Acoustic radiation torques on a pair of fluid viscous cylindrical particles with arbitrary cross-sections: Circular cylinders example

Abstract

The numerical prediction of the radiation torques in acoustofluidics and fluid dynamics applications is essential for the design and the understanding of the underlying physics as it allows quantitative analyses. In this work, closed-form analytical expressions for the acoustic radiation torques arising from multiple scattering effects between a pair of fluid viscous cylindrical particles of arbitrary cross-sections are derived. Plane progressive waves with an arbitrary incidence angle are considered. The multipole expansion method in cylindrical coordinates is used to describe the multiple scattering effects as well as the addition theorem of cylindrical wave functions. An effective incident acoustic field on a particular object is determined and used with the scattered field to derive the analytical expressions for the torques. The mathematical expressions for the radiation torque on each particle are formulated using partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. The analysis shows that the radiation torque expressions depend on the coupled expansion coefficients of both scatterers in addition to an interference factor coupled to the interparticle distance. Numerical examples illustrate the analysis for two fluid viscous circular cylindrical cross-sections immersed in a non-viscous fluid. Computations for the dimensionless radiation torque functions are performed with particular emphasis on varying the angle of incidence, the interparticle distance, and the sizes of the circular particles. Depending on the interparticle distance and incidence angle, the particles can yield rotational neutrality; they become unresponsive (i.e., “invisible”) to the angular momentum transfer caused by multiple scattering and cancellation effects. Moreover, the radiation torque functions can be positive implying a direction of rotation in the counter-clockwise direction, and under some conditions determined by the interparticle distance, angle of incident and particle size, they reserve sign, indicating an opposite spinning in the clockwise direction. This study provides a complete analytical method and computations of the acoustic radiation torques in multiple acoustic scattering by a pair of fluid viscous scatterers. The results can be used as a priori information in the design of acoustofluidic devices and other applications involving particle rotation and handling.