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dc.contributor.authorKoens, Lyndon Mathijsen
dc.contributor.authorLauga, Eric Laugaen
dc.identifier.citationKoens & Langa. Physics of Fluids (2016) Vol. 28, 013101. doi: 10.1063/1.4938566en
dc.description.abstractRibbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. For example, when a ribbon has half a twist and is bent into a circle it produces a Möbius strip. Significant effort has gone into determining the structural shapes of ribbons but less is know about their behavior in viscous fluids. In this paper, we determine, asymptotically, the leading-order hydrodynamic behavior of a slender ribbon in Stokes flows. The derivation, reminiscent of slender-body theory for filaments, assumes that the length of the ribbon is much larger than its width, which itself is much larger than its thickness. The final result is an integral equation for the force density on a mathematical ruled surface, termed as the ribbon plane, located inside the ribbon. A numerical implementation of our derivation shows good agreement with the known hydrodynamics of long flat ellipsoids and successfully captures the swimming behavior of artificial microscopic swimmers recently explored experimentally. We also study the asymptotic behavior of a ribbon bent into a helix, that of a twisted ellipsoid, and we investigate how accurately the hydrodynamics of a ribbon can be effectively captured by that of a slender filament. Our asymptotic results provide the fundamental framework necessary to predict the behavior of slender ribbons at low Reynolds numbers in a variety of biological and engineering problems.
dc.description.sponsorshipThis research was funded in part by the European Union through a Marie Curie CIG Grant and the Cambridge Trusts.
dc.publisherAmerican Institute of Physics
dc.rightsAttribution-NonCommercial 2.0 UK: England & Wales*
dc.titleSlender-ribbon theoryen
dc.description.versionThis is the author accepted manuscript. The final version is available from American Institute of Physics via
prism.publicationNamePhysics of Fluidsen
dc.contributor.orcidKoens, Lyndon Mathijs [0000-0003-2059-8268]
dc.contributor.orcidLauga, Eric Lauga [0000-0002-8916-2545]
rioxxterms.typeJournal Article/Reviewen

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Attribution-NonCommercial 2.0 UK: England & Wales
Except where otherwise noted, this item's licence is described as Attribution-NonCommercial 2.0 UK: England & Wales