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

Abstract

In a recent paper by Casado-Pascual [Phys. Rev. E 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.

Directed ratchet transport of cold atoms and fluxons driven by biharmonic fields: A unified view

“…We expect that the theory of RU will explain other different implementations of the ratchet effect, such as gating ratchets [28], directed transport in coupled systems without external bias [29], and ratchets without any periodic substrate potential [30]. Our current work is aimed at exploring these cases [31].…”