Deformation of an elastic cell in a uniform stream and in a circulatory flow

Blyth, M. G. and Parau, E. I. (2013) Deformation of an elastic cell in a uniform stream and in a circulatory flow. IMA Journal of Applied Mathematics, 78 (4). pp. 665-684. ISSN 0272-4960

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    Abstract

    The deformation of a circular, inextensible elastic cell is examined when the cell is placed into two different background potential flows: a uniform stream and a circulatory flow induced by a point vortex located inside the cell. In a circulatory flow a cell may deform into a mode m shape with m-fold rotational symmetry. In a uniform stream, shapes with two-fold rotational symmetry tend to be selected. In a weak stream a cell deforms linearly into an ellipse with either its major or its minor axis aligned with the oncoming flow. This marks an interesting difference with a bubble with constant surface tension in a uniform stream, which can only deform into a mode 2 shape with its major axis perpendicular to the stream (Vanden-Broeck & Keller, 1980b). In general, as the strength of the uniform stream is increased from zero, solutions emerge continuously from the cell configurations in quiescent fluid found by Flaherty et al. (1972). A richly populated solution space is described with multiple solution branches which either terminate when a cell reaches a state with a point of self-contact or loop round to continuously connect cell states which exist under identical conditions in the absence of flow.

    Item Type: Article
    Additional Information: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in the IMA Journal of Applied Mathematics following peer review. The definitive publisher-authenticated version M.G. Blyth, E.I. Parau, Deformation of an elastic cell in a uniform stream and in a circulatory flow, IMA J. Applied Maths.78(2013), 665-684. DOI: 10.1093/imamat/hxt014 is available online at: http://imamat.oxfordjournals.org/content/78/4/665
    Uncontrolled Keywords: inviscid flow,fluid-structure interaction,elastic cell
    Faculty \ School: Faculty of Science > School of Mathematics
    University of East Anglia > Faculty of Science > Research Groups > Fluid and Solid Mechanics
    Depositing User: Pure Connector
    Date Deposited: 05 Nov 2013 17:00
    Last Modified: 30 Aug 2018 00:44
    URI: https://ueaeprints.uea.ac.uk/id/eprint/44243
    DOI: 10.1093/imamat/hxt014

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