspensions is investigated by numerical simulation. The particle Reynolds number is zero, and the Péclet number is infinite (the particles are non-Brownian). Particle trajectories are calculated by Stokesian dynamics. Stokesian dynamics is a molecular-dynamics-like simulation that provides an accurate representation of the suspension hydrodynamics. Detailed in this thesis is a technique that accelerates the convergence of the mobility interactions among particles in an infinite suspension. The simulations are of a monolayer of identical spheres sedimenting in the plane of the monolayer. Relative motion among the spheres arises from hydrodynamic interactions. The displacement related to this relative motion may constitute a random walk, giving rise to diffusive behavior of the spheres. This hydrodynamically induced self-diffusivity has been seen in sheared suspensions of non-Brownian, neutrally buoyant spheres.

Results of the numerical simulations show that the motion of spheres in sedimenting suspensions is also diffusive. The diffusion coefficient is relatively insensitive to the nature of the microstructure, as expressed by the pair-distribution function and the short-time, self-diffusion coefficient. The coefficient of diffusion decreases as the concentration increases for concentrated suspensions (it increases in the shear case). The ratio of the diffusion coefficient to the velocity variance of the spheres should be proportional to the time scale of the diffusive interactions. The diffusion time scale and the diffusion velocity scale (the square root of the velocity variance) both decrease as the concentration increases. In the shear case, the velocity scale (sphere radius multiplied by the shear rate) is independent of concentration, and the time scale (the product of the square of the concentration and the inverse of the shear rate) increases with increasing concentration. At the lowest concentrations, the spheres whose centers are separated by less than 2.05 radii prefer to align in the direction of sedimentation. At the highest concentrations, the preferred alignment is in the perpendicular direction.

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