Effect of charge on the dynamics of an acoustically forced bubble

TL;DR

This paper theoretically investigates how charge affects the oscillation dynamics of a gas bubble under ultrasonic forcing, identifying limits of charge and regimes of stability influenced by charge and pressure.

Contribution

It introduces a theoretical framework for understanding the impact of charge on bubble oscillations and identifies the limits and stability regimes related to charge and ultrasonic pressure.

Findings

Charge influences the oscillation regime of bubbles.

A maximum charge limit depends on bubble radius and pressure amplitude.

An unstable regime exists and is suppressed with larger bubble size.

Abstract

The effect of charge on the dynamics of a gas bubble undergoing forced oscillations in a liquid due to incidence of an ultrasonic wave is theoretically investigated. The limiting values of the possible charge a bubble may physically carry are obtained. The presence of charge influences the regime in which the bubble's radial oscillations fall. The extremal compressive and expansive dimensions of the bubble are also studied as a function of the amplitude of the driving pressure. It is shown that the limiting value of the bubble charge is dictated both by the minimal value reachable of the bubble radius as well as the amplitude of the driving ultrasound pressure wave. A non-dimensional ratio zeta is defined that is a comparative measure of the extremal values the bubble can expand or contract to and find the existence of an unstable regime for zeta as a function of the driving pressure amplitude, Ps. This unstable regime is gradually suppressed with increasing bubble size. The Blake and the upper transient pressure thresholds for the system are then discussed.