T -matrix evaluation of three-dimensional acoustic radiation forces on nonspherical objects in Bessel beams with arbitrary order and location

Abstract

Acoustical radiation force (ARF) induced by a single Bessel beam with arbitrary order and location on a nonspherical shape is studied with the emphasis on the physical mechanism and parameter conditions of negative (pulling) forces. Numerical experiments are conducted to verify the T-matrix method (TMM) for axial ARFs. This study may guide the experimental set-up to find negative axial ARF quickly and effectively based on the predicted parameters with TMM, and could be extended for lateral forces. The present work could help to design acoustic tweezers numerical toolbox, which provides an alternate to the optic tweezers.

Three-Dimensional Trapping and Dynamic Axial Manipulation with Frequency-Tuned Spiraling Acoustical Tweezers: A Theoretical Study

“…The excitation frequencies are selected near the designed frequency f 0 = 40 MHz from f = 32 MHz to f = 45 MHz. In the regime of[37,43] MHz for (a) the Pyrex sphere, and of[37,44] MHz for (c) the cell, the axial trapping position z trap agrees exactly with the linear fitting (blue solid line). The effective restoring forces F z drop when the excitation frequencies are away from f 0 .…”

“…The analysis shows that cells can also be moved, while keeping a 3D trap when the frequency is tuned in the range f = [32,45] MHz. This leads to a maximum displacement range of about 650 μm with a linear trend observed in the regime f = [37,44] MHz, which is more than 57 times the size of the cell, and 16 times the wavelength. The trapping radiation force is maximum at the designed frequency f 0 = 40 MHz and drops with the excitation frequency away from f 0 , which is similar to the Pyrex particle case.…”

“…This agrees with the mathematical fact that a Bessel function can be written as the addition of Hankel functions of the first and second kinds (with a ratio of 1/2). To coincide with the radiation force derivations [44,56], the time harmonic here is chosen as e (−iωt) so that the converging Hankel vortex is described by the spherical Hankel function of the second kind h (2) n . An ideal converging Hankel spherical vortex is described in spherical coordinates (r, θ , ϕ) as [51] p * (r, θ , ϕ) = p 0 h (2) n (kr)P m n (cos θ)e i(mϕ−ωt) , (…”

“…With tweezers based on cylindrical vortices, (i) the selectivity remains limited [23] since the beam is only focused laterally, leading to spurious secondary rings whose intensity decreases as 1/r 2 ; (ii) particles can only be pushed or pulled [41][42][43][44] but not trapped in the axial direction, owing to the invariance of the intensity profile in this direction. Three-dimensional tweezers require that the particle is subjected to a restoring acoustic radiation force from all directions at the same time.…”

Particle Assembly with Synchronized Acoustic Tweezers

“…More recently, it was shown both theoretically and experimentally [21][22][23], that acoustical vortices can also be used to control the rotation of particles by using the pseudo-angular momentum carried by these helical structures. It is also noteworthy to underline that the calculations of the force and torque exerted by a vortex beam, initially calculated for spherical particles have been recently extended to nonspherical particles with the use of the T-matrix method [17,24,25]. * michael.baudoin@univlille.fr Experimentally, the approaches for the synthesis of acoustical vortices can be divided into three categories: The first one, that we will refer as the active array method, relies on arrays of transducers whose phase and/or amplitude can be tuned to synthesize a vortex in the surrounding fluid [1,4,7,19,20,22,[26][27][28][29][30][31].…”