Acoustic radiation torque of a viscoelastic sphere in a zero-order Mathieu beam

The exact expressions of the three-dimension acoustic radiation torque (ART) of a viscoelastic sphere arbitrarily positioned in a zero-order Mathieu beam (zMB) are derived in this paper. The effects of the ellipticity parameters, half-cone angles, dimensionless frequency, and particle position on the acoustic radiation torques of the spherical particle are studied. Simulation results show the axial ART is zero for an arbitrarily positioned viscoelastic PE sphere in a zMB, while for the x or y axis ART, it varies significantly with the particle position and beam parameters. For certain combinations of beam offset and parameters, axial and transverse torques alternate between positive and negative values as the half-cone angle varies. When ka is away from the resonance frequency, the value of the torque is approximately 0.001, which means the torque is small and the particle can be rotated in a uniform angular acceleration. Moreover, ART shows symmetrical about beam center when the offset is less than one wavelength. A finite element model was established to verify the theory and the comparative results agreed with each other except for the values of ART at the first resonant frequency, which is related to the absorption of the particles. The study helps to better understand the potential mechanism of the particle rotation manipulation in a zMB.