Nonlinear acoustic method for bubble density measurements in water

Nonlinear scattering due to bubble oscillations was theoretically and experimentally investigated for bubble size distribution measurements in water. If two primary acoustic waves of different frequencies are incident on a bubble, the difference frequency component of primary waves is produced in the scattered field. The incoherent scattering at the difference frequency from bubbles was theoretically studied. It was shown that the difference frequency amplitude is proportional to the density of bubbles having resonance frequencies close to the difference frequency. It allows the use of difference frequency measurements to determine the bubble density in water. For experimental investigations two focused transducers were used to increase the levels of primary waves in the interaction zone. One of the primary frequencies was kept constant 2.25 MHz while another was changed from 2.22 to 1.93 MHz, so that the observed difference frequency was varied from 30 to 320 kHz. This frequency band corresponds to the resonant bubble radii from 109 to 10 μm. For the bubble clouds produced in a laboratory tank by an electrolysis-type and a slit-type bubble maker the bubble densities were well estimated with the present nonlinear acoustic method.