Acoustic emission associated with the bursting of a gas bubble at the free surface of a non-Newtonian fluid

We report experimental measurements of the acoustic emission associated with the bursting of a gas bubble at the free surface of a non-Newtonian fluid. On account of the viscoelastic properties of the fluid, the bubble is generally elongated. The associated frequency and duration of the acoustic signal are discussed with regard to the shape of the bubble and successfully accounted for by a simple linear model. The acoustic energy exhibits a high sensitivity to the dynamics of the thin film bursting, which demonstrates that, in practice, it is barely possible to deduce from the acoustic measurements the total amount of energy released by the event. Our experimental findings provide clues for the understanding of the signals from either volcanoes or foams, where one observes respectively, the bursting of giant bubbles at the free surface of lava and bubble bursting avalanches.

Figure 1

Bursting event in the fast camera. (a) Initially, the bubble sits at the free surface. The film at the top is thinning due to the drainage. (b) The thin film suddenly breaks. One observes, in this specific example, that the film tears at its base. (c) As a result of the outgoing air flow and of the capillary forces, the remaining part of the bubble head is blown upwards and shrinks. The width of each image is 3 cm whereas the time difference between them is 0.8 ms. Here, the acoustic emission associated with the event does not last more than 2 ms, during which the bubble body clearly does not significantly deform.

Figure 2

Images of the bubble right before bursting and associated acoustic signals. In the images (scale bar, 1 cm), one notices that the bubbles are more elongated when the gel concentration $c$ is larger. In addition, we report the signal from the microphone. We observe that the typical frequency decreases and the characteristic duration of the acoustic emission increases when the bubble length is increased.

Figure 3

Wavelength $\lambda$ vs bubble length $L$. The resonant wavelength increases linearly with the bubble length, estimated from the open aperture to the tail. The offset ${\lambda }_0$ is accounted for by the radiation at the open end.

Figure 4

(a) Image of a bubble and definitions. The dotted curve corresponds to the proposed interpolation of the bubble profile by $\alpha \left(r\right)={\alpha }_0\text{cos}\left(\beta \frac{r}{L}\right)$ with ${\alpha }_0=0.378$ and $\beta =1.11$. (b) Slope $\frac{d\lambda }{dL}$ vs ${\alpha }_0$ for different ratio $\frac{\Phi }{L}$. The slope $\frac{d\lambda }{dL}$ is obtained from the solution of Eq. (1) taking into account the profile of the bubble wall. The full diamond corresponds to the bubble in (a).

Figure 5

Characteristic duration of the sound emission $n$, in number of periods, vs $L^2/{\Phi }^2$. The dependence of $n$ on the ratio $L/\Phi$ demonstrates that the damping of the acoustic signal is mainly governed by the radiation at the open end. (The slope of the gray line is 8, thus corresponding to $\xi =\frac{1}{8}$, see text.)

Figure 6

Ratio $E_a/E_T$ vs volume $V$. At a given volume $V$, the acoustic energy $E_a$ does not account for the amount of energy released by the bursting bubble. Inset: Ratio $E_a/E_T$ vs frequency $\omega$. The experimental results clearly demonstrate that the bubbles can be separated in two categories: Small bubbles that sit at the free surface before bursting (open symbols) and larger ones that cross the interface without stopping (full symbols).