Energy partition at the collapse of spherical cavitation bubbles

TL;DR

This study systematically investigates how energy is divided between rebound and shock in collapsing spherical cavitation bubbles, revealing a pressure-dependent relationship explained by a physical model involving liquid compressibility and gas behavior.

Contribution

It introduces a comprehensive experimental and theoretical analysis of energy partition in cavitation bubble collapse, highlighting a key non-dimensional parameter governing the process.

Findings

Energy partition depends systematically on liquid pressure.

A physical model accurately predicts the observed energy distribution.

The non-dimensional parameter $\xi$ governs the energy split.

Abstract

Spherically collapsing cavitation bubbles produce a shock wave followed by a rebound bubble. Here we present a systematic investigation of the energy partition between the rebound and the shock. Highly spherical cavitation bubbles are produced in microgravity, which suppress the buoyant pressure gradient that otherwise deteriorates the sphericity of the bubbles. We measure the radius of the rebound bubble and estimate the shock energy as a function of the initial bubble radius (2-5.6 mm) and the liquid pressure (10-80 kPa). Those measurements uncover a systematic pressure dependence of the energy partition between rebound and shock. We demonstrate that these observations agree with a physical model relying on a first-order approximation of the liquid compressibility and an adiabatic treatment of the non-condensable gas inside the bubble. Using this model we find that the energy partition between rebound and shock is dictated by a single non-dimensional parameter $\xi = \Delta p\gamma^6/[{p_{g0}}^{1/\gamma} (\rho c^2)^{1-1/\gamma}]$, where $\Delta p=p_\infty-p_v$ is the driving pressure, $p_{\infty}$ is the static pressure in the liquid, $p_v$ is the vapor pressure, $p_{g0}$ is the pressure of the non-condensable gas at the maximal bubble radius, $\gamma$ is the adiabatic index of the non-condensable gas, $\rho$ is the liquid density, and $c$ is the speed of sound in the liquid.