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arXiv · 1503.08422

The many-body reciprocal theorem and swimmer hydrodynamics

Dario Papavassiliou·Gareth P. Alexander
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Abstract

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.

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Dario Papavassiliou, Gareth P. Alexander. 2015-03-29. The many-body reciprocal theorem and swimmer hydrodynamics. https://doi.org/10.1209/0295-5075/110/44001

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