Comment on "Directed motion of spheres by unbiased driving forces in viscous fluids beyond the Stokes' law regime"

TL;DR

This paper critiques a recent explanation of directed sphere motion in viscous fluids, proposing that ratchet universality and vibrational mechanics better explain the observed phenomena.

Contribution

It challenges the previous formalism and demonstrates that ratchet universality and vibrational mechanics offer a more accurate explanation.

Findings

Previous formalism is generally incorrect.

Ratchet universality explains the phenomena effectively.

Vibrational mechanics provides a satisfactory theoretical framework.

Abstract

In a recent paper by Casado-Pascual [Phys. Rev. E \textbf{97}, 032219 (2018)], directed motion of a sphere immersed in a viscous fluid and subjected to zero-average biharmonic forces is studied. The author explains the dependence on the relative amplitude of the two harmonic components of the average terminal velocity from the perspective of a general formalism. In this Comment, this explanation is shown to be in general incorrect, while the theory of ratchet universality together with the vibrational mechanics approach provide a satisfactory explanation of major aspects of the observed phenomena.