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Slender-Body Theory for Stokes Flow and Flagellar Hydrodynamics


Johnson, Robert Edward (1977) Slender-Body Theory for Stokes Flow and Flagellar Hydrodynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HYMQ-AH77.


The singularity method for Stokes flow is used to examine the flow past slender bodies possessing finite centerline curvature, in a viscous, incompressible fluid without any appreciable inertia effects. The motion of a slender toroidal ring in Stokes flow is considered first. The symmetry of the geometry and absence of ends has made an accurate analysis possible; the result of this problem elucidates the general flow characteristics present for bodies moving in an arbitrary manner with a finite centerline curvature. Using the methods developed here it is possible to calculate the force/length to higher orders in the slenderness parameter, ϵ, than has previously been possible. In particular, we find the Stokeslet strength with an error of O(ϵ²). The solution of the torus problem serves as an effective guide in extending the theory to slender bodies of circular cross section with arbitrary centerline configurations and spheroidal ends. In all the cases considered, the no-slip boundary condition is satisfied by distributing appropriate Stokeslets, doublets, rotlets, sources, stresslets, and quadrupoles on the body centerline up to an error term of O(ϵ² lnϵ), which is sufficient for practical application. From the general slender body analysis we find an integral equation which determines the Stokeslet strength up to the term of O(ϵ²). The general theory is then applied to examine the propulsion of flagellated microorganisms, including an approximate solution for the interaction between cell body and flagella. A final brief note is made on the thrust enhancing capabilities of oscillating non-spherical cell bodies.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Engineering Science
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Wu, Theodore Yao-tsu
Thesis Committee:
  • Unknown, Unknown
Defense Date:17 May 1977
Record Number:CaltechETD:etd-04212004-114339
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1435
Deposited By: Imported from ETD-db
Deposited On:22 Apr 2004
Last Modified:02 Dec 2022 23:59

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