Pattern instability of a soft elastic thin film under van der Waals forces

The surface stability and morphology evolution of a soft elastic film subjected to surface interactions such as van der Waals forces are investigated in the present paper. The three-dimensional analytical solution is obtained for the critical van der Waals force of bifurcation in terms of the surface energy, film thickness and elastic constants. The conditions of formation of different bifurcation modes (e.g., the two-dimensional periodic pattern and the three-dimensional doubly-periodic pattern) of films can be given from this solution by specifying the ratio of the wavenumbers in two directions. It is found that the wave length is proportional to the film thickness in both the two- and three-dimensional bifurcation modes when the surface energy is ignored, and that the surface energy of the film has a tendency to oppose the occurrence of inhomogeneous deformation. The three-dimensional, doubly-periodic morphology is more feasible energetically than the two-dimensional one. The obtained three-dimensional solution shows a good agreement with experimental results. In addition, we put forward both two- and three-dimensional finite element simulations of this instability problem. The numerical results are also in excellent consistency with our analytical results.