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.

The directional motion of sessile drops can be induced by slanted mechanical vibrations of the substrate, which induce drop deformations combining both axisymmetric and antisymmetric modes. In this paper, we establish quantitative trends from experiments conducted within a large range of parameters, namely, the amplitude $A$ and frequency $f$ of the forcing, the liquid viscosity $\eta$, and the angle between the substrate and the forcing axis $\alpha$. These experiments are carried out on weak-pinning substrates. For most parameters sets, the averaged velocity $\langle v\rangle$ grows linearly with $A$. We extract the mobility, defined as $s=\frac{\mathrm{\Delta }\langle v\rangle }{\mathrm{\Delta }A}$. It is found that $s$ can show a sharp maximal value close to the resonance frequency of the first axisymmetric mode $f_p$. The value of $s$ tends to be almost independent on $\eta$ below 50 cSt, while $s$ decreases significantly for higher $\eta$. Also, it is found that for peculiar sets of parameters, particularly with $f$ far enough from $f_p$, the drop moves in the reverse direction. Finally, we draw a relationship between $\langle v\rangle$ and the averaged values of the dynamical contact angles at both sides of the drop over one period of oscillation.

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.

We study the size and shape of the final deposit obtained when a drop with colloidal particles has dried on a ultra-hydrophobic surface made of micro-posts. As expected, most of the particles lie inside a circular area, whose radius roughly corresponds to the Laplace pressure threshold for liquid impalement inside the structure (Cassie–Wenzel transition), inducing a coffee-stain deposit due to contact-line pinning. Less expected is the observation of tiny deposits on top of posts in the area external to the main ring, despite the low macroscopic liquid/solid friction. Experiments are carried out varying the concentration in particles and initial volume of drops, in order to determine the influence of these parameters on the size distribution of deposits. A microscopic insight of the tiny deposits is proposed, based on recent experiments of non-volatile liquid sliding drops.