APPLICATIONS OF ONE-DIMENSIONAL BUBBLES TO LITHOTRIPSY, AND TO DIVER RESPONSE TO LOW-FREQUENCY SOUND

Experimental, analytical, and numerical investigations into the dynami cs of a cylindrical gas pocket in a liquid (a ''one-dimensional'' bubb le) are described. One wall of the bubble (the gas-liquid interface) m ay move. The other walls (the curved wall, and the other end of the cy linder) are bounded by rigid surfaces. The equation of motion of a dam ped, forced, one-dimensional bubble is obtained, a nonlinearity arisin g through the amplitude-dependence of the oscillator stiffness. Analyt ical solutions to reduced forms of this equation give the natural freq uency of undamped oscillations in the linear limit. In the nonlinear r egime of finite-amplitude free oscillation the fundamental frequency i s found to be amplitude-dependent. Whilst analytical solutions of the undamped, unforced form of the equation of motion can be obtained in p hase space, the full nonlinear damped forced equation must be solved n umerically. These solutions are compared with those of the linear unda mped analysis, and with experimental measurements. Two relevant cases of such bubbles are studied: First, air bubbles trapped within the ear canals of divers and driven by high-amplitude low frequency sound; se cond, the theoretical potential of bubbles in blood to cause haemorrha ge of lung blood vessels during lithotripsy.