Effect of charge on the dynamics of an acoustically forced bubble

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 ultrasonic pressure wave. A non-dimensional ratio ζ is defined that is a comparative measure of the extremal values the bubble can expand or contract to, and we find the existence of an unstable regime for ζ as a function of the driving pressure amplitude, P_s. This unstable regime is gradually suppressed with increasing bubble size. The Blake and the upper transient pressure thresholds for the system are then discussed. (paper)