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