Acoustic waves can generate steady streaming within a fluid owing to the generation of viscous boundary layers near walls of typical thickness $\delta$. In microchannels, the acoustic wavelength $\lambda$ is adjusted to twice the channel width $w$ to ensure a resonance condition, which implies the use of MHz transducers. Recently, though, intense acoustic streaming was generated by acoustic waves of a few kHz (hence with $\lambda \gg w$), owing to the presence of sharp-tipped structures of curvature radius at the tip $r_c$ smaller than $\delta$. The present study quantitatively investigates this sharp-edge acoustic streaming via the direct resolution of the full Navier-Stokes equation using the finite element method. The influence of $\delta ,r_c$, and viscosity $\nu$ on the acoustic streaming performance is quantified. Our results suggest choices of operating conditions and geometrical parameters, in particular the dimensionless tip radius of curvature $r_c/\delta$ and the liquid viscosity.

Acoustic streaming can be generated around sharp structures, even when the acoustic wavelength is much larger than the vessel size. This sharp-edge streaming can be relatively intense, owing to the strongly focused inertial effect experienced by the acoustic flow near the tip. We conducted experiments with particle image velocimetry to quantify this streaming flow through the influence of liquid viscosity $\nu$ , from 1 mm ${}^2$ /s to 30 mm ${}^2$ /s, and acoustic frequency f from 500 Hz to 3500 Hz. Both quantities supposedly influence the thickness of the viscous boundary layer $\delta ={\left(\frac{\nu }{\pi f}\right)}^{1/2}$ . For all situations, the streaming flow appears as a main central jet from the tip, generating two lateral vortices beside the tip and outside the boundary layer. As a characteristic streaming velocity, the maximal velocity is located at a distance of $\delta$ from the tip, and it increases as the square of the acoustic velocity. We then provide empirical scaling laws to quantify the influence of $\nu$ and f on the streaming velocity. Globally, the streaming velocity is dramatically weakened by a higher viscosity, whereas the flow pattern and the disturbance distance remain similar regardless of viscosity. Besides viscosity, the frequency also strongly influences the maximal streaming velocity.

Acoustic waves can generate steady streaming within a fluid owing to the generation of viscous boundary layers near walls, of typical thickness $\delta$. In microchannels, the acoustic wavelength $\lambda$ is adjusted to twice the channel width $w$ to ensure a resonance condition, which implies the use of MHz transducers. Recently though, intense acoustic streaming was generated by acoustic waves of a few kHz (hence with $\lambda \gg w$), owing to the presence of sharp-tipped structures of curvature radius at the tip $r_c$ smaller than $\delta$. The present study quantitatively investigates this sharp-edge acoustic streaming via the direct resolution of the full Navier-Stokes equation, using Finite Element Method. The influence of $\delta$, $r_c$ and viscosity $\nu$ on the acoustic streaming performance are quantified. Our results suggest choices of operating conditions and geometrical parameters, via dimensionless quantities $r_c/\delta$ and $\delta/w$ and provide guidelines on how to obtain strong, optimal sharp-edge acoustic streaming.