Instabilities and pattern miniaturization in confined and free elastic-viscous bilayers

We present an analysis of the instabilities engendered by van der Waals forces in bilayer systems composed of a soft elastic film (<10 microm) and a thin (<100 nm) viscous liquid film. We consider two configurations of such systems: (a) Confined bilayers, where the bilayer is sandwiched between two rigid substrates, and (b) free bilayers, where the viscous film is sandwiched between a rigid substrate and the elastic film. Linear stability analysis shows that the time and length scales of the instabilities can be tuned over a very wide range by changing the film thickness and the material properties such as shear modulus, surface tension, and viscosity. In particular, very short wavelengths comparable to the film thickness can be obtained in bilayers, which is in contrast to the instability wavelengths in single viscous and elastic films. It is also shown that the instabilities at the interfaces of the free bilayers are initiated via an in-phase "bending" mode rather than out-of-phase "squeezing" mode. The amplitudes of deformations at both the elastic-air and elastic-viscous interfaces become more similar as the elastic film thickness decreases and its modulus increases. These findings may have potential applications in the self-organized patterning of soft materials.