Comment on: arXiv:2008.08305 "Scallop Theorem and Swimming at the Mesoscale" by M. Hubert, O. Trosman, Y. Collard, A. Sukhov, J. Harting, N. Vandewalle, and A.-S. Smith, Phys. Rev. Letters \vc{126}, 224501 (2021)

TL;DR

This paper critically compares different analytical expressions for the mean swimming velocity of a two-sphere model, confirming the high accuracy of the first harmonic approximation against exact solutions.

Contribution

It provides a detailed comparison between the exact, harmonic, and previously derived expressions for the swimming velocity in the Oseen two-sphere model.

Findings

First harmonic approximation closely matches the exact solution.

The derived expression in the original letter is validated.

The approximation simplifies analysis without significant loss of accuracy.

Abstract

The expression for the mean swimming velocity of the Oseen two-sphere model derived in the Letter [arXiv:2008.08305] is compared with an exact one derived earlier, as well as one derived in first harmonic approximation. The latter is found to be a very accurate approximation to the exact result.