Hovering of an actively driven fluid-lubricated foil

TL;DR

This paper presents a theoretical and numerical study of how an elastically deforming, fluid-lubricated foil can hover near a wall by breaking time-reversal symmetry, with implications for biology and soft robotics.

Contribution

The authors develop a new elastohydrodynamic model that explains the hovering mechanism of a soft foil near a wall, supported by scaling laws and numerical simulations.

Findings

The soft foil breaks time-reversal symmetry, enabling hovering.

A scaling law predicts equilibrium height and maximum weight.

Numerical results agree qualitatively with experiments.

Abstract

Inspired by recent experimental observations of a harmonically excited elastic foil hovering near a wall while supporting substantial weight, we develop a theoretical framework that describes the underlying physical effects. Using elastohydrodynamic lubrication theory, we quantify how the dynamic deformation of the soft foil couples to the viscous fluid flow in the intervening gap. Our analysis shows that the soft foil rectifies the reversible forcing, breaking time-reversal symmetry; the relative spatial support of the forcing determines whether the sheet is attracted to or repelled from the wall. A simple scaling law predicts the time-averaged equilibrium hovering height and the maximum weight the sheet can sustain before detaching from the surface. Numerical simulations of the governing equation corroborate our theoretical predictions, are in qualitative agreement with experiments, and might explain the behavior of organisms while providing design principles for soft robotics.