Generic flow profiles induced by a beating cilium

TL;DR

This paper develops a multipole expansion to describe low Reynolds number flows generated by beating cilia, analyzing different ciliary motion models and identifying flow modes based on symmetry.

Contribution

It introduces a new multipole expansion framework for cilia-induced flows, capturing key flow modes and symmetries at low Reynolds numbers.

Findings

The expansion includes 3 quadratic and 6 cubic terms.

Different ciliary motion models produce distinct flow modes.

Flow modes are characterized by symmetry properties.

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.