Linear oscillations of a compressible hemispherical bubble on a solid substrate

Abstract

The linear natural and forced oscillations of a compressible hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account by application of the Hocking condition, which eventually leads to nontrivial interaction of the shape and volume oscillations. Resonant phenomena, mostly pronounced for the bubble with the fixed contact line or with the fixed contact angle, are found out. A double resonance, where independent of the Hocking parameter an unbounded growth of the amplitude occurs, is detected. The limiting case of weakly compressible bubble is studied. The general criterion identifying whether the compressibility of a bubble can be neglected is obtained.

Bubble dynamics atop an oscillating substrate: Interplay of compressibility and contact angle hysteresis

“…Particularly, we show that such coupling results not only in a simple combination of known effects. More importantly, it can also lead to a novel generic feature, which is not possible in previous setups, 6,7 where these two factors come into play separately. The paper is outlined as follows.…”

“…For instance, a simplified model of a compressible bubble atop vibrated substrate that neglects the coupling with the substrate predicts trivial volume oscillations. As the real picture is much more intricate, 6 this rough but representative example testifies to the necessity of finer models of the contact line motion. The importance of this argument is further augmented, when quantitative agreement between the theory and experiment is required, see also Sec.…”

“…7 Apart from shape oscillations typical of any deformable object, a compressible bubble additionally possesses the breathing eigenmode corresponding to radial pulsations. For a sessile bubble, the contact line dynamics causes the interaction of this mode with the eigenmodes of shape oscillations even within the linear problem, 6 contrary to the necessarily nonlinear coupling for a spherical bubble. 19 Another prominent feature caused by compressibility is a "double resonance," which means that under certain conditions, two modes simultaneously, one of the modes of shape oscillations and the breathing mode, are resonantly amplified.…”

“…The latter issue is important for obtaining a deep insight, which is typically lost when one resorts to direct numerical simulations. This strategy has recently been applied to separately explore the impact of the compressibility of bubble 6 and the contact angle hysteresis. 7 Apart from shape oscillations typical of any deformable object, a compressible bubble additionally possesses the breathing eigenmode corresponding to radial pulsations.…”

“…[1][2][3][4][5][6][7] While the ability to predict the contact line motion and, therefore, to control the wetting processes is generally important for technological applications, 8,9 these setups can also be used to manipulate small droplets over surfaces. [10][11][12] Instead of substrate vibrations, oscillations of drops and bubbles can be induced by electrowetting, see Refs.…”