Acoustic manipulation: Bessel beams and active carriers

In this paper, we address the interaction of zero-order acoustic Bessel beams as an acoustic manipulation tool, with an active spherical shell, as a carrier in drug, agent, or material delivery systems, in order to investigate the controllability of exerted acoustic radiation force as the driver. The active body is comprised of a spherical elastic shell stimulated in its monopole mode of vibrations with the same frequency as the incident wave field via an internally bonded and spatially uniformly excited piezoelectric actuator. The main aim of this work is to examine the performance of a nondiffracting and self-reconstructing zero-order Bessel beam to obtain the full manipulability condition of active carriers in comparison with the case of a plane wave field. The results unveil some unique potentials of the Bessel beams in the company of active carriers, with emphasis on the consumed power of the actuation system. This paper will widen the path toward the single-beam robust acoustic manipulation techniques and may lead to the prospect of combined tweezers and fields, with applications in delivery systems, microswimmers, and trapper designs.

Figure 1

(a) Schematic of the problem: A Bessel beam illuminating an active spherical body and exerting radiation force upon it. (b) Configuration of problem: A bilaminate PZT4-steel spherical shell where $a$ and $c$ are the outer and inner radius of the sphere, respectively; $b$ is the interface radius, submerged in water, which is insonified by a Bessel beam of cone angle $\beta$. $V$ is the applied harmonic voltage on the piezoelectric actuator.

Figure 2

Acoustic radiation force function $Y$, versus nondimensional frequency $k_{f}a$, of an aluminum spherical shell with $c/a=0.96$ submerged in water and interacting with a Bessel beam with (a) $\beta ={45}^{\circ }$ and (b) $\beta ={60}^{\circ }$.

Figure 3

Acoustic radiation force function $Y$, of a bilaminate PZT4-steel spherical shell, submerged in water and insonified by a Bessel beam as (a) a function of cone angle, $0^{\circ }\le \beta \le {80}^{\circ }$ and (b) $\beta =0^{\circ },{10}^{\circ },{20}^{\circ },{30}^{\circ },{60}^{\circ }$ versus dimensionless frequency (size factor) $k_{f}a$.

Figure 4

Normalized minimum required voltage to achieve the radiation force of $Y_d=-1$ on the bilaminate PZT4-steel spherical shell, as (a) the amplitude as a function of cone angle, $0^{\circ }\le \beta \le {80}^{\circ }$ and dimensionless frequency (size factor), $k_{f}a$; (b) the phase versus dimensionless frequency (size factor) $k_{f}a$; (c) the amplitude versus dimensionless frequency (size factor) $k_{f}a$, and for selected cone angles, $\beta =0^{\circ },{10}^{\circ },{20}^{\circ },{45}^{\circ },{60}^{\circ }$.

Figure 5

Manipulated radiation force to $Y_d=-1$ for selected ranges of cone angles and size factor as $5^{\circ }<\beta <{15}^{\circ }$, $2<k_{f}a<10$, ${60}^{\circ }<\beta <{75}^{\circ }$, $20<k_{f}a<30$, ${30}^{\circ }<\beta <{45}^{\circ }$, $40<k_{f}a<48$.

Figure 6

Logarithm of the required normalized power to generate $Y_d=-1$ on the sphere: (a) 3D plot as a function of cone angle $\beta$, and dimensionless frequency (size factor); (b) 2D plot as a function of cone angle and for selected size factors $k_{f}a=10,20,30,40,50$.

Figure 7

2D directivity pattern of form function amplitude over the sphere interacting with progressive plane wave: (a) $\beta =0^{\circ }$ and (e) $\beta ={30}^{\circ }$ at $k_{f}a=5$ in the cases of passive sphere (solid curve), canceled radiation force, i.e., $Y_d=0$ (long-dash curve), and $Y_d=-1$ (short-dash curve). 3D directivity pattern of form function amplitude of what came before at ($\beta =0^{\circ }$) and $k_{f}a=5$ in the cases of (b) passive sphere, (c) $Y_d=0$, and (d) $Y_d=-1$. 3D directivity pattern of form function amplitude over the sphere interacting with a Bessel beam of cone angle $\beta ={30}^{\circ }$ at $k_{f}a=5$ in the cases of (f) passive sphere, (g) $Y_d=0$, and (h) $Y_d=-1$. (The gray plane represents the $\theta =0$ plane.)

Figure 8

Asymmetry index versus size factor for the cases of passive sphere (solid curve), canceled radiation force, i.e., $Y_d=0$ (long-dash curve), and $Y_d=-1$ (short-dash curve) for (a) $\beta =0^{\circ }$ and (b) $\beta ={30}^{\circ }$.