Nonlinear evolution of a spherical standing wave in an acoustically excited liquid drop

When focusing of an intensive ultrasonic beam on liquid-air boundary, a phenomenon called ultrasonic atomization takes place. At moderate levels of ultrasound intensity an acoustic fountain is observed that has the form of a chain of drops, which begin to explode after the fountain is created. The mechanism of these explosions is still unclear. In this work a nonlinear theory of such phenomenon is developed. It is supposed that harmonics of standing waves are formed in a liquid drop because of acoustic nonlinearity, and that process leads further either to pressure amplification at the drop center and formation of a superheated vapor bubble; both effects may be a reason of drop explosion. The theoretical model is based on a quadratic approximation of a wave equation for acoustic pressure in a viscous spherical liquid drop. The solution was taken in the form of a series of harmonics with unknown coefficients. The method of slowly varying amplitudes is applied for further simplification. On the basis of the numerical solution of this problem the wave spectrum in the drop center at different time moments was calculated and the time profile of acoustic pressure in the drop center was predicted; it is strongly distorted with the course of time: at first the sharp section is formed, and then the strong negative and positive peaks appear around it. Observed growth of the negative pressure in the drop center denotes an existence of cavitation in the drop that can be the reason of bubble formation leading further to the drop explosion.