High speed and acceleration micrometric jets induced by GHz streaming: a numerical study with direct numerical simulations

Gigahertz acoustic streaming microjets, with the capability of achieving fluid speeds up to meters per second, open new avenues for precision fluid and particle manipulation at microscales. However, theoretical and numerical investigations of acoustic streaming at these frequencies remain relatively scarce due to significant challenges including: (i) The inappropriateness of classical approaches, rooted in asymptotic development, for addressing high-speed streaming with flow velocities comparable to the acoustic velocity, and (ii) the numerical cost of direct numerical simulations generally considered as prohibitive. In this paper, we investigate high-frequency bulk acoustic streaming using high-order finite difference direct numerical simulations. First, we demonstrate that high-speed micrometric jets of several meters per second can only be obtained at high frequencies, due to diffraction limits. Second, we establish that the maximum jet streaming speed at a a given actuation power scales with the frequency to the power of 3/2 in the low attenuation limit and linearly with the frequency for strongly attenuated waves. Lastly, our analysis of transient regimes reveals a dramatic reduction in the time required to reach the maximum velocity as the frequency increases, following a power-law relationship of -5/2. This phenomenon results in remarkable accelerations within the Mega-g range at gigahertz frequencies.