Theoretical analysis of the spontaneous surface instability for thin soft elastic films

The spontaneous surface instability induced by the van der Waals force in a soft elastic thin film perfectly bonded to a rigid substrate is investigated theoretically using the bifurcation theory of elastic continua. The analytical solution of the critical condition is obtained. Detailed examinations on the effect of surface tension, thickness and elastic properties of the film show that the characteristic wavelength of the deformation bifurcation mode depends on the film thickness via an exponential relation, with the power index in the range from 0.75 to 1.0.