Singular Perturbation in Acoustic Cavitation

Pattern formation in acoustic cavitation

A new approach for the theoretical description of structure formation in acoustic avitation is developed. The model consists of two coupled partial differential equations describing the spatiotemporal evolution of the sound field amplitude and the bubble concentration. Linear stability analysis and numerical simulation• of the pattern formation are presented. The relation between this approach ...

Chemical Effects of Acoustic Cavitation

A novel high-frequency, high-power, pilot-plant scale sonochemical reactor was developed and used to study the degradation of dichloromethane, trichloroethylene, phenol, and methyl orange in aqueous solutions. The degradation rates of trichloroethylene, dichloromethane, and phenol were found to exceed those of similar frequency, small-scale bench reactors by factors ranging from 2.5 to 7. The d...

Singular perturbation theory

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...

Geometric Singular Perturbation Theory

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 ca...