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Related Experiment Video

Updated: May 18, 2026

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions

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Published on: February 17, 2019

Analytical approximations for the collapse of an empty spherical bubble.

D Obreschkow¹, M Bruderer, M Farhat

¹The University of Western Australia, ICRAR, 35 Stirling Highway, Crawley, WA 6009, Australia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

This study presents accurate approximations for spherical bubble collapse dynamics, crucial for understanding cavitation phenomena in fluid dynamics. The findings offer improved models for bubble collapse prediction.

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Area of Science:

Fluid Dynamics
Acoustics
Nonlinear Dynamics

Background:

The Rayleigh equation models spherical bubble dynamics in liquids.
Accurate solutions are essential for understanding cavitation and fluid phenomena.
Existing solutions lack a closed-form expression, necessitating approximations.

Purpose of the Study:

To develop accurate, simplified approximations for the Rayleigh equation.
To provide a more accessible model for spherical bubble collapse.
To validate approximations against experimental cavitation data.

Main Methods:

Analytical approximation of the Rayleigh equation solution.
Development of a series expansion for bubble radius as a function of time.
Comparison of approximated solutions with high-precision microgravity cavitation data.

Main Results:

An approximation r(0)(t)=(1-t^2)^(2/5) was found with <1% error.
A refined approximation r(*)(t)=r(0)(t)[1-a(1)Li(2.21)(t^2)] achieves 0.001% accuracy.
Approximations show strong agreement with experimental cavitation data.

Conclusions:

The developed approximations offer highly accurate and practical solutions for Rayleigh-Plesset equation dynamics.
These approximations are valuable for modeling cavitation and bubble collapse in various physical scenarios.
The study validates the utility of these approximations in microgravity experiments.