Acoustical pulling force of a limited-diffracting annular beam centered on a sphere

A rigorous method is developed to investigate the generation of a negative (attracting) force acting in the opposite direction of wave propagation using a limited-diffracting single annular piezo-ring transducer. Based on the Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions, the expression for the incident velocity potential field (which is an exact solution of the Helmholtz equation) is derived analytically, and exact closed-form partial-wave series expansions for the incident and scattered fields are obtained without any approximations. The total (incident + scattered) field expression is used to evaluate the time-averaged acoustic radiation force (ARF) on a sphere centered on the beam's axis in a nonviscous fluid. Numerical predictions for the scattering and ARF performed with particular emphasis on the annular-ring's radial thickness, the distance separating the sphere from the acoustic source, the size of the transducer, as well as the sphere's elastic properties, reveal some conditions where a pulling axial ARF directed toward the annular ring-source surface arises. The simplicity and reliability of the annular-ring geometry demonstrated here provides a substantial solution with widespread applications in the experimental design of acoustical limited-diffracting beams operating over an extended axial depth-of-field for contactless and dexterous particle manipulation.