Acoustic radiation force of high-order Bessel beam standing wave tweezers on a rigid sphere

Background and objective: Particle manipulation using the acoustic radiation force of Bessel beams is an active field of research. In a previous investigation, [F.G. Mitri, Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers, Annals of Physics 323 (2008) 1604-1620] an expression for the radiation force of a zero-order Bessel beam standing wave experienced by a sphere was derived. The present work extends the analysis of the radiation force to the case of a high-order Bessel beam (HOBB) of positive order m having an angular dependence on the phase phi. Method: The derivation for the general expression of the force is based on the formulation for the total acoustic scattering field of a HOBB by a sphere [F.G. Mitri, Acoustic scattering of a high-order Bessel beam by an elastic sphere, Annals of Physics 323 (2008) 2840-2850; F. G. Mitri, Equivalence of expressions for the acoustic scattering of a progressive high order Bessel beam by an elastic sphere, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 56 (2009) 1100-1103] to derive the general expression for the radiation force function Y(Jm),(st)(ka,beta,m), which is the radiation force per unit characteristic energy density and unit cross-sectional surface. The radiation force function is expressed as a generalized partial wave series involving the half-cone angle beta of the wave-number components and the order m of the HOBB. Results: Numerical results for the radiation force function of a first and a second-order Bessel beam standing wave incident upon a rigid sphere immersed in non-viscous water are computed. The rigid sphere calculations for Y(Jm),(st)(ka,beta,m) show that the force is generally directed to a pressure node when m is a positive even integer number (i.e. Y(Jm),(st)(ka,beta,m) > 0), whereas the force is generally directed toward a pressure antinode when m is a positive odd integer number (i.e. Y(Jm),(st)(ka,beta,m) < 0). Conclusion: An expression is derived for the radiation force on a rigid sphere placed along the axis of an ideal non-diffracting HOBB of acoustic standing (or stationary) waves propagating in an ideal fluid. The formulation includes results of a previous work done for a zero-order Bessel beam standing wave (m = 0). The proposed theory is of particular interest essentially due to its inherent value as a canonical problem in particle manipulation using the acoustic radiation force of a HOBB standing wave on a sphere. It may also serve as the benchmark for comparison to other solutions obtained by strictly numerical or asymptotic approaches. (C) 2009 Elsevier B. V. All rights reserved.