Applications of one-dimensional bubbles to lithotripsy, and to diver response to low frequency sound

Experimental, analytical, and numerical investigations into the dynamics of a cylindrical gas pocket in a liquid (a "one-dimensional" bubble) are described . One wall of the bubble (the gas-liquid interface) may move. The other walls (the curved wall, and the other end of the cylinder) are bounded by rigid surfaces. The equation of motion of a damped , forced, one-dimensional bubble is obtained, a nonlinearity arising through the amplitude-dependence of the oscillator stiffness. Analytical solutions to reduced forms of this equation give the natural frequency of undamped oscillations in the linear limit. [n the nonlinear regime of finite-amplitude free oscillation the fundamental frequency is found to be amplitude-dependent . Whilst analytical solutions of the undamped , un forced form of the equation of motion can be obtained in phase space, the full nonlinear damped forced equation must be solved numerically. These solutions are compared with those of the linear undamped analysis, and with experimental measurements. Two relevant cases of such bubbles arc studied: First, air bubbles trapped within the ear canals of divers and driven by high-amplitude low frequency sound; second, the theoretical potential of bubbles in blood to cause haemorrhage of lung blood vessels during lithotripsy