The initial acceleration of a buoyant spherical bubble revisited
Abstract
An analytical derivation of the buoyancy-induced initial acceleration of a spherical gas bubble in a host liquid is presented. The theory makes no assumptions further than applying the two-phase incompressible Navier-Stokes equations, showing that neither the classical approach using potential theory nor other simplifying assumptions are needed. The result for the initial bubble acceleration as a function of the gas and liquid densities, classically built on potential theory, is retained. The result is reproduced by detailed numerical simulations. The accelerated, although stagnant state of the bubble induces a pressure distribution on the bubble surface which is different from the result related to the Archimedean principle, emphasizing the importance of the non-equilibrium state for the force acting on the bubble.
Keywords
Cite
@article{arxiv.2411.10916,
title = {The initial acceleration of a buoyant spherical bubble revisited},
author = {Dieter Bothe and Jun Liu and Pierre-Etienne Druet and Tomislav Maric and Matthias Niethammer and Günter Brenn},
journal= {arXiv preprint arXiv:2411.10916},
year = {2025}
}