Acoustic radiation force of high-order Bessel beam standing wave tweezers on a rigid sphere |
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Authors: | FG Mitri |
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Institution: | Mayo Clinic, College of Medicine, Department of Physiology and Biomedical Engineering, Ultrasound Research Laboratory, 200 First Street SW, Rochester MN 55905, United States |
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Abstract: | Background and objectiveParticle 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 ?.MethodThe 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,β,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 β of the wave-number components and the order m of the HOBB.ResultsNumerical 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,β,m) show that the force is generally directed to a pressure node when m is a positive even integer number (i.e. YJm,st(ka,β,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,β,m)<0).ConclusionAn 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. |
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Keywords: | PACS: 43 20 +g 43 25 +y 47 35 Rs |
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