| Issue |
EPL
Volume 110, Number 4, May 2015
|
|
|---|---|---|
| Article Number | 44001 | |
| Number of page(s) | 6 | |
| Section | Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics | |
| DOI | https://doi.org/10.1209/0295-5075/110/44001 | |
| Published online | 04 June 2015 | |
The many-body reciprocal theorem and swimmer hydrodynamics
Department of Physics and Centre for Complexity Science, University of Warwick Gibbet Hill Road, Coventry, CV4 7AL, UK
Received: 26 March 2015
Accepted: 8 May 2015
We present a reinterpretation and extension of the reciprocal theorem for swimmers, extending its application from the motion of a single swimmer in an unbounded domain to the general setting, giving results for both swimmer interactions and general hydrodynamics. We illustrate the method for a squirmer near a planar surface, recovering standard literature results and extending them to a general squirming set, to motion in the presence of a ciliated surface, and expressions for the flow field throughout the domain. Finally, we present exact results for the hydrodynamics in two dimensions which shed light on the near-field behaviour.
PACS: 47.63.Gd – Swimming microorganisms / 87.10.-e – General theory and mathematical aspects / 47.15.G- – Low-Reynolds-number (creeping) flows
© EPLA, 2015
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