Acoustic streaming outside and inside a fluid particle undergoing monopole and dipole oscillations

An analytical theory is developed for acoustic streaming induced by an acoustic wave field inside and outside a spherical fluid particle, which can be a liquid droplet or a gas bubble. The particle is assumed to undergo the monopole (pulsation) and the dipole (translation) oscillation modes. The dispersed phase and the carrier medium are considered to be immiscible, compressible, and viscous. The developed theory allows one to calculate the acoustic streaming both outside and inside the fluid particle. In contrast to earlier works, no restrictions are imposed on the thickness of the outer and inner viscous boundary layers with respect to the particle radius. A numerical implementation of the obtained analytical results is used to evaluate the acoustic streaming for different experimentally relevant configurations, such as an air bubble in water, a water droplet in oil, and a water droplet in air, considering both traveling and standing acoustic waves. The results show the richness of streaming pattern variations that arise in bubbles and droplets.