Instability of ultrathin viscoelastic freestanding films

The linear stability of freestanding thin films under the influence of attractive van der Waals forces is investigated for three rheological models, viz., Newtonian viscous films, viscoelastic solid films, and Jeffreys viscoelastic liquid films, with the aim of studying the role of rheology on the instability. Thin freestanding viscous films are unconditionally unstable, whereas the shear modulus in thin freestanding solid viscoelastic films governs the onset of instability. Interestingly, elasticity plays a dual role with regard to the stability of freestanding solid and liquid films: while it has a stabilizing influence on the former, it is destabilizing in the latter. Linear stability results of Jeffreys viscoelastic freestanding films are compared with those from supported films in the inertialess limit. The instability of Jeffreys viscoelastic freestanding film is unaffected by the relaxation time, but is enhanced with decrease in the viscosity ratio (μr, the ratio of solvent viscosity to total viscosity). The dominant length scale of instability in Jeffreys viscoelastic freestanding film shifts toward shorter wavelengths with decrease in μr. For μ r → 0, the maximum growth rate remains bounded in a freestanding viscoelastic film in the presence of inertia, but diverges in its absence, similar to supported viscoelastic films. In general, our results show that freestanding thin films exhibit faster dynamics than supported thin films. The mode of deformation of the freestanding film (viz., bending or squeezing) is not imposed a priori in our analysis and is found to be a squeezing (symmetric) mode with equal amplitudes at the interfaces.