Efficiency of swimming of micro-organism and singularity in shape space

TL;DR

This paper investigates how the shape and size of micro-organisms affect their swimming efficiency in 2D fluids, revealing unbounded efficiency for flagellates due to a shape space singularity.

Contribution

It introduces a model linking shape space singularities to swimming efficiency, explaining the size hierarchy among micro-organisms.

Findings

Flagellates can have unbounded swimming efficiency.

Ciliates have a finite upper bound on efficiency.

Shape space singularity explains efficiency differences.

Abstract

Micro-organisms can be classified into three different types according to their size. We study the efficiency of the swimming of micro-organism in two dimensional fluid as a device for helping the explanation of this hierarchy in the size. We show that the efficiency of flagellate becomes unboundedly large, whereas that of ciliate has the upper bound. The unboundedness is related to the curious feature of the shape space, that is, a singularity at the basic shape of flagellate.