Orbital Angular Momentum Transfer to Stably Trapped Elastic Particles in Acoustical Vortex Beams

The controlled rotation of solid particles trapped in a liquid by an ultrasonic vortex beam is observed. Single polystyrene beads, or clusters, can be trapped against gravity while simultaneously rotated. The induced rotation of a single particle is compared to a torque balance model accounting for the acoustic response of the particle. The measured torque ($\sim 10\mathrm{pN}\mathrm{m}$ for a driving acoustic power $\sim 40\mathrm{W}/{\mathrm{cm}}^2$) suggests two dominating dissipation mechanisms of the acoustic orbital angular momentum responsible for the observed rotation. The first takes place in the bulk of the absorbing particle, while the second arises as dissipation in the viscous boundary layer in the surrounding fluid. Importantly, the dissipation processes affect both the dipolar and quadrupolar particle vibration modes suggesting that the restriction to the well-known Rayleigh scattering regime is invalid to model the total torque even for spheres much smaller than the sound wavelength. The findings show that a precise knowledge of the probe elastic absorption properties is crucial to perform rheological measurements with maneuverable trapped spheres in viscous liquids. Further results suggest that the external rotational steady flow must be included in the balance and can play an important role in other liquids.

Figure 1

Schematic view of the ultrasonic vortex beam trapping a janus polystyrene particle coated with a thin layer of gold. The negative acoustic gradient force, $F_a$, balances the gravity force $F_g$. The transfer of OAM from the beam to the particle and fluid bulk applies a torque $\mathrm{\Gamma }$ driving an on-axis rotation. A photograph of a trapped and rotating particle is also shown.

Figure 2

OAM transfer to a stably trapped particle. In (a) snap shots are shown of one complete revolution of a polystyrene particle with $a=174\mu \mathrm{m}$. (b) Rotational acoustic flow generated by the absorption of the AV in the fluid bulk. An injected drop of ink allows for the observation of the developing flow upon emission of the AV. (c) Computation of the acoustic torque as a function of the particle radius and particle vibration modes (see text). The measured torque with error bars (see text) are added for two independent rotation experiments with spherical probes having $a=172$ and $174\mu \mathrm{m}$, respectively.

Figure 3

Simultaneous trapping and rotation of clusters formed by three or five polystyrene particles. The particle sizes are 352, 280, and $320\mu \mathrm{m}$ (top to bottom) and 380, 320, 320, 320, and $268\mu \mathrm{m}$ (top to bottom).