Influence of a longitudinal and tilted vibration on stability and dewetting of a liquid film

Abstract

We consider the dynamics of a thin liquid film in the attractive substrate potential and under the action of a longitudinal or a tilted vibration. Using a multiscale technique we split the film motion into the oscillatory and the averaged parts. The frequency of the vibration is assumed high enough for the inertial effects to become essential for the oscillatory motion. Applying the lubrication approximation for the averaged motion we obtain the amplitude equation, which includes contributions from gravity, van der Waals attraction, surface tension, and the vibration. We show that the longitudinal vibration leads to destabilization of the initially planar film. Stable solutions corresponding to the deflected free surface are possible in this case. Linear analysis in the case of tilted vibration shows that either stabilization or destabilization is possible. Stabilization of the dewetting film by mechanical action (i.e., the vibration) was first reported by us [Phys. Rev. E 77, 036320 (2008)]. This effect may be important for applications. Also, it is shown that the tilted vibration causes the averaged longitudinal fluid flow, which can be used to transport microparticles.

Shallow-water models for a vibrating fluid

“…Similar, but more general, equations without long wave approximation had been derived earlier by Lyubimov et al (2003) and by Yudovich (2003). Somewhat similar averaged equations had also been obtained for more complicated systems, which involve not only a free surface, but also some additional physical effects, such as Marangoni effect (see Zen'kovskaya et al , 2007, and references therein) or van der Waals forces between a rigid substrate and a liquid film (Shklyaev et al , 2008(Shklyaev et al , , 2009). Here we focus on the pure effect of the vibration on free-surface flows.…”

Stability of a liquid bridge under vibration

“…[29], and several asymptotic models for liquid films (but not bridges) under high-frequency vibration were examined in Refs. [30][31][32][33][34][35][36][37] . Vibrating bridges, in turn, were examined in Ref.…”

Effect of high-frequency in-plane substrate vibration on a three-phase contact angle

“…[4][5][6] This phenomenon is usually observed at substrate vibration frequencies ranging from 10 to 10 4 Hz for displacing [7][8][9] and climbing 10,11 drops. MHz frequency substrate vibration further invokes thin boundary layer flows, [12][13][14] which may result in spreading of liquid films when substrate vibration takes the form of a propagating Rayleigh wave.…”