Acoustic streaming outside and inside a fluid particle undergoing arbitrary axisymmetric oscillations

An analytical theory is developed that allows to calculate acoustic streaming outside and inside a fluid (or gas) particle immersed in another fluid (or gas) and undergoing arbitrary axisymmetric oscillations, which can include shape modes of any order. The internal and external fluids are assumed immiscible, viscous, and compressible. No restrictions are imposed on the ratio of the particle radius to the viscous penetration depth and the acoustic wavelength both outside and inside the particle. To illustrate the capabilities of the developed theory, numerical examples are provided. The results show that in the case of an air bubble in water, the gas motion inside the bubble affects the external acoustic streaming when the relative thickness of the viscous boundary layer at the bubble surface is small, a situation that occurs for large bubbles and/or high driving frequencies. In the case of a water droplet in air, more complicated steaming patterns are observed for bigger droplets. In particular, strong external near-wall vortices can develop with increasing droplet size. The results for a glycerin droplet in water also show that the streaming pattern changes noticeably with the droplet size. In particular, the direction of the main external streaming, as well as the position and the direction of rotation of near-wall vortices, can change.