HomePublications

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

Research output: Contribution to journalArticle

Open Access permissions

Open

Documents

DOI

Authors

Organisational units

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.

Details

Original languageEnglish
Pages (from-to)665-684
Number of pages20
JournalIMA Journal of Applied Mathematics
Volume78
Issue number4
DOIs
Publication statusPublished - 1 Aug 2013
Peer-reviewedYes

Keywords

    Research areas

  • inviscid flow, fluid-structure interaction, elastic cell

Bibliographic note

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

View graph of relations

ID: 8638836

Related by author
  1. The deformation and stability of an elastic cell in a uniform flow

    Research output: Contribution to journalArticle

  2. The non-local AFM water-wave method for cylindrical geometry

    Research output: Contribution to journalArticle

  3. The stability of capillary waves on fluid sheets

    Research output: Contribution to journalArticle

  4. Solitary waves on a ferrofluid jet

    Research output: Contribution to journalArticle

  5. Hydroelastic waves on fluid sheets

    Research output: Contribution to journalArticle

Related by journal
  1. Stability of a Twisted Plateau Border with Line Tension and Bending Stiffness

    Research output: Contribution to journalArticle

  2. The trajectory of slender curved liquid jets for small Rossby number

    Research output: Contribution to journalArticle

  3. On the complex singularities of the inverse Langevin function

    Research output: Contribution to journalArticle