Two-dimensional Stokes flow driven by elliptical paddles

Cox, Stephen M.; Finn, Matthew D.

Abstract

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.

Citation

Cox, S. M., & Finn, M. D. (2007). Two-dimensional Stokes flow driven by elliptical paddles. Physics of Fluids, 19(11), https://doi.org/10.1063/1.2789970

• Journal Article Type: Article
• Publication Date: Jan 1, 2007
• Deposit Date: Mar 26, 2010
• Publicly Available Date: Mar 26, 2010
• Journal: Physics of Fluids
• Print ISSN: 1070-6631
• Electronic ISSN: 1089-7666
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 19
• Issue: 11
• DOI: https://doi.org/10.1063/1.2789970
• Public URL: https://nottingham-repository.worktribe.com/output/1017294
• Publisher URL: http://pof.aip.org/phfle6/v19/i11/p113102_s1