Wave processes and self-organization processes in bubbly liquids

Nail Gumerov, Galiia Gilmanova

A phenomenon of bubble self-organization related self-action of the acoustic field is strongly nonlinear effect, which occurs, for example, in acoustic cavitation and sonochemical reactors. It is due to a two-way field-particle interaction, when the bubbles change their position and sizes due to the acoustic radiation and other forces and rectified diffusion; so the acoustic properties of the medium vary in space and time, which leads to restructuring of the acoustic field. So far, mathematical models of the phenomenon are studied in very simplified settings because of the complexity of the problem (especially in the three-dimensional formulation).

In a weak high-frequency acoustic field bubbles "vibrate" with the frequency of the sound field, which, in fact, has no effect on this field. However, in consideration of non-linearity bubbles drift in the relatively slow time scale (due to the Bjerknes forces) and grow or collapse (due to the rectified diffusion). That is what leads to a restructuring of the field, which is quite sensitive to the presence of bubbles. Secondary effects, such as coagulation and fragmentation of bubbles, can also play an important role in the reconstruction of the field.

We have developed and tested a 2D and 3D codes for simulation of bubble self-organization. Pseudospectral iterative solvers for the Helmholtz equation with spatially non-uniform wavenumber and Lagrangian methods for tracking the dynamics of each (!) bubble in a system are in the core of these codes. Simulations show interesting spatio-temporal behavior of the bubbles and the acoustic field. Particularly effects of bubble clustering, filamentation, etc., observed earlier in acoustic cavitation experiments were also found numerically and explained (in certain limits).

Top: Distribution of the wave amplitude in a certain section and distribution of bubbles obtained after 5 seconds of action of acoustic field for the system with 1000 bubbles. Bottom: the same, but for the undersaturated gas liquid with taking into account gravity force
Evolution of bubble structures in the liquid under the influence of an acoustic field