Citation
Subramanian, Ganesh (2002) Inertial effects in suspension dynamics. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd07042002114141
Abstract
This work analyses the role of small but finite particle inertia on the microstructure of suspensions of heavy particles subjected to an external flow. The magnitude of particle inertia is characterized by the Stokes number, St, defined as the ratio of the inertial relaxation time of a particle to the flow time scale. Fluid inertia is neglected so that the fluid motion satisfies the quasisteady Stokes equations. The statistics of the particles is governed by a FokkerPlanck equation in position and velocity space. For small St, a multiple scales formalism is developed to solve for the phasespace probability density of a single spherical Brownian particle in a linear flow. Though valid for an arbitrary flow field, the method fails for a spatially varying mass and drag coefficient. In all cases, however, a ChapmanEnskoglike formulation provides a valid multiscale description of the dynamics both for a single Brownian particle and a suspension of interacting particles. For long times, the leading order solution simplifies to the product of a local Maxwellian in velocity space and a spatial density satisfying the Smoluchowski equation. The higher order corrections capture both shorttime momentum relaxations and longtime deviations from the Maxwellian. The inertially corrected Smoluchowski equation includes a nonFickian term at O(St). The pair problem is solved to O(St) for nonBrownian spherical particles in simple shear flow. In contrast to the zero inertia case, the relative trajectories of two particles are asymmetric. Open trajectories in the plane of shear suffer a downward displacement in the velocity gradient direction. The surface of the reference sphere `repels' nearby trajectories that spiral out onto a new stable limit cycle in the shearing plane. This limit cycle acts as a local attractor; inplane trajectories from an initial offset of [...] or less approach the limit cycle. The topology of the offplane trajectories is more complicated because the gradient displacement changes sign away from the plane of shear. The 'neutral' offplane trajectory with zero net gradient displacement acts to separate trajectories spiralling onto contact from those that go off to infinity. The aforementioned asymmetry leads to a nonNewtonian rheology and selfdiffusivities in the gradient and voriticity directions that scale as [...], respectively.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  hydrodynamic interactions; inertial diffusion; shearinduced diffusion; trajectory analysis 
Degree Grantor:  California Institute of Technology 
Division:  Chemistry and Chemical Engineering 
Major Option:  Chemical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  15 April 2002 
NonCaltech Author Email:  ganesh (AT) caltech.edu 
Record Number:  CaltechETD:etd07042002114141 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd07042002114141 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2808 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  05 Jul 2002 
Last Modified:  12 Dec 2014 18:10 
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