Presence of surfactants controls the stability of bubble chains in carbonated drinks

Bubbles appear when a carbonated drink is poured in a glass. Very stable bubble chains are clearly observed in champagne, showing an almost straight line from microscopic nucleation sites from which they are continuously formed. In some other drinks such as soda, such chains are not straight (not stable). Considering pair interactions for spherical clean bubbles, bubble chains should not be stable, which contradicts these observations. The aim of this work is to explain the conditions for bubble chain stability. For this purpose, experiments and direct numerical simulation are conducted. The bubble size as well as the level of interface contamination are varied to match the range of parameters in typical drinks. Both factors are shown to affect the bubble chain stability. The transition from stable to unstable behavior results from the reversal of the lift force, which is induced by the bubble wake. A criteria based on the production of vorticity at the bubble surface is proposed to identify the conditions of transition from stable to unstable bubble chains. Beyond carbonated drinks, understanding bubble clustering has impact in many two-phase problems of current importance.

Figure 1

Bubble chains forming from a capillary in a clean fluid. The flow rate through the capillary increases from 2 to 10 ml/min, from left to right. The bubble frequency ranges from 6 to 18 bubbles/s. $\mathrm{Ar}\approx 150$, $\mathrm{Bo}\approx 0.2$, and $\mathrm{La}=0$ (see the movies in the Supplemental Material [50]).

Figure 2

The effect of bubble size and surface contamination on a bubble chain. (a) The bubble size increases (from left to right) for a liquid without surfactants, $\mathrm{La}=0$; $\mathrm{Ar}=(150$, 240, 1050), and $\mathrm{Bo}=(0.18$, 0.25, 0.66) for left, center, and right images. (b) The bubble size is approximately the same, but the amount of surfactant increases (from left to right). $\mathrm{La}=(0$, 0.1, 0.5), $\mathrm{Ar}=(240$, 150, 225), and $\mathrm{Bo}=(0.24$, 0.21, 0.32) for left, center, and right images. $R$ is the bubble radius (see the movies in the Supplemental Material [50]).

Figure 3

Simulation of two interacting bubbles ascending in a fluid. [(a) and (c)] The trajectories of the two bubbles, where distances are in bubble radius units; [(b) and (d)] streamwise isovorticity surfaces around the bubbles, ${\omega }_x{U}_B/R=\pm 0.05$. For both cases $\mathrm{Bo}=0.05$ and $\mathrm{Ar}=400$; for [(a) and (b)] $\mathrm{La}=0$ and for [(b) and (c)] $\mathrm{La}=1.0$ (see the movies in the Supplemental Material [50]).

Figure 4

Dispersion angle of the bubble chain. [(a) and (b)] Images of superposed bubbles over time for the 1 and 10 ml/min, respectively, shown in Fig. 1. In (c), the dispersion angle is shown as a function of the dimensionless bubble frequency, $f{R}^2/\nu$, for all experiments conducted using the capillary with diameter $d_C=0.16$ mm.

Figure 5

Maximum normalized azimuthal vorticity on bubble surface as function of Bond number (a) and Langmuir number (b). Filled and empty symbols show unstable and stable chains, respectively. The dashed line shows the threshold value of ${\omega }_{\text{max}}R/U_B=2.65$. The red circles, blue squares, and black triangles shown simulations for different values of Bo but $\mathrm{La}=0$, $\mathrm{La}=1$, or $\mathrm{La}=2$, respectively. The blue diamonds, magenta stars, and green sideways triangles show simulations for which both Bo and La were varied. Note that the Ar was also varied in the simulations ($400<\mathrm{Ar}<11000$).

Figure 6

Stability map showing the stable and unstable chain behavior in terms of the Bond number and the product of the rigidity parameter with the Langmuir number. Filled and empty symbols show unstable and stable chains, respectively. Circles and stars show experimental data, while squares and triangles show numerical results. The data enclosed in the rectangle correspond to cases for $\mathrm{La}\mathrm{\Lambda }=0$ (clean fluids). The dashed line presents an line for which ${\omega }_{\text{max}}R/U_B\approx 2.65$ which marks the transition. The stars (blue, black, red, and magenta) show the measurements conducted with carbonated water, beer, sparkling wine, and champagne, respectively. The yellow, orange, and blue shaded areas represent the expected range of values for champagne, beer, and water, respectively, according to Table 1.

Figure 7

Map of the normalized azimuthal vorticity on bubble surface for (a) $\mathrm{La}=0$, $\mathrm{Bo}=0.06$, $\mathrm{Ar}=400$ and (b) $\mathrm{La}=0$, $\mathrm{Bo}=0.2$, and $\mathrm{Ar}=11000$.

Figure 8

(a) Map of the normalized azimuthal vorticity on bubble surface for $\mathrm{La}=2.0$, $\mathrm{Bo}=0.2$, and $\mathrm{Ar}=11000$. (b) The map of normalized surfactant concentration, $\mathrm{\Gamma }/{\mathrm{\Gamma }}_{\max }$, corresponding to the case in (a).