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https://hdl.handle.net/2142/21585
Description
Title
Mechanics of polydisperse suspensions
Author(s)
Revay, Joseph Michael
Issue Date
1992
Doctoral Committee Chair(s)
Higdon, Jonathan J.L.
Department of Study
Chemical and Biomolecular Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Language
eng
Abstract
This work describes the results of numerical simulations for polydisperse sedimentation of equal sized spheres, e.g. particles of different density. Using the stokesian dynamics algorithm, mobility matrices are computed for random particle configurations and ensemble averages taken to calculate the mean mobility matrices. It is shown that the settling velocities of individual particle species may be expressed (4.39) in terms of two scalar functions of total volume fraction. These are the self mobility M$\sb{\rm o}$ (eq. short time self diffusion coefficient) and the interaction mobility M$\sb{\rm I}$. This latter tensor is related to the velocity of a force free tracer particle in a suspension of identical particle subjected to a unit force. Numerical values for M$\sb{\rm o}$ and M$\sb{\rm I}$ are calculated for a range of volume fractions from $\phi$ = 0.025 to 0.55. All results show excellent agreement with the dilute theory of Batchelor (1982). Simple algebraic expressions are given which well correlate the numerical results.
"To study the streaming phenomenon that may occur in suspensions of two types of particles we employed average mass and momentum equations which describe the fluid and particle motion as though they were interpenetrating media. Solution of these equations allows investigation of the evolution of convective streams or blobs of particles from a bidisperse suspension subject to an initial random disturbance. Here we follow the evolution of the initial disturbance through the exponential growth period. At relatively short times, t $\ll$ 1, locally periodic concentration patterns developed which resulted in a flow field characterized by centers of circulation. Following this exponential growth period, the resulting bulk flow became strong relative to the particle velocities, ""freezing"" any structure present in the suspension. These structures were then convected throughout the cell for the remainder of the simulation. The results indicate that the bulk flow field is defined by the largest length scale given by the size of the cell, while the concentration field chose the smallest length scale determined by the number of Fourier modes. This combination did not allow for complete lateral segregation of the individual particle species or the formation of convective vertical streams that have been observed experimentally."
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