Radiation torque, streaming, and viscous absorption due to orthogonal waves in slightly viscous fluids

Abstract

Torque generated by orthogonal waves in slightly viscous fluids is analyzed to explore its connection with the near-boundary viscous absorption and streaming [Zhang and Marston, J. Acoust. Soc. Am. 131, 2917–2921 (2014)]. The analysis is based on a viscous correction and beam superposition of vortex fields. The analysis reports an approximation for the torque on a compressible small solid sphere and the viscous power absorption [Eqs. (15) and (21) in Zhang and Marston]. The torque expression in the dense sphere limit recovers prior expressions using near-boundary flow and streaming analyses: [Busse and Wang, J. Acoust. Soc. Am. 69, 1634–1638 (1981)] and [Lee and Wang, J. Acoust. Soc. Am. 85, 1081–1088 (1989)]. Our analysis extends prior results to give the torque on small compressible solid spheres of finite mass. The torque does not depend explicitly on the compressibility of the sphere, but does depend on the density of the sphere. Our analysis also gives the proportional relationship between the torque and the near-boundary viscous absorption. The results are generalized to cases of standing orthogonal waves and acoustic vortex fields, and other small axisymmetric obstacles such as circular cylinders and disks. [Work supported by the 2013-14 F. V. Hunt Postdoctoral Fellowship (Zhang) and by ONR (Marston).]