Arbitrary extension of the antibubble lifetime

An antibubble is an uncommon fluid object with a unique structure: a liquid globule is wrapped by a thin air film, with the whole being immersed in a liquid bath. In short, the antibubble is the opposite of a soap bubble. The antibubble has been regarded as a promising candidate for various industrial applications since two components can be separated only by an air layer before mixing. However, the use of the antibubble is limited by the short lifetime $(\approx 1 \min )$ and the broad distribution of the lifetimes. We demonstrate a simple and efficient method to extend the lifetime of the antibubbles. The proposed system consists of a liquid surface covered by a layer of bubbles under which antibubbles are generated. The liquid is then vertically shaken. Above a given acceleration threshold that depends on the frequency, the lifetime of the antibubbles is significantly increased. Under vibrations, antibubbles were kept alive up to 13 h. As soon as the vibration is stopped, the antibubble collapses immediately. The antibubble popping can therefore be programmed. A model based on the dynamical air drainage in the air shell of the antibubble is proposed to account for these observations.

Figure 1

(a) Top view of the foam layer. Three neighboring bubbles form a locus and the generated antibubble is trapped in it to avoid any lateral motion. The black scale bar indicates 20 mm while the blue one indicates 2 mm. (b) Dynamics of an antibubble under vertical vibration ($f$ = 40 Hz, $A_m$ = 0.067 mm). It maintains a spherical shape during vibration. The scale bar indicates 1 mm.

Figure 2

[(a), (b)] CDF of the antibubble lifetime varying with the vibration acceleration for $f$ = 30 Hz and $f$ = 60 Hz, respectively. The solid lines are fitted with the Weibull statistical model. (c) Variation of the statistical expectation of the antibubble lifetime, $E$, with the vibration acceleration. The solid symbols in (a), (b), and (c) indicate that at least one antibubble survives 900 s; otherwise, it is a hollow symbol. (d) Variation of the threshold acceleration for the long-lived antibubbles with the vibration frequency.

Figure 3

Sketch of the vibrating antibubbles under a foam layer. The symbols $B$ and $\overline{B}$ indicate the bubble and antibubble, respectively. On the right, the mechanical model of the system is presented. The foam layer is modeled by a spring and the antibubble as a mass that is attached to the spring. The vibration of the plate ($A_m,f$) induces the vibration of the spring-mass (the bubbles) with an amplitude $A_B$, which in turn produces the motion of the antibubble with an amplitude $A_{\overline{B}}$.

Figure 4

The amplitude ratio $\lambda =A_B/A_m$ divided by $r^2$ is plotted as a function of $r$ for the three considered bubble diameters (see legend).The purple line is fitted with Eq. (6).

Figure 5

(a) The threshold maximum speed $2\pi f{A}_m^{*}$ as a function of the reduced frequency for the six combinations of antibubbles and bubbles. The curves correspond to the model Eq. (6). (b) Values of $\xi /\beta$ obtained by fitting Eq. (6) as a function of the bubble diameter $d$.