Effect of external tension on the wetting of an elastic sheet

Abstract

Recent studies of elasto-capillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupré (YLD) problem: The capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness. Here, we consider a two-dimensional model where the sheet is subjected to an external tensile load and the drop is characterized by a well-defined Young's contact angle ${\theta }_Y$. Using a combination of numerical, variational, and asymptotic techniques, we discuss wetting as a function of the applied tension. We find that, for wettable surfaces with $0<{\theta }_Y<\pi /2$, complete wetting is possible below a critical applied tension thanks to the deformation of the sheet in contrast with rigid substrates requiring ${\theta }_Y=0$. Conversely, for very large applied tensions, the sheet becomes flat and the classical YLD situation of partial wetting is recovered. At intermediate tensions, a vesicle forms in the sheet, which encloses most of the fluid and we provide an accurate asymptotic description of this wetting state in the limit of small bending stiffness. We show that bending stiffness, however small, affects the entire shape of the vesicle. Rich bifurcation diagrams involving partial wetting and ``vesicle'' solution are found. For moderately small bending stiffnesses, partial wetting can coexist both with the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendo-capillary length, ${\lambda }_{\text{BC}}$, and find that the shape of the drop is determined by the ratio $A/{\lambda }_{\text{BC}}^2$, where $A$ is the area of the drop.

arXiv comment19 pages, 11 figures

References in corpus (15)

• Capillary origami: spontaneous wrapping of a droplet with an elastic sheet
• Elastocapillarity: Surface Tension and the Mechanics of Soft Solids
• Universal deformation of soft substrates near a contact line and the direct measurement of solid surface stresses
• The Deformation of an Elastic Substrate by a Three-Phase Contact Line
• Static wetting on deformable substrates, from liquids to soft solids
• Contact angles on a soft solid: from Young's law to Neumann's law
• Drops on soft solids: Free energy and double transition of contact angles
• Soft wetting and the Shuttleworth effect, at the crossroads between thermodynamics and mechanics
• Droplet-Induced Budding Transitions of Membranes
• The bending of an elastic beam by a liquid drop: A variational approach
• Partial wetting of thin solid sheets under tension
• Liquid droplets act as "compass needles" for the stresses in a deformable membrane
• Measuring surface tensions of soft solids with huge contact-angle hysteresis
• On the singular nature of the elastocapillary ridge
• Wetting and wrapping of a floating droplet by a thin elastic filament