Viscous torque on spherical micro particles in two orthogonal acoustic standing wave fields

Abstract

This paper reports the experimental results of the acoustic rotation of spherical micro particles because of two orthogonal standing waves. When the standing waves are excited at equal frequency but with a phase shift between two external voltage signals there is an acoustic streaming around the particles. This streaming is due to a time averaging of the acoustic wave field and produces a nonzero viscous torque on the particles, driving them to rotate. The work investigates the micro-particle rotation due to the viscous torque and predict the particle's steady state rotational velocity. The previous theoretical discussions [Nyborg, J. Acoust. Soc. Am. 85, 329-339 (1958); Lee and Wang, J. Acoust. Soc. Am. 85, 1081-1088 (1989)] of the viscous torque on a non-rotating sphere are expanded to allow free rotations. The analytical calculations provide a deeper understanding of the viscous torque and explain the experimental observations of rotating particles. A macroscopic experimental device is designed to provide the necessary boundary conditions for the viscous torque to rotate spherical particles. The experiments not only show good agreement with the analysis, but also demonstrate that the viscous torque due to acoustic streaming may dominate for the case of near-spherical particle dynamics.

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

“…Therefore, measuring their value for our spheres could largely improve the torque balance. Importantly, the fact that absorption within the sphere is the dominating driving mechanism contrasts with previous results restricting the description to the viscous boundary layer around the sphere [23,25] or neglecting absorption processes entirely [33]. Finally, within the particle size range considered theoretically, the large contribution of the quadrupolar oscillation mode, even for a/λ < 0.05 (see the close view in Fig.2c), is in contradiction with the common assumption that it can be neglected in the long wavelength (Rayleigh) scattering regime (a/λ 1).…”

“…The angular speed Ω = 2π × f r 70 rad/s suggests that the driving acoustic torque Γ on the spheres is balanced by the drag Γ D = −8πµa 3 Ω −10 pN.m acting in the opposite direction in a fluid of density ρ = 1000 kg/m 3 and viscosity µ = 1mP a · s for which the low Reynolds number approximation Re= a 2 Ω/ν 1 holds. Note that inertial effects acting in a time scale of a few milliseconds [23] are unresolved with this setup.…”

Controlled rotation and translation of spherical particles or living cells by surface acoustic waves

“…In addition, it is shown that the high frequency used in the experiment (above 35 MHz) allows tenths of micron size particles to be simultaneously put in motion in the same minute volume. These characteristics open new perspectives for labs on chips since torques used up to now to manipulate objects were obtained under action of bulk acoustic waves (BAW) 18 or evanescent waves 19 in the MHz range. Compared to optical tweezers, the transfer of momentum from acoustic streaming is an additional tool to generate torques for particles of various compositions and shapes and which have no equivalent in optics.…”

Controllable Micro-Particle Rotation and Transportation Using Sound Field Synthesis Technique

“…Continuous rotation of tile, syringe and other axisymmetric objects has been realized using acoustic vortex beam that is generated by thermoacoustic or individually addressed transducers [28][29][30][31][32]. Another way to rotate the micro-particle is employing the viscous torque resulted from the acoustic streaming in the viscous boundary layer around the particle [33][34][35]. The above-mentioned two methods are applicable to continuous rotation, especially spherical object, but are unable to stop at certain angular position [27,28,[33][34][35].…”

“…Another way to rotate the micro-particle is employing the viscous torque resulted from the acoustic streaming in the viscous boundary layer around the particle [33][34][35]. The above-mentioned two methods are applicable to continuous rotation, especially spherical object, but are unable to stop at certain angular position [27,28,[33][34][35].…”