Reversals of Acoustic Radiation Torque in Bessel Beams Using Theoretical and Numerical Implementations in Three Dimensions

Zhixiong Gong, Philip L. Marston, and Wei Li

Phys. Rev. Applied 11, 064022 – Published 11 June 2019

Abstract

Acoustic radiation torque (ART) plays an important role in the subject of acoustophoresis, which could induce the spinning rotation of particles on their own axes. The partial wave series method (PWSM) and T matrix method (TMM) are employed to investigate the three-dimensional radiation torques of both spherical and nonspherical objects in a single Bessel beam over broader frequencies (from Rayleigh scattering to geometric-optics regimes), with emphasis on the parametric conditions for torque reversal and the corresponding physical mechanisms. For elastic objects, the dipole, quadrupole, and even several higher-scattering modes are dominant to induce the axial ARTs beyond the Rayleigh limit with a relatively large offset from the particle centroid to the beam axis in Bessel beams. The reversals appear with parametric conditions (including wave number, cone angle, and offset) for the extrema or null values of the corresponding cylindrical Bessel functions. The reversal of transverse ART from a rigid nonspherical particle is also investigated in an ordinary Bessel beam and the geometrical surface roughness is briefly studied for the effect on the radiation torques. This suggests the possibility of acoustic tweezers controlling the spinning motion of particles within and beyond the Rayleigh limit.

Received 10 January 2019
Revised 1 May 2019

DOI:https://doi.org/10.1103/PhysRevApplied.11.064022

Physics Subject Headings (PhySH)

Acoustic interactions Beam techniques Microfluidics Particle-laden flows Single-particle dynamics

Acoustic techniques Ultrasound techniques

Particles & FieldsPhysics of Living SystemsAccelerators & Beams

Authors & Affiliations

Zhixiong Gong^1,2,†, Philip L. Marston², and Wei Li^1,*

¹School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
²Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814, USA

^*hustliw@hust.edu.cn
^†Present address: Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Polytechniques Hauts-de-France, UMR 8520-IEMN, International laboratory LIA/LICS, F-59000 Lille, France.

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Vol. 11, Iss. 6 — June 2019

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Images

Figure 1
Schematic of an arbitrarily shaped object in a nonviscous fluid illuminated by a Bessel beam with arbitrary topological charge and location.
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Figure 2
The two-dimensional axial acoustic radiation toque pattern of a viscoelastic solid sphere $(b / a = 0)$ vs $(k a, β)$ with $k a$ the dimensionless frequency and $β$ the cone angle of the first-kind Bessel beam (order $M = 1$ ). The modulus of the dimensionless resonance backscattering form function (see text) from the solid sphere by an ordinary plane wave is scaled by a ratio of 20 with the magenta solid line. The frequencies of the quadrupole $(n = 2)$ and octupole $(n = 3)$ scattering are marked out where the axial ART peaks occur.
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Figure 3
The two-dimensional axial acoustic radiation toque patterns for (a–c) spherical shell with aspect ratio $b / a = 0.99$ and (d–i) solid sphere with $b / a = 0$ . The first-order for (a–f) and second-order for (g–i) Bessel beams are considered with off-axis incidence (The offset is in the length unit of meter.): $(x_{0}, y_{0}) = (π / k a, π / k a)$ for the first, $(x_{0}, y_{0}) = (2 π / k a, 2 π / k a)$ for the second, and $(x_{0}, y_{0}) = (3 π / k a, 3 π / k a)$ for the third column, respectively. The numbers of scattering modes $(n = 2, 3, 4)$ are also marked out in panels (e) and (f) at frequencies where the axial ART reverses.
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Figure 4
(a) The two-dimensional axial ARTs pattern of a PE solid sphere $(b / a = 0)$ illuminated by the first-order $(M = 1)$ Bessel beam with a fixed offset , $(x_{0}, y_{0}) = (5, 5)$ . (b) The cylindrical Bessel function of the first kind versus $k_{r} R_{0} = k \sin β R_{0}$ . The ART reversals occur on the $β - k a$ lines with the parameters of $β$ and $k a$ , which makes $J_{1} (k \sin β R_{0})$ the extremum or zero values.
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Figure 5
(a) The schematic of a rigid spheroid (aspect ratio $b / a = 0.5$ ) centered on the axis of the zeroth-order Bessel beam $(M = 0)$ with the incident polar angle $θ_{i}$ . (b, c) the transverse ARTs $Γ_{y}$ curves versus the incident angle $θ_{i}$ in the Rayleigh $(k a = 0.0628)$ and geometric-optics regimes $(k a = 10)$ . Different cone angles are selected with $β = 0^{\circ}$ (plane wave case) and $β = 30^{\circ}$ , $45^{\circ}$ , $60^{\circ}$ , and $80^{\circ}$ . (d) The geometrical ray diagram of the zeroth-order Bessel beam with oblique incidence to qualitatively explain the reversal of the transverse $ART Γ_{y}$ .
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Figure 6
Similar to Figs. 5 and 5 except that the aspect ratio of the rigid spheroid is $b / a = 0.8$ with rough surfaces at dimensionless frequencies (a) $k a = 0.0628$ and (b) $k a = 10$ , respectively. The rough spheroid is still rotationally axisymmetric. The two-dimensional rough spheroids are depicted at the bottom with the relative roughness $δ / a = 0$ (smooth spheroid), 0.01, 0.03, and 0.05.
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