Recursive algorithm for solving the axial acoustic radiation force exerted on rigid spheres at the focus of acoustic vortex beams

The trapping capability of focused acoustic vortex (FAV) beams along the radial and axial directions has significant potential in biomedical applications. However, analyses based on the acoustic gradient force are only applicable to tiny particles when acoustic scattering is neglected, and the ideal Bessel beams are still difficult to implement in experiments. In the present work, the axial acoustic radiation force (A-ARF) exerted on objects at the focus for FAV beams is calculated based on an annular spherical transducer with a continuous phase spiral. Through a partial wave series expansion, a recursive algorithm based on acoustic scattering is proposed to calculate the acoustic field for FAV beams with arbitrary order. The A-ARF distributions exerted on rigid spheres with respect to k(0)a (the product of the wave number and the sphere radius) are simulated. The results demonstrate that the A-ARF created by on-axis acoustic reflection is mainly manifested as a pushing force for FAV beams of all orders. The pulling force produced by off-axis scattering is more likely to be exerted on spheres with a smaller k(0)a in higher-order FAV beams constructed by narrower transducers. The A-ARF generated by a ring-array of sectorial transducers with more than 16 sources can be estimated from the equivalent result produced by the continuous model. The favorable results demonstrate the validity of the recursive algorithm for solving the A-ARF of FAV beams and the feasibility of experimental ring-arrays of spherical sources, suggesting the potential for the application of dual-directional object manipulation in biomedical fields. Published under an exclusive license by AIP Publishing.