The purpose of this thesis is to study the problem of a low Reynolds number
swimmer that is in very close proximity to a wall or solid boundary in a non-
Newtonian fluid. We assume that it moves by propagating waves down its length
in one direction, creating a thrust and therefore propelling it in the opposite
direction. We model the swimmer as an infinite, inextensible waving sheet.
We consider two main cases of this swimming sheet problem. In the first
case, the type of wave being propagated down the length of the swimmer is
specified. We compare the swimming speeds of viscoelastic shear thinning,
shear thickening and Newtonian fluids for a fixed propagating wave speed. We
then compare the swimming speeds of these same fluids for a fixed rate of work
per wavelength. In the latter situation, we find that a shear thinning fluid
always yields the fastest swimming speed regardless of the amplitude of the
propagating waves. We conclude that a shear thinning fluid is optimal for the
swimmer. Analytical results are obtained for various limiting cases. Next, we
consider the problem with a Bingham fluid. Yield surfaces and flow profiles are
obtained.
In the second case, the forcing along the length of the swimmer is specified,
but the shape of the swimmer is unknown. First, we solve this problem for a
Newtonian fluid. Large amplitude forcing yields a swimmer shape that has a
plateau region following by a large spike region. It is found that there exists
an optimal forcing that will yield a maximum swimming speed. Next, we solve
the problem for moderate forcing amplitudes for viscoelastic shear thickening
and shear thinning fluids. For a given forcing, it is found that a shear thinning
fluid yields the fastest swimming speed when compared to a shear thickening
fluid and a Newtonian fluid. The difference in swimming speeds decreases as
the bending stiffness of the swimmer increases. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/1503 |
| Date | 11 1900 |
| Creators | Pachmann, Sydney |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Format | 815483 bytes, application/pdf |
| Rights | Attribution-NonCommercial-NoDerivatives 4.0 International, http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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