Estimation of acoustical streaming: theoretical model, Doppler measurements and optical visualisation.

An approximate solution for the streaming velocity generated by flat and weakly focused transducers was derived by directly solving the Dirichlet boundary conditions for the Poisson equation, the solution of the Navier-Stokes equation for the axial components of the streaming velocity. The theoretical model was verified experimentally using a 32 MHz pulsed Doppler unit. The experimental acoustical fields were produced by three different 4 mm diameter flat and focused transducers driven by the transmitter generating the average acoustic power within the range from 1 microW to 6 mW. The streaming velocity was measured along the ultrasonic beam from 0 to 2 cm. 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 to 40 grams of starch in 1 l of distilled water. For applied acoustic powers, the streaming velocity changed linearly from 0.2 to 40 mm/s. Both, the theoretical solutions for plane and focused waves and the experimental results were in good agreement. The streaming velocity field was also visualised using the particle image velocimetry (PIV) and two different evaluation methods. The first based on the FFT-based cross-correlation analysis between small sections for each pair of images and the second employing the algorithm of searching for local displacements between several images.