Direct numerical smulation of Gigahertz acoustic streaming

Gigahertz acoustic streaming allows the generation of high-speed micrometric jets that offer myriad possibilities for fluid and particle manipulation. We investigate high-frequency bulk (of Eckart type) streaming using high-order finite difference direct numerical simulations. Such simulations are rare because of their high computing cost, due to the wide spectrum of scales involved in these flows. We solve the Navier–Stokes compressible equations and compute transient and steady acoustic streaming. The simulations cover a wide range of parameters, and by coupling them with a scale analysis, we notably elucidate the scaling law dependency of acoustic streaming on frequency. It is shown that high-speed micrometric jets of several meters per second can only be obtained at high frequencies, due to diffraction limits. The possibilty of in-depth study of several aspects of the flow and limits of the models are also allowed by these simulations: temporal evolution of the streaming flow, characteristics of the source terms (Reynolds stresses) that generate streaming, limits of classical asymptotic developments. Finally, we quantify the maximum time required to reach the maximum jet speed as the frequency increases. This reveals that accelerations within the Mega-g range occur, opening new possibilities for generating ultra-short, high-speed microjets.