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Bubble cascade may form not only in stout beers.

In a glass of stout beer, a very large number of small dispersed bubbles form a texture motion of a bubble swarm moving downwards. Such a cascading motion is caused by a gravity-driven hydrodynamic instability and depends on the interbubble distance. To estimate these two corresponding indicators, an experimentally measured velocity profile is required and, thus, is obtained a posteriori. However, it is unknown why the bubble cascade is observed only in stout beer with nitrogen, such as Guinness beer. To address this question via a priori estimation, here, we develop a mathematical continuum model of film flow in bubbly liquid, uncovering the essential dynamics among many physical processes occurring simultaneously in a glass. To validate the proposed model, we perform a numerical simulation of the distribution of massless Lagrangian particles in an inclined container. We investigate the effects of particle concentration, inclination angle, particle diameter, and container size on the cascading film flow. The results reveal that the motion and waviness of clear-fluid film can be successfully estimated a priori to experiments or simulations. Moreover, it is found that the continuum behavior of particles in the film flow is analogous to the continuum description of rarefied gas dynamics. These findings explain how the cascading bubbles in a pint glass of stout beer satisfy the continuum assumption and suggest a general condition for the onset of the cascade, for instance, a 200-l drum for carbonated water.