  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.
