Orbital Angular Momentum Transfer to Stably Trapped Elastic Particles in Acoustical Vortex Beams
Résumé
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 (∼ 10 pNm for a driving acoustic power ∼ 40 W/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, whilst 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 manoeuvrable 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. Since the demonstration of particle trapping and manipulation of transparent particles by a single focused laser beam by Ashkin et al [1], "optical tweezers" that can pull a trapped particle in all three directions have found numerous applications, particularly in the bio-physical research [2, 3]. Using the radiation pressure of sound, rather than light, it was recently demonstrated that "acoustical tweezers" could operate as three dimensional traps for elastic particles using a single ultrasonic vortex beam first numerically [4] and then experimentally [5, 6]. The change in nature of the propagating wave presents several advantages for contactless manipulation as the possibility to operate through turbid media, allow penetration in tissue, largely increase the magnitude of the trapping force and the size of the particles. The attraction in the direction of the intensity gradient of transparent, dielectric, objects in optical tweezers relies on the transfer of the momentum carried by photons. It is however well established that photons can also carry angular momentum and exert torques [7]. This important degree of freedom has proven important for the controlled rotation of optically trapped particles with spin or orbital angular momentum (OAM) of photons [8-12]. In contrast, longitudinal acoustic waves in liquids do not carry momentum [13], but instead can induce a mean stress, after exchange of a flux of momentum-e.g. by scattering or absorption-either it be linear or angular. Rayleigh first analyzed and quantified the torque exerted on a disk suspended in a sound field[14]. In that particular case the torque is understood as a consequence of the uneven radiation pressure exerted on the surface of a disk unaligned with the sound propagation direction [15] in a way that any object of irregular form could experience a net radiation torque. Accounting for the finite size of the viscous boundary layer δ = 2µ ρω around an object's surface, where ω is the pulsation, µ the dynamic viscosity and ρ the density of the suspending fluid respectively, the elliptical motion of fluid particles in a system of out-of phase orthogonal standing waves can induce the rotation of axisymmetric objects [16, 17]. Combined with acous-tical levitation [18, 19], systems of counter-propagating waves have been selected as an advantageous method to induce the rotation of matter in air [20, 21] and are at the basis of the rotation of spherical, cylindrical and anisotropic particles, including cells, in fluids [22-25]. The momentum flux vector, or Poynting vector, of an acoustical vortex (AV) will locally point in the direction of the helicoidal wavefront offering an additional degree of freedom under which it will be exchanged: the OAM of sound. The direct OAM transfer to matter has been observed in air [26, 27] and water [28-30] through absorption or chiral scattering [31]. AVs have recently been used to simultaneously levitate and rotate particles in air [32] but the lack of viscosity leads, however, to an off-axis rotational instability that can be controlled at the expense of the decrease of the net OAM transfer [33]. Nonetheless, the physical mechanisms driving the acoustic torque is unclear. No absorption processes were considered , suggesting that the main mechanisms leading the particle to spin around its axis were overlooked. Additionally , the demonstration of the coexistence of the axial negative gradient force [6] and driving torque is not evident. A negative gradient force, pulling a particle against the acoustical momentum flux, is a crucial feature in the development of acoustical tweezers. In liquids , acoustic radiation forces and torques have experi-arXiv:1804.01272v3 [physics.flu-dyn]
Domaines
Acoustique [physics.class-ph]
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