  An adhesively stressed thin film of a soft hydrogel confined between two
rigid flat substrates auto-roughens with its dominant wavelength exhibiting
pronounced dependence on the film thickness (H). A linear stability analysis
confirmed that this long wavelength instability (~7H) is due to an
elasto-capillary effect, the implementation of which required direct
measurements of the surface tension and the elasticity of the gel. The surface
tension of the gel was estimated from the fundamental spherical harmonic of a
hemispherical cap of the gel that was excited by an external noise. The shear
modulus of the gel was determined from its resonant shear mode in a confined
geometry. During the course of this study, it was found that a high density
steel ball submerges itself inside the gel by balancing its excess weight with
the accumulated strain induced elastic force that allows another estimation of
its elastic modulus. The large ratio (1.8 mm) of the surface tension to its
elasticity ascertains the role of elasto-capillarity in the adhesion induced
pattern formation with such gels. Experimental results are in accord with a
linear stability analysis that predicts that the rescaled wavelength is linear
with H, which modifies the conventional stress to pull-off a rigid flat object
from a very soft film by a multiplicative factor. The analysis also suggests
some new results related to the role of the finite dilation of a material in
interfacial pattern formation that may have non-trivial consequences in the
adhesive delamination of very thin and/or soft elastic films via self-generated
cracks.
