Acoustic Rotational Manipulation Using Orbital Angular Momentum Transfer

We report on the first quantitative test of acoustic orbital angular momentum transfer to a sound absorbing object immersed in a viscous liquid. This is done by realizing an original experiment that is to spin a millimeter-size target disk using an ultrasonic vortex beam. We demonstrate the balance between the acoustic radiation torque calculated from the Brillouin stress tensor and the viscous torque evaluated from the steady state spinning frequency. Moreover, we unveil a rotational acoustic streaming phenomenon that results from the acoustic angular momentum transfer to the host fluid. We show that it lowers the viscous torque, thereby restoring the torque balance.

Figure 1

(a) Sketch of the experimental setup. (b) Zoom on the acoustic target, a sound absorbing millimeter-size disk. (c) Zoom on the central part of the disk where the needle is inserted into the hole (see text for details).

Figure 2

(a) Magnitude and (b) phase of the acoustic pressure. Markers: experimental data; solid curves: paraxial model simulations; dashed curves: Laguerre-Gauss approximation of the acoustic vortex beam given by Eq. (1). The disk radius $R$ corresponds to $k_{1}R=12$. (c) Dimensionless magnitude and (d) phase of the acoustic pressure measured along the circle $C$ of maximal magnitude (markers) in the focal plane corresponds to $k_{1}x\simeq \pm 5$, the solid curves being the expected values from the Laguerre-Gauss beam approximation.

Figure 3

(a) Spinning disk frequency $f_{\mathrm{disk}}$ (markers) and predicted average rotation frequency of the (partially sound-absorbing) fluid 1 $⟨f_{\mathrm{flow}}⟩$ (see text for details) versus $U^2$. The solid line is the best linear fit to the experimental data. (b) Magnitudes of the radiation torque ${\Gamma }_{\mathrm{rad}}$ evaluated using Eq. (2) (solid curve), of the viscous torque ${\Gamma }_{\mathrm{visc}}$ evaluated from $f_{\mathrm{disk}}$ measurements using Eq. (7) (circles), and of the viscous torque ${\Gamma }_{\mathrm{visc}}^{\prime }$ taking into account the fluid rotation using Eq. (10) (squares).