Acoustic Radiation Force and Torque Acting on Asymmetric Objects in Acoustic Bessel Beam of Zeroth Order Within Rayleigh Scattering Limit

Abstract

Acoustic momentum exchange between objects and the surrounding fluid can be quantified in terms of acoustic radiation force and torque, and depends on several factors including the objects’ geometries. For a one-dimensional plane wave type, the induced torque on the objects with arbitrary shape becomes a function of both, direct polarization and Willis coupling, as a result of shape asymmetry, and has only in-plane components. Here, we investigate, in the Rayleigh scattering limit, the momentum transfer to objects in the non-planar pressure field of an acoustic Bessel beam with axisymmetric wave front. This type of beam is selected since it can be practically realized by an array of transducers that are cylindrically arranged and tilted at the cone angle β which is a proportionality index of the momentum distribution in the transverse and axial propagation directions. The analytical expressions of the radiation force and torque are derived for both symmetric and asymmetric objects. We show the dependence of radiation force and torque on the characteristic parameters β and radial distance from the beam axis. By comparing against the case of a plane travelling plane wave, zero β angle, we demonstrated that the non-planar wavefront of a zeroth order Bessel beam causes an additional radial force and axial torque. We also show that, due to Willis coupling, an asymmetric object experiences greater torques in the θ direction, by minimum of one order of magnitude compared to a plane travelling wave. Further, the components of the partial torques owing to direct polarization and Willis coupling act in the same direction, except for a certain range of cone angle β. Our findings show that a non-planar wavefront, which is quantified by β in the case of a zeroth-order Bessel beam, can be used to control the magnitude and direction of the acoustic radiation force and torque acting on arbitrarily shaped objects, implying that the wavefront should be adjusted according to the object’s shape to impart acoustic momentum in all directions and achieve a desired acoustophoretic response.