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Inertial Effects in Suspension Dynamics


Subramanian, Ganesh (2002) Inertial Effects in Suspension Dynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DSMP-HV88.


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 quasi-steady Stokes equations. The statistics of the particles is governed by a Fokker-Planck equation in position and velocity space. For small St, a multiple scales formalism is developed to solve for the phase-space 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 Chapman-Enskog-like formulation provides a valid multi-scale 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 short-time momentum relaxations and long-time deviations from the Maxwellian. The inertially corrected Smoluchowski equation includes a non-Fickian term at O(St).

The pair problem is solved to O(St) for non-Brownian spherical particles in simple shear flow. In contrast to the zero inertia case, the relative trajectories of two particles are asymmetric. Open trajectories in 'repels' nearby trajectories that spiral out onto a new stable limit cycle in the shearing plane. This limit cycle acts as a local attractor; in-plane trajectories from an initial offset of O(St¹/²) or less approach the limit cycle. The topology of the off-plane trajectories is more complicated because the gradient displacement changes sign away from the plane of shear. The 'neutral' off-plane 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 non-Newtonian rheology and self-diffusivities in the gradient and voriticity directions that scale as St² ln St and St2, respectively.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:hydrodynamic interactions; inertial diffusion; shear-induced diffusion; trajectory analysis
Degree Grantor:California Institute of Technology
Division:Chemistry and Chemical Engineering
Major Option:Chemical Engineering
Minor Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Brady, John F.
Thesis Committee:
  • Brady, John F. (chair)
  • Campbell, Charles Soutter
  • Hunt, Melany L.
  • Corngold, Noel Robert
  • Wang, Zhen-Gang
Defense Date:15 April 2002
Record Number:CaltechETD:etd-07042002-114141
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2808
Deposited By: Imported from ETD-db
Deposited On:05 Jul 2002
Last Modified:14 Jan 2022 01:04

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