Bubble Dynamics in N Dimensions

TL;DR

This paper explores the behavior of spherical bubbles in N-dimensional fluids to gain insights into their dynamics, re-deriving key equations and analyzing how dimensionality affects nonlinear phenomena and timescales.

Contribution

It extends classical bubble dynamics to N dimensions, providing new analytical results and numerical insights into how higher dimensions influence bubble behavior.

Findings

Bubbles are faster in higher dimensions.

Nonlinear behavior occurs at lower amplitudes in higher dimensions.

Unique features are observed in three-dimensional bubble dynamics.

Abstract

Cavitation and bubble dynamics are central concepts in engineering, the natural sciences, and the mathematics of fluid mechanics. Due to the nonlinear nature of their dynamics, the governing equations are not fully solvable. Here, the dynamics of a spherical bubble in an N-dimensional fluid are discussed in the hope that examining bubble behavior in N dimensions will add insight to their behavior in three dimensions. Several canonical results in bubble dynamics are re-derived, including the Rayleigh collapse time, the Rayleigh-Plesset equation, and the Minnaert frequency. Numerical simulations are used to examine the onset of nonlinear behavior. Overall, the dynamics of bubbles are faster at higher dimensions, with nonlinear behavior occurring at lower amplitudes. Several features are found to be unique to three dimensions, including the trend of nonlinear behaviour and apparent coincidences in timescales.