Instability and rupture of ultrathin freestanding viscoelastic solid films

We analyze the instability of viscoelastic solid freestanding thin films under the influence of van der Waals forces using linear stability analysis and nonlinear simulations. Linear stability analysis shows that the zero-frequency elastic modulus governs the onset of instability and stabilizes the film beyond a critical value analogous to thin supported viscoelastic solid films. However, for freestanding solid films, the critical shear modulus is found to be independent of surface tension, unlike that of thin supported viscoelastic solid films. It is further shown that freestanding viscoelastic solid films with higher moduli can be destabilized for a given film thickness and Hamaker constant compared to supported solid films. In contrast to thin viscoelastic liquid films where the growth rate is enhanced due to elastic effects but length scale is unaltered, freestanding films with solidlike viscoelasticity show a retarded growth rate and enhanced length scale. The presence of solidlike viscoelasticity has a stabilizing effect and affects all the key aspects of instability such as critical wave number, dominant wave number, and maximum growth rate. We numerically solve the set of coupled nonlinear evolution equations for film thickness and tangential displacement in order to elucidate the dynamics of film rupture. Our simulations show that, consistent with the linear stability predictions, an increase in the elastic modulus delays film rupture. The dynamics exhibits self-similarity in the vicinity of film rupture and the film thins as (tr - t)3/4, where tr is the rupture time and tr - t is the time remaining until film rupture. The scaling exponent 3/4 obtained for a thin freestanding viscoelastic solid film is significantly greater than the scaling exponent (1/3) for a thin freestanding viscous film.

Automated summary

In this study, the instability of viscoelastic solid freestanding thin films under the influence of van der Waals forces was analyzed using linear stability analysis and nonlinear simulations. The results showed that the zero-frequency elastic modulus played a crucial role in determining the onset of instability and stabilizing the film, similar to thin supported viscoelastic solid films. However, the critical shear modulus of freestanding solid films was found to be independent of surface tension, unlike thin supported viscoelastic solid films. Furthermore, it was demonstrated that freestanding viscoelastic solid films with higher moduli could be destabilized compared to supported solid films for a given film thickness and Hamaker constant.