Elastohydrodynamics of a pre-stretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators

摘要

The interaction of an elastic sheet with a thin viscous film appears in awide range of natural phenomena and can be utilized as an actuation mechanismfor surface deformations, applicable to microfluidics, optics, and softrobotics. Implementation of such configurations inherently takes place overfinite domains and often requires pre-stretching of the sheet. Under theassumptions of strong pre-stretching and small deformations of the lubricatedelastic sheet, we derive Green's functions describing the deformation in afinite domain due to external forces acting either directly on the sheet orthrough the fluid, accounting for both bending and stretching effects. Usingthese Green's functions we provide a closed-form solution for the case of asquare-shaped actuation and present the effect of pre-stretching on thedynamics of the deformation. We further study the dependence of the deformationmagnitude on the spatial wavenumber, revealing its effect on the transitionbetween stretching and bending dominant regimes. Finally, we present the effectof spatial discretization of the forcing (representing practical actuation) onthe achievable resolution.