Simulation of bubble motion in acoustic cavitation

The many particle problem of moving cavitation bubbles in a liquid exposed to ultrasound need certain ingredients: Besides N bubbles and their positions ~xi and velocities ~ui, one has to specify the bubble sizes and shapes. Mechanisms for nucleation and annihilation or coalescence of bubbles have to be introduced, and a sound field distribution has to be given. Additionally, a liquid motion can be considered. At last, the forces on the bubbles have to be specified, which is probably most important. Recently, a rather simple approach for particle simulation of acoustic cavitation bubble motion has been proposed [1,2]. There, spherical nonlinearly oscillating bubbles, all of the same size (R0 = 5 m) are considered. Bubbles appear at certain fixed nucleation sites, and vanish if they get too close to each other. The sound field considered is a standing wave [(1,1,1) mode] in a cubic container driven at 20 kHz, and with no streaming liquid. The forces acting on the bubbles are added mass [ 12 Vi _ ~ui], a phenomenological drag [ ( + j~uij)~ui], the primary Bjerknes force [ hrpex(~xi)Viit] and the secondary Bjerknes force [see next section], where V ( V ) denote the (mean) bubble volume and pex the external pressure. With these assumptions, certain streamer patterns found in an experiment were reproduced using real world quantities. In particular, a repelling pressure antinode was modelled.