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

Gigahertz acoustic streaming enables the synthesis of localized microjets reaching speeds of up to meters per second, offering tremendous potential for precision micromanipulation. However, theoretical and numerical investigations of acoustic streaming at these frequencies remain so far 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 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 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. Last, our analysis of transient regimes reveals a dramatic reduction in the time required to reach the maximum velocity as the frequency increases (power law in -5/2), leading to characteristic time on the order of μs at gigahertz frequencies, and hence accelerations within the Mega-g range.