The initial acceleration of a buoyant spherical bubble revisited

TL;DR

This paper provides a rigorous analytical derivation of the initial acceleration of a buoyant spherical bubble in a liquid, validated by numerical simulations, highlighting the importance of non-equilibrium effects on the force experienced by the bubble.

Contribution

It offers a derivation that does not rely on classical potential theory or simplifying assumptions, extending understanding of bubble dynamics from fundamental equations.

Findings

The initial acceleration formula matches classical results based on density ratios.

Numerical simulations confirm the analytical derivation.

Pressure distribution on the bubble surface differs from Archimedean predictions due to non-equilibrium effects.

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.