Abstract
When a submerged bubble is initially at rest in a stagnant low viscosity liquid such as water, buoyancy forces accelerate the bubble upwards. The increasing relative velocity of the bubble with the surrounding liquid provokes deformations on the bubble shape that affect its vertical acceleration and also induce surface tension driven oscillations. Our theoretical model, which is compared with full Navier–Stokes simulations predicts, with a reasonable accuracy, both the position of the bubble centre of mass, as well as the time varying bubble shape under those conditions for which the Reynolds number is large, the amplitude of the deformation is small, the bubble interface is free of surfactants and the bubble rises following a straight vertical path. The model can be used as a first approximation to describe the initial instants of the unsteady buoyancy driven rising of millimetre sized bubbles typically generated in water aerators.
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J. M. Gordillo thanks financial support by the Spanish Ministry of Education under project DPI2011-28356-C03-01 and the Junta de Andalucía under project P08-TEP-03997.