Walker, BJ;
Curtis, MP;
Ishimoto, K;
Gaffney, EA;
(2020)
A regularised slender-body theory of non-uniform filaments.
Journal of Fluid Mechanics
, 899
, Article A3. 10.1017/jfm.2020.434.
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Abstract
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 slender-body 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 with explicit numerical examples for a wide variety of slender bodies, and highlight a potential robustness of our methodology beyond its rigorously justified scope.
| Type: | Article |
|---|---|
| Title: | A regularised slender-body theory of non-uniform filaments |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/jfm.2020.434 |
| Publisher version: | https://doi.org/10.1017/jfm.2020.434 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Low-Reynolds-number flows: Slender-body theory |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10141573 |
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