A simple model of ultrasound propagation in a cavitating liquid. Part II: Primary Bjerknes force and bubble structures

TL;DR

This paper develops a nonlinear acoustic model to analyze bubble dynamics and structures in cavitating liquids, revealing the impact of traveling waves on bubble expulsion and formation of various bubble structures.

Contribution

It introduces a nonlinear propagation model linking wave attenuation to bubble dynamics, explaining the formation of bubble structures like cones, streamers, and flares in cavitating liquids.

Findings

High wave attenuation near emitters causes large Bjerknes forces.

Bubble structures such as cones, streamers, and flares are explained by sound velocity gradients.

The model's predictions align well with experimental observations.

Abstract

In a companion paper, a reduced model for propagation of acoustic waves in a cloud of inertial cavitation bubbles was proposed. The wave attenuation was calculated directly from the energy dissipated by a single bubble, the latter being estimated directly from the fully nonlinear radial dynamics. The use of this model in a mono-dimensional configuration has shown that the attenuation near the vibrating emitter was much higher than predictions obtained from linear theory, and that this strong attenuation creates a large traveling wave contribution, even for closed domain where standing waves are normally expected. In this paper, we show that, owing to the appearance of traveling waves, the primary Bjerknes force near the emitter becomes very large and tends to expel the bubbles up to a stagnation point. Two-dimensional axi-symmetric computations of the acoustic field created by a large area immersed sonotrode are also performed, and the paths of the bubbles in the resulting Bjerknes force field are sketched. Cone bubble structures are recovered and compare reasonably well to reported experimental results. The underlying mechanisms yielding such structures is examined, and it is found that the conical structure is generic and results from the appearance a sound velocity gradient along the transducer area. Finally, a more complex system, similar to an ultrasonic bath, in which the sound field results from the flexural vibrations of a thin plate, is also simulated. The calculated bubble paths reveal the appearance of other commonly observed structures in such configurations, such as streamers and flare structures.