Two-dimensional Stokes flow driven by elliptical paddles
A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been restricted to...
| Main Authors: | , |
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| Format: | Article |
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American Institute of Physics
2007
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| Online Access: | https://eprints.nottingham.ac.uk/1261/ |
| _version_ | 1848790572213469184 |
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| author | Cox, Stephen M. Finn, Matthew D. |
| author_facet | Cox, Stephen M. Finn, Matthew D. |
| author_sort | Cox, Stephen M. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been
restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically. |
| first_indexed | 2025-11-14T18:14:45Z |
| format | Article |
| id | nottingham-1261 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:14:45Z |
| publishDate | 2007 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-12612020-05-04T20:28:43Z https://eprints.nottingham.ac.uk/1261/ Two-dimensional Stokes flow driven by elliptical paddles Cox, Stephen M. Finn, Matthew D. A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically. American Institute of Physics 2007 Article PeerReviewed Cox, Stephen M. and Finn, Matthew D. (2007) Two-dimensional Stokes flow driven by elliptical paddles. Physics of Fluids, 19 (11). pp. 113102-1. ISSN 1070-6631 http://pof.aip.org/phfle6/v19/i11/p113102_s1 doi:10.1063/1.2789970 doi:10.1063/1.2789970 |
| spellingShingle | Cox, Stephen M. Finn, Matthew D. Two-dimensional Stokes flow driven by elliptical paddles |
| title | Two-dimensional Stokes flow driven by elliptical paddles |
| title_full | Two-dimensional Stokes flow driven by elliptical paddles |
| title_fullStr | Two-dimensional Stokes flow driven by elliptical paddles |
| title_full_unstemmed | Two-dimensional Stokes flow driven by elliptical paddles |
| title_short | Two-dimensional Stokes flow driven by elliptical paddles |
| title_sort | two-dimensional stokes flow driven by elliptical paddles |
| url | https://eprints.nottingham.ac.uk/1261/ https://eprints.nottingham.ac.uk/1261/ https://eprints.nottingham.ac.uk/1261/ |