title: Microscale flow dynamics of ribbons and sheets.
abstract: Numerical study of the hydrodynamics of thin sheets and ribbons presents difficulties associated with resolving multiple length scales. To circumvent these difficulties, asymptotic methods have been developed to describe the dynamics of slender fibres and ribbons. However, such theories entail restrictions on the shapes that can be studied, and often break down in regions where standard boundary element methods are still impractical. In this paper we develop a regularised stokeslet method for ribbons and sheets in order to bridge the gap between asymptotic and boundary element methods. The method is validated against the analytical solution for plate ellipsoids, as well as the dynamics of ribbon helices and an experimental microswimmer. We then demonstrate the versatility of this method by calculating the flow around a double helix, and the swimming dynamics of a microscale "magic carpet".
authors.affiliation: School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. t.d.johnson@bham.ac.uk and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Rd, Cambridge CB3 0WA, UK.
authors.forename: Thomas D
authors.identifier: http://orcid.org/0000-0002-9370-7720
authors.initials: TD
authors.lastname: Montenegro-Johnson
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Rd, Cambridge CB3 0WA, UK.
authors.forename: Lyndon
authors.initials: L
authors.lastname: Koens
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Rd, Cambridge CB3 0WA, UK.
authors.forename: Eric
authors.initials: E
authors.lastname: Lauga