Dissertation
A 3D bacterial swimming model coupled with external fluid mechanics using the immersed boundary method
Washington State University
Doctor of Philosophy (PhD), Washington State University
08/2007
DOI:
https://doi.org/10.7273/000005696
Abstract
We introduce a 3D motile rod-shaped bacterial model with a single polar °ag-
ellum which is based on the con¯guration of a monotrichous type of bacteria such
as Pseudomonas aeruginosa. The structure of the model bacterial cell consists of a
cylindrical body together with the °agellar forces produced by the rotation of a helical
°agellum. The bacterial cell body is constructed from a set of immersed boundary
points and elastic links. The helical °agellum is assumed to be rigid and modeled
as a set of discrete points along the helical °agellum and °agellar hook. A set of
°agellar forces are applied along this rotating helical curve as the °agellum rotates.
An additional set of torque balance forces are applied tangentially on the cell body
to drive the counter-revolution of the body and provide torque balance.
The °uid °ow that drives the model bacterial cell is governed by the incompress-
ible Navier-Stokes equations with a force density contributed from the elasticity of
the cell body, the rotation of the °agellum, and the torque balance forces. The model
is based on the immersed boundary method introduced by Peskin to model the °uid
°ow of the heart. We solve the Navier-Stokes equations numerically for the °uid ve-
locity at each time step by Fast Fourier Transform methods and advect the bacterial
cell at the local °uid velocity.
This fully 3D model is loosely based on an earlier 2D model for bacterial swimming
introduced by Dillon, Fauci and Gaver in 1995. Numerical simulations of the bacterial
swimming model are presented. We show simulations that demonstrate ¯rst order
convergence as the numerical mesh is re¯ned. We also show simulations of the model
helical centroid trajectory, the model behavior in forward and backward swimming
and the hydrodynamic interaction of two or more motile cells from various initial
con¯gurations as well as the hydrodynamic in°uence of walls and tubes on the model
swimming.
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Details
- Title
- A 3D bacterial swimming model coupled with external fluid mechanics using the immersed boundary method
- Creators
- Chia-Yu Hsu
- Contributors
- Robert Dillon (Chair) - Washington State University, Department of Mathematics and Statistics
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 166
- Identifiers
- 99901054763501842
- Language
- English
- Resource Type
- Dissertation