Hovering of an actively driven fluid-lubricated foil

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.

revised version, V2

References in corpus (6)

• Flexive and Propulsive Dynamics of Elastica at Low Reynolds Numbers
• DuMu${}^{\text{x}}$ 3 -- an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling
• Soft lubrication
• Self-sustained lift and low friction via soft lubrication
• Regimes of Soft Lubrication
• Lift at low Reynolds number

Cited by in corpus (1)

• Theory and simulation of elastoinertial rectification of oscillatory flows in two-dimensional deformable rectangular channels