A Study Of The Axial Acoustic Radiation Force In An Axially Rigid Sphere In A Focused Vortex Sound Field

Since Ashkin won the 2018 Nobel Prize in Physics by optical tweezers,the manipulation of separated objects by using various kinds of physical methods has become a research hotspot.With the spiral phase wavefront and the center phase singularity,vortex beams can be used to capture,push-pull and rotate objects,and thus show great application prospects in the field of non-contact object manipulation.For the existing limitations of the object size and penetration depth,the construction and application of acoustic vortex(AV)beams have been investigated.The unique annular pressure distribution and the orbital angular momentum(OAM)of AV beams can be applied to realize the rotational manipulation and the center accumulation of objects from um to mm scale,which can also be applied in targeted drug delivery and show prosperous prospect in medical diagnoses and treatments.Because of the spiral phase of AV beams,existing studies focus mainly on the cross-sectional performance of object manipulations with less attention on the axial properties,which restricts the axial positioning of the precise object manipulation by AV beams.Whereas,some conclusions based on the acoustic gradient force(AGF)can only be applied for tiny particles by ignoring acoustic scattering.In order to further analyze the influence of acoustic scattering in AV beams and break through the size limitation of on-axis object manipulations,the axial acoustic radiation force(ARF)is studied by using non-AV beams or ideal Bessel beams.However,they are difficult to be implemented in experiments,and the theoretical conclusion on the axial ARF lacks of practical applications.Therefore,the construction of experiment applicable AV beams shows its great significance in future studies.To solve the limitation of the axial ARF for AV beams,an annular spherical transducer model with a continuous phase spiral is proposed to construct focused AV(FAV)beams of arbitrary orders,and the axial ARF exerted on objects is analyzed based on acoustic scattering.With the partial wave series expansion(PWSE),the incident and scattered acoustic velocity potential of FAV beams are derived,and the formulae of the axial ARF exerted on on-axis elastic/rigid spheres are obtained.To achieve the axial manipulation of small rigid particles along the axial direction,distributions of the axial ARF exerted on rigid spheres with respect to k₀a(product of the wave number and the sphere radius)and?_inner are simulated.The results indicate that small particles can form pushing and pulling forces alternately along the beam axis,while the pulling areas formed by large particles are mainly located in the pre-focal region.With the increase of the topological charge of the FAV beam,the axial ARF decreases,including the pushing and pulling forces.Also,with the increase of?_inner,the distribution of the axial ARF show an expanding trend from the focal point with a significant decreased number of the pulling and pushing regions and an increased axial width.Results demonstrate that the frequency of the direction variation of the axial ARF is small for FAV beams constructed by a narrower transducer with a larger hollow core,which is conducive to the stable capture of particles.In order to enhance the capability of object trapping,FAV beams are designed to concentrate acoustic energy to the focal region in a limited volume.The acoustic fields of FAV beams with l=0 to 3 are simulated,and the axial ARFs exerted on rigid spheres are calculated for transducers with various configurations.Furthermore,an analytical recursive solution for FAV beams is derived based on the geometric focusing characteristics,followed by the calculations of the axial ARFs exerted on spheres with respect to?_inner and R₀ for transducers with various configurations.It is proved that,for rigid spheres located at focus in FAV beams,the increase of the topological charge,the increase of?_inner and the decrease of R₀ all contribute to a decreasing axial ARF.The FAV beam of an arbitrary order can produce two pulling force areas in the k₀a-?_innerspace,which correspond to a smaller and larger k₀a,respectively.The 1^st pulling force is more likely to exert on spheres with a smaller k₀a for the FAV beam of a higher-order constructed by a transducer with a bigger hollow core,and the 2^nd pulling force can also be formed on larger spheres for the focused AV beam generated by a much narrower transducer.In conclusion,based on the theory of acoustic scattering,the acoustic field of FAV beams formed by the annular spherical transducer is employed to study the pulling and pushing forces exerted on on-axis spherical objects.The design breaks through the limitation of manipulating small particles using ideal high-order Bessel beams,which proves the feasibility of generating FAV beams by the phase-coded approach with the ring-array of discrete sources.The feasibility of three-dimensional stable manipulation for on-axis rigid spheres can be realized by the axial AGF,providing the theoretical basis for the acoustic manipulation in biomedical applications.