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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. [ABSTRACT FROM AUTHOR]

This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace-Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge. [ABSTRACT FROM AUTHOR]

We describe a simple model of a bubbly two-phase flow which is able to explain why waves propagate downward when a pint of Guinness is poured, and also how the waves are generated. Our theory involves a physically based regularization of the basic equations of the two-phase flow, using interphasic pressure difference and virtual mass terms, together with bulk or eddy viscosity terms. We show that waves can occur through an instability analogous to that which forms roll waves in inclined fluid flows, and we provide a description of the form of these waves, and compare them to observations. Our theory provides a platform for the description of waves in more general bubbly two-phase flows, and the way in which the flow breaks down to form slug flow. [ABSTRACT FROM AUTHOR]

We examine the dynamics of a thin film of viscous fluid on the inside surface of a cylinder with horizontal axis, rotating about this axis. The stability of the film has been previously explored using the leading-order lubrication approximation, under which it was found to be neutrally stable. In the present paper, we examine how the stability of the film is affected by higher-order corrections, such as inertia (described by the material derivatives in the Navier–Stokes equations), surface tension, and the hydrostatic pressure gradient. Assuming that these effects are weak, we derive an asymptotic equation which takes them into account as perturbations. The equation is used to examine the stability of the steady-state distribution of film around the cylinder (rimming flow) with respect to linear disturbances with harmonic dependence on time (normal modes). It is shown that hydrostatic pressure gradient does not affect those at all, and the effect of surface tension is weak—whereas inertia always causes instability. The inertial instability, however, can be inhibited by viscosity, which can make the characteristic time of growth so large that the film would be effectively stable. [ABSTRACT FROM AUTHOR]

We consider steady flow of a thin viscous liquid film over a small two-dimensional topography and develop a Green’s function for the linearized problem. The solutions so obtained can be used to analyze the effect of arbitrary small substrate defects on the coating applied to a substrate. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]