Alternative pathways of dewetting for a thin liquid two-layer film

Abstract

We consider two stacked ultrathin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Depending on the long-range van der Waals forces and the ratio of the layer thicknesses, the system follows different pathways of dewetting. The instability may be driven by varicose or zigzag modes and leads to film rupture either at the liquid-gas interface or at the substrate. We predict that the faster layer drives the evolution and may accelerate the rupture of the slower layer by orders of magnitude, thereby promoting the rupture of rather thick films.

Stability of a bi-layer free film: simultaneous or individual rupture events?

“…In addition, the uniform state admits both sinuous (zigzag) and varicose perturbation modes, where the perturbed interfaces are in phase or in antiphase respectively. Fully nonlinear simulations elucidated that the film ruptured distinctly in either the upper layer or the lower layer (Pototsky et al 2004) but also demonstrated the existence of periodic (non-uniform) solutions that coarsen in time (Pototsky et al 2005(Pototsky et al , 2006. Further analysis of this system also uncovered oscillatorydewetting behaviour in the presence of surfactants (Fisher & Golovin 2007), while a classification of the distinct rupture modes was made by Ward (2011).…”

“…4.6d ) and so there are two temporal branches for the growth rate, one or both of which can become unstable across the parameter space (similar to Pototsky et al 2004). We note that the discriminant of (4.6a) can be shown to be strictly non-negative and thus the growth rate is always real, precluding the existence of travelling wave solutions.…”

“…Thus, in contrast to the surfactant-free case, perturbations to the system can now be either varicose (h ′ 2 > 0) or sinuous (h ′ 2 < 0) (analogous to the varicose and zigzag modes reported by Pototsky et al 2004).…”

“…The stability of a bi-layer liquid film on a solid substrate (with two fluid-fluid interfaces) bears many similarities to the experimental system outlined above, where the layers can exhibit dewetting and rupture, with application to the flow of mucus on the lining of the airways (Craster & Matar 2000;Matar et al 2002), the tear film (Zhang et al 2003) or to industrial coating processes (Pototsky et al 2004(Pototsky et al , 2005Fisher & Golovin 2005). The stability of this bi-layer system to van der Waals attractions has been widely studied, where the system exhibits two temporal branches, one or both of which can be unstable (Pototsky et al 2004;Fisher & Golovin 2005).…”

“…The stability of this bi-layer system to van der Waals attractions has been widely studied, where the system exhibits two temporal branches, one or both of which can be unstable (Pototsky et al 2004;Fisher & Golovin 2005). In addition, the uniform state admits both sinuous (zigzag) and varicose perturbation modes, where the perturbed interfaces are in phase or in antiphase respectively.…”