Bubble Dynamics in N Dimensions

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.

8 pages, 5 figures

References in corpus (3)

• Analytical Approximations for the Collapse of an Empty Spherical Bubble
• Equilibrium configurations of fluids and their stability in higher dimensions
• Comment on: "Analytical approximations for the collapse of an empty spherical bubble"

Cited by in corpus (5)

• Analytical solutions for problems of bubble dynamics
• Evolution of spherical cavitation bubbles: parametric and closed-form solutions
• Vanishing in Fractal Space: Thermal Melting and Hydrodynamic Collapse
• From Cavitation to Astrophysics: Explicit Solution of the Spherical Collapse Equation
• Mapping Driven Oscillations in the Size of a Bubble to the Dynamics of a Newtonian Particle in a Potential