FEM calculation of an acoustic field in a sonochemical reactor

The spatial distribution of the acoustic amplitude in a sonochemical reactor has been numerically calculated using the finite element method (FEM). In the FEM program, the acoustic field in a sonochemical reactor is coupled with the vibration of the reactor’s wall. The present calculations have revealed that the thin (thick) glass or stainless steel wall is nearly a free (rigid) boundary and that the glass wall is freer than the stainless steel wall. The influence of the attenuation coefficient of ultrasound on the acoustic field has also been studied in order to see the effect of bubbles on the acoustic field. As the attenuation coefficient increases, the vibration amplitude of the reactor’s wall becomes smaller and the acoustic emission from the vibrating wall becomes weaker. The qualitative feature of the spatial pattern of sonochemiluminescence from an aqueous luminol solution has been reproduced by the calculation when the attenuation coefficient is in the range of 0.5–5 m−1. When the attenuation coefficient is less than about 0.05 m−1, the standing wave pattern of an acoustic field in the liquid is very complex due to the acoustic emission from the vibrating wall. The present calculations have also revealed that some stripes of pressure antinodes have also been disconnected when the radius of the transducer is much smaller than the side length of the vibrating plate. The dependence of the acoustic field on the liquid height is also discussed.