Travelling waves are hydrodynamically optimal for long-wavelength flagella
Fluid Dynamics
2020-11-18 v1 Soft Condensed Matter
Biological Physics
Abstract
Swimming eukaryotic microorganisms such as spermatozoa, algae and ciliates self-propel in viscous fluids using travelling wave-like deformations of slender appendages called flagella. Waves are predominant because Purcell's scallop theorem precludes time-reversible kinematics for locomotion. Using the calculus of variations on a periodic long-wavelength model of flagellar swimming, we show that the planar flagellar kinematics maximising the time-averaged propulsive force for a fixed amount of energy dissipated in the surrounding fluid correspond for all times to waves travelling with constant speed, potentially on a curved centreline, with propulsion always in the direction opposite to the wave.
Cite
@article{arxiv.2011.08778,
title = {Travelling waves are hydrodynamically optimal for long-wavelength flagella},
author = {Eric Lauga},
journal= {arXiv preprint arXiv:2011.08778},
year = {2020}
}