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dc.contributor.authorWalker, B. J.
dc.contributor.authorCurtis, M. P.
dc.contributor.authorIshimoto, K.
dc.contributor.authorGaffney, E. A.
dc.date.accessioned2022-06-06T11:42:13Z
dc.date.available2022-06-06T11:42:13Z
dc.date.issued2020-07-14
dc.identifier.citationWalker, B. J., Curtis, M. P., Ishimoto, K., & Gaffney, E. A. (2020). A regularised slender-body theory of non-uniform filaments. Journal of Fluid Mechanics, 899. doi:10.1017/jfm.2020.434
dc.identifier.issn1469-7645
dc.identifier.issn0022-1120
dc.identifier.doi10.1017/jfm.2020.434
dc.identifier.urihttp://hdl.handle.net/10754/678694
dc.description.abstractResolving 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.
dc.description.sponsorshipB.J.W. is supported by the UK Engineering and Physical Sciences Research Council (EPSRC), grant EP/N509711/1. K.I. is supported by JSPS-KAKENHI for Young Researchers (18K13456) and JST, PRESTO grant number JPMJPR1921. This publication is based, in part, on work supported by award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
dc.publisherCAMBRIDGE UNIV PRESS
dc.relation.urlhttps://www.cambridge.org/core/product/identifier/S0022112020004346/type/journal_article
dc.subjectslender-body theory
dc.titleA regularised slender-body theory of non-uniform filaments
dc.typeArticle
dc.identifier.journalJOURNAL OF FLUID MECHANICS
dc.identifier.wosutWOS:000548433900001
dc.contributor.institutionUniv Oxford, Wolfson Ctr Math Biol, Math Inst, Oxford, England
dc.contributor.institutionHampton Sch, Hanworth Rd, Hampton TW12 3HD, Middx, England
dc.contributor.institutionKyoto Univ, Res Inst Math Sci, Kyoto 6068502, Japan
dc.identifier.volume899
kaust.grant.numberKUK-C1-013-04
dc.identifier.eid2-s2.0-85088381948


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