Physics of Beer Tapping

The popular bar prank known in colloquial English as beer tapping consists in hitting the top of a beer bottle with a solid object, usually another bottle, to trigger the foaming over of the former within a few seconds. Despite the trick being known for a long time, to the best of our knowledge, the phenomenon still lacks scientific explanation. Although it seems natural to think that shock-induced cavitation enhances the diffusion of ${\mathrm{CO}}_2$ from the supersaturated bulk liquid into the bubbles by breaking them up, the subtle mechanism by which this happens remains unknown. Here, we show that the overall foaming-over process can be divided into three stages where different physical phenomena take place in different time scales: namely, the bubble-collapse (or cavitation) stage, the diffusion-driven stage, and the buoyancy-driven stage. In the bubble-collapse stage, the impact generates a train of expansion-compression waves in the liquid that leads to the fragmentation of preexisting gas cavities. Upon bubble fragmentation, the sudden increase of the interface-area-to-volume ratio enhances mass transfer significantly, which makes the bubble volume grow by a large factor until ${\mathrm{CO}}_2$ is locally depleted. At that point buoyancy takes over, making the bubble clouds rise and eventually form buoyant vortex rings whose volume grows fast due to the feedback between the buoyancy-induced rising speed and the advection-enhanced ${\mathrm{CO}}_2$ transport from the bulk liquid to the bubble. The physics behind this explosive process sheds insight into the dynamics of geological phenomena such as limnic eruptions.

Figure 1

Sequence of images corresponding to the instants right after the pressure wave starts to propagate through the beer. To ensure a continuous bubble cloud, a metal disk was placed at the bottom of the bottle in this experiment, what effectively introduces a large number of nucleation sites. Scale bar: 10 mm.

Figure 2

A bubble of initial radius $R_0\approx 180\mu \mathrm{m}$, induced by a laser pulse nearly a second before the impact, grows after the passage of the expansion wave reaching the bubble location at instant ($a$). After the instant of maximum radius ($b$), the bubble collapses at some point between frame ($c$) and the previous one, turning into a bubble cloud. Panel ($d$) shows the bubble cloud 0.1 ms after instant ($c$). The Rayleigh-Plesset equation has been integrated numerically (red solid line, see Supplemental Material [7]) for a bubble subjected to a pressure pulse with an amplitude, $p_A=100\mathrm{kPa}$, and period, $T=0.24\mathrm{ms}$, measured at the bubble’s location with a hydrophone. Notice that, after the implosion, $t\approx 0.22\mathrm{ms}$, the Rayleigh-Plesset equation no longer describes the behavior of the bubble since it is only valid for a single bubble, not for a bubble cloud. (see Movies S1 and S2).

Figure 3

Upper plot: Time evolution of the size of a bubble cloud, $L_{\mathrm{c}}$, after the shock-induced collapse of an already existing bubble (blue circles) and after a laser-induced bubble implosion (red squares). Three different stages have been marked qualitatively: diffusion driven, depletion, and buoyancy driven. Black solid lines depict the scaling laws $L_{\mathrm{c}}\sim t^{1/2}$ (diffusion driven) and $L_{\mathrm{c}}\sim t^2$ (buoyancy driven). Lower plot: Time evolution of the top of the bubble cloud corresponding to the same cases of the upper plot. Notice how, at long times, the plume approaches a steady rising velocity. Letters denote the instants corresponding to the images in the lower panels (scale bar: 1 mm). (See Movie S3 in the Supplemental Material [7]).