Morris, Jeffrey Franklin (1994) Suspensions: microstructure, diffusion, and inhomogeneous flow. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd01102008085702
Abstract
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A theory of selfdiffusivity in sheared suspensions valid for any particle volume fraction [phi], Peclet number Pe, and lengthscale of disturbance in [phi] is developed. The theory is applied to the determination of the full tensor selfdiffusivity in a weakly sheared (Pe << 1) suspension of hydrodynamicallyinteracting hard spheres and a stronglysheared (Pe >> 1) suspension of hard spheres without hydrodynamic interactions, both at [phi] << 1.
The influence of weak Brownian motion alone and in conjunction with a repulsive interparticle force of hardsphere type upon the pairdistribution function, g(r) where r is the separation vector of a pair of particles, is analyzed for a suspension of spheres at Pe >> 1 and [phi] << 1. At large Pe, the radial fluxes of pair probability due to advection and Brownian diffusion balance in a thin [...] boundary layer at contact, with a the sphere radius. The boundarylayer analyses demonstrate that Brownian diffusion renders g finite at contact in the absence of interparticle forces, and that within the boundary layer there is generally a large excess of pair probability along the compressional axes. By calculation of the bulk normal stress differences in the case with repulsive forces, it is shown how this asymmetry of the microstructure yields nonNewtonian constitutive behavior in the limit Pe[superscript 1] = 0.
Hydrodynamic resistance functions relating the particle and bulk motions to the bulk isotropic stress are developed. Application of these functions is demonstrated by calculations of the shearinduced correction to the osmotic pressure and the particle contribution to the pressure in a sheared lattice.
Pressuredriven flow in a channel at vanishing Reynolds number of a suspension of particles denser than the suspending fluid has been dynamically simulated by Stokesian Dynamics over ranges of the particle fraction, channel width, and a buoyancy parameter characterizing the relative strength of the buoyancy to shearing forces. The predictions of the flow by the suspensionbalance model are in good agreement with simulation results.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Major Option:  Chemical Engineering 
Thesis Committee: 

Defense Date:  19 May 1994 
Record Number:  etd01102008085702 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd01102008085702 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  109 
Collection:  CaltechTHESES 
Deposited By:  Imported from ETDdb 
Deposited On:  24 Jan 2008 
Last Modified:  25 Dec 2012 14:57 
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