Optimal frequency for undulatory motion in granular media

TL;DR

This paper investigates the optimal undulatory frequency for swimming in granular media like sand, revealing that the best performance aligns with the second vibrational mode and is influenced by the rheology of the medium.

Contribution

It introduces a quasi-2D granular model that links swimming efficiency to vibrational modes and medium rheology, advancing understanding of sand swimming mechanics.

Findings

Optimal frequency matches the second vibrational mode.

Swimming speed depends non-monotonically on frequency and bed height.

Rheology characterization explains the underlying mechanism.

Abstract

Sand is a highly dissipative system, where the local spatial arrangements and densities depend strongly on the applied forces, resulting in fluid-like or solid-like behaviour. This makes sand swimming challenging and intriguing, raising questions about the nature of the motion and how to optimize the design of artificial swimmers able to swim in sand. Recent experiments suggest that lateral undulatory motion enables efficient locomotion, with a non-monotonic dependence of the swimming speed on the undulatory frequency and the height of the sediment bed. Here, we propose a quasi-2D granular model, where the effect of the bed height is modeled by a coarse-grained frictional force with the substrate. We show that the optimal frequency coincides with the second vibrational mode of the swimmer and explain the underlying mechanism through a characterization of the rheology of the medium. Potential implications in the design of artificial swimmers are discussed.