A regularised slender-body theory of non-uniform filaments
Resolving the detailed hydrodynamics of a slender body immersed in highly-viscous Newtonian fluid has been the subject of extensive research, applicable to a broad range of biological and physical scenarios. In this work, we expand upon classical theories developed over the past fifty years, derivin...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Cambridge University Press
2020
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| _version_ | 1826296885019672576 |
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| author | Walker, BJ Curtis, MP Ishimoto, K Gaffney, EA |
| author_facet | Walker, BJ Curtis, MP Ishimoto, K Gaffney, EA |
| author_sort | Walker, BJ |
| collection | OXFORD |
| description | Resolving the detailed hydrodynamics of a slender body immersed in highly-viscous
Newtonian fluid has been the subject of extensive research, applicable to a broad
range of biological and physical scenarios. In this work, we expand upon classical
theories developed over the past fifty years, deriving an algebraically-accurate slenderbody theory that may be applied to a wide variety of body shapes, ranging from
biologically-inspired tapering flagella to highly-oscillatory body geometries with only
weak constraints, most-significantly requiring that cross sections be circular. Inspired by
well-known analytic results for the flow around a prolate ellipsoid, we pose an ansatz for
the velocity field in terms of a regular integral of regularised Stokes-flow singularities with
prescribed, spatially-varying regularisation parameters. A detailed asymptotic analysis is
presented, seeking a uniformly-valid expansion of the ansatz integral, accurate at leading
algebraic order in the geometry aspect ratio, to enforce no slip boundary conditions
and thus analytically justify the slender-body theory developed in this framework. The
regularisation within the ansatz additionally affords significant computational simplicity
for the subsequent slender-body theory, with no specialised quadrature or numerical
techniques required to evaluate the regular integral. Furthermore, in the special case of
slender bodies with a straight centreline in uniform flow, we derive a slender-body theory
that is particularly straightforward via use of the analytic solution for a prolate ellipsoid.
We evidence the validity of our simple theory by explicit numerical example for a wide
variety of slender bodies, and highlight a potential robustness of our methodology beyond
its rigorously-justified scope. |
| first_indexed | 2024-03-07T04:23:13Z |
| format | Journal article |
| id | oxford-uuid:cbba9e9d-2d9b-4e3f-bfeb-bc7d5b2a2e4b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:23:13Z |
| publishDate | 2020 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:cbba9e9d-2d9b-4e3f-bfeb-bc7d5b2a2e4b2022-03-27T07:16:56ZA regularised slender-body theory of non-uniform filamentsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cbba9e9d-2d9b-4e3f-bfeb-bc7d5b2a2e4bEnglishSymplectic ElementsCambridge University Press2020Walker, BJCurtis, MPIshimoto, KGaffney, EAResolving the detailed hydrodynamics of a slender body immersed in highly-viscous Newtonian fluid has been the subject of extensive research, applicable to a broad range of biological and physical scenarios. In this work, we expand upon classical theories developed over the past fifty years, deriving an algebraically-accurate slenderbody theory that may be applied to a wide variety of body shapes, ranging from biologically-inspired tapering flagella to highly-oscillatory body geometries with only weak constraints, most-significantly requiring that cross sections be circular. Inspired by well-known analytic results for the flow around a prolate ellipsoid, we pose an ansatz for the velocity field in terms of a regular integral of regularised Stokes-flow singularities with prescribed, spatially-varying regularisation parameters. A detailed asymptotic analysis is presented, seeking a uniformly-valid expansion of the ansatz integral, accurate at leading algebraic order in the geometry aspect ratio, to enforce no slip boundary conditions and thus analytically justify the slender-body theory developed in this framework. The regularisation within the ansatz additionally affords significant computational simplicity for the subsequent slender-body theory, with no specialised quadrature or numerical techniques required to evaluate the regular integral. Furthermore, in the special case of slender bodies with a straight centreline in uniform flow, we derive a slender-body theory that is particularly straightforward via use of the analytic solution for a prolate ellipsoid. We evidence the validity of our simple theory by explicit numerical example for a wide variety of slender bodies, and highlight a potential robustness of our methodology beyond its rigorously-justified scope. |
| spellingShingle | Walker, BJ Curtis, MP Ishimoto, K Gaffney, EA A regularised slender-body theory of non-uniform filaments |
| title | A regularised slender-body theory of non-uniform filaments |
| title_full | A regularised slender-body theory of non-uniform filaments |
| title_fullStr | A regularised slender-body theory of non-uniform filaments |
| title_full_unstemmed | A regularised slender-body theory of non-uniform filaments |
| title_short | A regularised slender-body theory of non-uniform filaments |
| title_sort | regularised slender body theory of non uniform filaments |
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