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