Sinking bubbles in stout beers

A surprising phenomenon witnessed by many is the sinking bubbles seen in a settling pint of stout beer. Bubbles are less dense than the surrounding fluid so how does this happen? Previous work has shown that the explanation lies in a circulation of fluid promoted by the tilted sides of the glass. However, this work has relied heavily on computational fluid dynamics (CFD) simulations. Here we show that the phenomenon of sinking bubbles can be predicted using a simple analytic model. To make the model analytically tractable we work in the limit of small bubbles and consider a simplified geometry. The model confirms both the existence of sinking bubbles and the previously proposed mechanism.