Eur. Phys. J. E (2012) 35: 72
https://doi.org/10.1140/epje/i2012-12072-3

Regular Article

Generic flow profiles induced by a beating cilium

¹ J. Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
² Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

^* e-mail: andrej.vilfan@ijs.si

Received: 18 April 2012
Revised: 29 June 2012
Accepted: 3 July 2012
Published online: 15 August 2012

Abstract

We describe a multipole expansion for the low-Reynolds-number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.