Surface instability of viscoelastic thin films

The surfaces of thin, liquid films can be unstable due to thinning van der Waals interactions, leading to the formation of holes in the initially uniform film. These instabilities can be greatly retarded in viscoelastic materials (and completely inhibited in elastic materials) even when the finite frequency shear modulus, $E$, is small compared to the infinite frequency modulus, $G$. This occurs when $E/G\gg (a/h_{0})^{5}\ll 1$ where $a$ is a molecular size and $h_{0}$ is the film thickness. We relate the growth rate of the instability to the dynamic viscosity, $\eta~(\omega)$, with examples for the cases of a polymer brush, an elastic fluid (gel), and a transient polymer network, described by reptation dynamics