Bubble nucleation in stout beers

Bubble nucleation in weakly supersaturated solutions of carbon dioxide—such as champagne, sparkling wines, and carbonated beers—is well understood. Bubbles grow and detach from nucleation sites: gas pockets trapped within hollow cellulose fibers. This mechanism appears not to be active in stout beers that are supersaturated solutions of nitrogen and carbon dioxide. In their canned forms these beers require additional technology (widgets) to release the bubbles which will form the head of the beer. We extend the mathematical model of bubble nucleation in carbonated liquids to the case of two gases and show that this nucleation mechanism is active in stout beers, though substantially slower than in carbonated beers and confirm this by observation. A rough calculation suggests that despite the slowness of the process, applying a coating of hollow porous fibers to the inside of a can or bottle could be a potential replacement for widgets.

Figure 1

Geometry of a gas pocket trapped in a cellulose fiber.

Figure 2

Results of the numerical solution of Eqs. (9) and (10). The black line shows the numerical solution, the gray line shows the $N_1+N_2\gg 1$ limit, and the dashed black line shows the $\epsilon \ll 1$ limit. (a) Rate of growth of the gas pocket. (b) Evolution of the concentration of CO${}_2$ in the gas pocket.

Figure 3

Bubble nucleation in stout from a cellulose fiber taken from a coffee filter. The scale bar is $50\hspace{0.5em}\mu \text{m}$ in each figure. The arrows show (1) a gas pocket in the fiber which nucleates a bubble; (2) the bubble fed by gas from pocket 1; (3) a bubble nucleated on the outside of the fiber. (a) The air pocket (1) has reached maximum size. (b) The air pocket (1) has created bubble (2). (c) Bubble (2) has visibly detached from the fiber, air pocket (1) is starting to refill with gas. (a), (b), and (c) are frames from a movie. (b) is $80\hspace{0.5em}\mathrm{ms}$ after (a), (c) is $520\hspace{0.5em}\mathrm{ms}$ after (a).

Figure 4

Process used to construct Fig. 5. The figure was constructed from 200 frames of a movie. (a) One of the frames from the movie. (b) Each frame was rotated to make the fiber vertical, and a strip of pixels (indicated by arrows) extracted. (c) The strips of pixels from each frame of the movie were laid side by side to make Fig. 5.

Figure 5

Growth of the gas pocket. The construction of the figure is described in the main text and illustrated in Fig. 4. This figure shows the growth of the gas pocket within the cellulose fiber shown in Fig. 3. As in Fig. 3 dark colors correspond to gas and light colors to liquid. The columns of pixels from the frames corresponding to parts (a), (b), and (c) of Fig. 3 are indicated. The location of the gas pocket indicated by a (1) in Fig. 3 is shown. Vertical lines indicate the times at which bubbles are created by the fiber.