Acoustic streaming: comparison of low-amplitude linear model with streaming velocities measured by 32-MHz Doppler

The pressure gradient along the ultrasonic beam results in medium streaming. Following Nyborg's analysis of the Navier-Stokes equation, Wu and Du developed an approximate solution for the streaming velocity generated by flat and weakly focused transducers. We have modified their solution of the Poisson equation by directly deriving the Dirichlet boundary conditions to be applied for this type of equation. Our numerical results (for the linear case) were about one half smaller for flat and weakly focused on Gaussian beam transducers compared to the results by Wu and Du. The theoretical calculations were verified using a purpose-designed 32-MHz pulsed Doppler unit. The applied average acoustic power was changed from 1 microW to 6 mW, the burst width was 0.5 microseconds and the pulse repetition frequency was 32 kHz. The experiments were done on 4-mm-diameter flat and focused (focal distance = 8 and 12 mm) transducers. The streaming was measured along the ultrasonic beam from 0-20 mm; at all positions, the maximum Doppler frequency was estimated from the recorded spectra. Streaming was induced in a solution of water and corn starch. The experimental results showed that, for a given acoustic power, the streaming velocity was independent of the starch density in water changed from 0.3-40 g of starch in 1 l of distilled water. For applied acoustic powers, the streaming velocity changed linearly from 0.2-40 mm/s. Both the theoretical solutions for plane and focused waves and the experimental results were in good agreement.