Direct measurement of small spherical particle rotation driven by the acoustic viscous torque

We report a new method for measuring fast rotations up to 13500 rpm of micrometer sized spherical particles utilizing an optical trap [A. Lamprecht et al., Lab Chip 16, 2682–2693 (2016)]. In an acoustofluidic flow cell, a single spherical particle rotates due to the acoustic viscous torque produced by two phase-shifted orthogonal standing waves. The Lorentzian power spectrum of the trapped and rotating particle has additional peaks at frequencies that correlate with its rotational speed. In one of our experiments the thickness of the viscous boundary layer δ around the particle is roughly as large as the particle radius R itself. We use a water glycerol mixture with a dynamic viscosity of μ_ff = 0.06 Pa s to increase δ. Our experiment validates recent numerical research that predicts power rotational speeds for the case δ ≈ R compared to the simplified theoretical formula valid for δ ≪ R [Lee and Wang, J. Acoust. Soc. Am. 85, 1081–1088 (1989)].