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


METHODS
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 YJm,st(ka,beta,m)<0), 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 YJm,st(ka,beta,m)<0), show that the force is generally directed to a pressure node when m is a positive even integer number (i.e. YJm,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. YJm,st(ka,beta,m)<0).


CONCLUSIONS
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.
Mitri
F G
FG
Department of Physiology and Biomedical Engineering, Ultrasound Research Laboratory, Mayo Clinic, College of Medicine, Rochester MN 55905, United States. mitri@ieee.org
D000162:Acoustics; D003198:Computer Simulation; D008846:Micromanipulation / Q000379:methods*; D008863:Microspheres; D008956:Models, Chemical; D009038:Motion; D053758:Nanoparticles / Q000737:chemistry* / Q000528:radiation effects*