Capillary buckling of a thin film adhering to a sphere

TL;DR

This study combines theory and experiments to analyze how capillary forces induce buckling and wrinkling in a thin film wrapped around a sphere, revealing the critical conditions and modes of instability.

Contribution

It introduces a novel combined theoretical and experimental framework to understand capillary-induced buckling in thin films on spherical substrates, including a non-linear solution and stability analysis.

Findings

Contact area destabilizes from symmetric to wrinkled as sphere radius increases.

The stability analysis accurately predicts the wrinkling threshold and wavelength.

The model captures the effect of a moving free boundary on instability.

Abstract

We present a combined theoretical and experimental study of the buckling of a thin film wrapped around a sphere under the action of capillary forces. A rigid sphere is coated with a wetting liquid, and then wrapped by a thin film into an initially cylindrical shape. The equilibrium of this cylindrical shape is governed by the antagonistic effects of elasticity and capillarity: elasticity tends to keep the film developable while capillarity tends to curve it in both directions so as to maximize the area of contact with the sphere. In the experiments, the contact area between the film and the sphere has cylindrical symmetry when the sphere radius is small, but destabilises to a non-symmetric, wrinkled configuration when the radius is larger than a critical value. We combine the Donnell equations for near-cylindrical shells to include a unilateral constraint with the impenetrable sphere, and the capillary forces acting along a moving edge. A non-linear solution describing the axisymmetric configuration of the film is derived. A linear stability analysis is then presented, which successfully captures the wrinkling instability, the symmetry of the unstable mode, the instability threshold and the critical wavelength. The motion of the free boundary at the edge of the region of contact, which has an effect on the instability, is treated without any approximation.