Effect of external tension on the wetting of an elastic sheet

Recent studies of elastocapillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupre (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 due 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 with both the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendocapillary length, lambda BC, and find that the shape of the drop is determined by the ratio A/lambda 2BC, where A is the area of the drop.

Automated summary

Recent studies have focused on the capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness. Wetting behavior is discussed as a function of applied tension using numerical, variational, and asymptotic techniques. Complete wetting is possible for wettable surfaces with a defined Young's contact angle below a critical applied tension. A vesicle forms in the sheet at intermediate tensions, enclosing most of the fluid, and the shape of the drop is determined by the ratio of area to a tension-dependent bendocapillary length.