Viscous adhesion in vibrating sheets: elastohydrodynamics with inertia and compressibility effects

Inspired by recent experiments demonstrating that vibrating elastic sheets can function as seemingly contactless suction cups, we investigate the elastohydrodynamic hovering of a thin elastic sheet vibrating near a wall. Previous theoretical work suggests that the hovering height results from a balance between the active forcing that triggers the vibrations, the bending stresses associated with the sheet’s deformation, the viscous lubrication flow between the sheet and the wall, and the sheet’s weight. Here, we extend this analysis beyond the asymptotic regime of weak forcing and explore the regime of strong forcing through numerical simulations. We identify the scalings for the equilibrium hovering height and the maximum load that can be supported. We further quantify the influence of fluid inertia and compressibility: both effects are found to introduce repulsive contributions to the net force on the sheet, which can significantly reduce its adhesive strength. Beyond providing insights into soft contactless grippers and swimming near surfaces, our analysis is relevant to the elastohydrodynamics of squeeze films and near-field acoustic levitation.