The beauty and complexity of the shapes and dynamics of bubbles rising in liquid have fascinated scientists for centuries. Here we perform simulations on an initially spherical bubble starting from rest. We report that the dynamics is fully three-dimensional, and provide a broad canvas of behaviour patterns. Our phase plot in the Galilei-Eotvos plane shows five distinct regimes with sharply defined boundaries. Two symmetry-loss regimes are found: one with minor asymmetry restricted to a flapping skirt; and another with marked shape evolution. A perfect correlation between large shape asymmetry and path instability is established. In regimes corresponding to peripheral breakup and toroid formation, the dynamics is unsteady. A new kind of breakup, into a bulb-shaped bubble and a few satellite drops is found at low Morton numbers. The findings are of fundamental and practical relevance. It is hoped that experimenters will be motivated to check our predictions.

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Dynamics of an initially spherical bubble rising in quiescent liquid

Numerical simulation of bubble rising in viscous liquid

Influence of surface tension implementation in Volume of Fluid and coupled Volume of Fluid with Level Set methods for bubble growth and detachment

Shapes and paths of an air bubble rising inside a liquid are investigated experimentally. About three hundred experiments are conducted in order to generate a phase plot in the Galilei and Eotvos numbers plane, which separates distinct regimes in terms of bubble behaviour. A wide range of the Galilei and Eotvos numbers are obtained by using aqueous glycerol solutions of different concentrations as the surrounding fluid and by varying the bubble size. The dynamics are investigated in terms of shapes, topological changes, and trajectories of the bubbles. Direct numerical simulations are conducted to study the bubble dynamics, which show excellent agreement with the experiments. To the best of our knowledge, this is the first time an experimentally obtained phase plot showing the distinct behaviour of an air bubble rising in a quiescent medium is reported for such a large range of Galilei and Eotvos numbers.

Shapes and paths of an air bubble rising in quiescent liquids

A coupled level-set and volume-of-fluid method for the buoyant rise of gas bubbles in liquids

A computational study of the effect of initial bubble conditions on the motion of a gas bubble rising in viscous liquids

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A computational study of the effect of initial bubble conditions on the motion of a gas bubble rising in viscous liquids