Sierou, Asimina (2002) Accelerated Stokesian dynamnics : development and application to sheared nonBrownian suspensions. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd01202009160503
Abstract
A new implementation of the conventional Stokesian Dynamics (SD) algorithm, called Accelerated Stokesian Dynamics (ASD), is presented. The equations governing the motion of N particles suspended in a viscous fluid at low particle Reynolds number are solved accurately and efficiently, including all hydrodynamic interactions, but with a significantly lower computational cost of O(N ln N). The main differences from the conventional SD method lie in the calculation of the manybody longrange interactions, where the Ewaldsummed wavespace contribution is calculated as a Fourier Transform sum, and in the iterative inversion of the now sparse resistance matrix. The ASD method opens up an entire new class of suspension problems that can be investigated, including particles of nonspherical shape and a distribution of sizes, and can be readily extended to other lowReynoldsnumber flow problems. The new method is applied to the study of sheared nonBrownian suspensions.
The rheological behavior of a monodisperse suspension of nonBrownian particles in simple shear flow in the presence of a weak interparticle force is studied first. The availability of a faster numerical algorithm permits the investigation of larger systems (typically of N = 512 — 1000 particles), and accurate results for the suspension viscosity, first and second normal stress differences and the particle pressure are determined as a function of the volume fraction. The system microstructure, expressed through the pairdistribution function, is also studied and it is demonstrated how the resulting anisotropy in the microstructure is correlated with the suspension nonNewtonian behavior. The ratio of the normal to excess shear stress is found to be an increasing function of the volume fraction, suggesting different volume fraction scalings for different elements of the stress tensor. The relative strength and range of the interparticle force is varied and its effect on the shear and normal stresses is analyzed. Volume fractions above the equilibrium freezing volume fraction (ø ≈ 0.494) are also studied, and it is found that the system exhibits a strong tendency to order under flow for volume fractions below the hardsphere glass transition; limited results for ø = 0.60, however, show that the system is again disordered under shear.
Selfdiffusion is subsequently studied and accurate results for the complete tensor of the shearinduced selfdiffusivities are determined. The finite, and oftentimes large, autocorrelation time requires the meansquare displacement curves to be followed for longer times than was previously thought necessary. Results determined from either the meansquare displacement or the velocity autocorrelation function are in excellent agreement. The longitudinal (in the flow direction) selfdiffusion coefficient is also determined, and it is shown that the finite autocorrelation time introduces an additional coupled term to the longitudinal selfdiffusivity, a term which previous theoretical and numerical results omitted. The longitudinal selfdiffusivities for a system of nonBrownian particles are calculated for the first time as a function of the volume fraction.
Item Type:  Thesis (Dissertation (Ph.D.)) 

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

Defense Date:  27 July 2001 
Record Number:  etd01202009160503 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd01202009160503 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  257 
Collection:  CaltechTHESES 
Deposited By:  Imported from ETDdb 
Deposited On:  22 Jan 2009 
Last Modified:  25 Dec 2012 14:58 
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