Fluid Velocity Fluctuations in a Suspension of Swimming Protists

TL;DR

This study investigates fluid velocity fluctuations in suspensions of swimming protists, revealing conditions for Gaussian velocity distributions and identifying deviations caused by near-field effects through experiments and simulations.

Contribution

It demonstrates that Gaussian velocity distributions occur when the leading flow singularity is a Stokeslet, and not for higher multipoles, supported by numerical and experimental evidence.

Findings

Gaussian velocity distribution when leading singularity is a Stokeslet

Deviations from Gaussianity due to near-field effects

Experimental confirmation with Volvox carteri

Abstract

In dilute suspensions of swimming microorganisms the local fluid velocity is a random superposition of the flow fields set up by the individual organisms, which in turn have multipole contributions decaying as inverse powers of distance from the organism. Here we show that the conditions under which the central limit theorem guarantees a Gaussian probability distribution function of velocities are satisfied when the leading force singularity is a Stokeslet, but are not when it is any higher multipole. These results are confirmed by numerical studies and by experiments on suspensions of the alga Volvox carteri, which show that deviations from Gaussianity arise from near-field effects.