Acoustic Sensing of Forces Driving Fast Capillary Flows

The popping sound of a bursting soap bubble is acquired using microphone arrays and analyzed using spherical harmonics decomposition. Using the theoretical framework of aeroacoustics, we demonstrate that this acoustic emission originates mainly from the capillary stresses exerted by the liquid soap film on the air and that it quantitatively reflects the out-of-equilibrium evolution of the flowing liquid film. This constitutes the proof of concept that the acoustic signature of violent events of physical or biological origin could be used to measure the forces at play during these events.

Figure 1

(a) High-speed imaging of the triggered bursting of a 2 mL fresh bubble. (b) Sketch of the setup showing one circular acoustic antenna of eight MEMS microphones (colored circles) and the two large bandwidth microphones BK1 and BK2. (c) Signals acquired by the 44 mm radius acoustic antenna. (d) Schematic of the bubble bursting showing the capillary forces. (e) Monopolar, dipolar, and quadrupolar contributions to the pressure signal measured on the bubble top. (f) Pressure acquired by top BK1 (blue curve) and bottom BK2 (red curve) microphones at 30 mm from a 1 mL fresh bubble. Solid lines correspond to the average over 5 experiments and shaded areas are bounded by the maximum and minimum. Quasistatic model (out-of-equilibrium model) is plotted as dashed lines (solid lines).

Figure 2

(a) High-speed images of the spontaneous bursting of a 0.5 mL long-lived bubble. The red arrow tips indicate the thickness shock wave. (b) Thickness shock wave velocity $v_{\mathrm{s}}$ (blue) and rim velocity $v_{\mathrm{r}}$ (red) as a function of the initial film thickness $e_0$. Inset: Film thickness after the shock wave $e_1(\theta ,t)$ versus its initial thickness before the shock wave $e_0(\theta )$. (c) Sketch of the bursting soap bubble illustrating the influence of the shock wave on the bursting dynamic. Enlargements: Capillary forces when the film is at rest (A) and is out-of-equilibrium flowing (B). The in-plane flow induces a centripetal acceleration (bold, black arrow). (d) Pressure signals of the spontaneous bursting of 0.5 mL bubbles recorded by top BK1 (blue curve) and bottom BK2 (red curve) microphones at 30 mm, averaged over three bursting events (solid lines), the shaded areas being bounded by the maximum and minimum of the three signals. Quasistatic model (out-of-equilibrium model) is plotted as dashed lines (solid lines).