Interaction between particles and bubbles driven by ultrasound: Acoustic radiation force on an elastic particle immersed in the ideal fluid near a bubble
Introduction
It has developed an important technology for the manipulation of small particles (e.g. atoms, cells, organelles, DNA, etc.) by using ultrasound wave. The potential application can be extent to many fields, such as biomedical engineering, materials science, and nanotechnology [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. Based on the sound scattering theory, the pressure field around particles is influenced by the distribution of particles and other objects, and particles will be subjected to acoustic radiation force because of the nonlinear features of particle-wave interactions in the acoustic wave field, which can be interpreted as the time-averaged second-order force on the surface of the particles [11]. Radiation force plays an important role in acoustic manipulation, acoustic tweezers and acoustic suspension, and it is able to express as a pulling or pushing effect on objects.
According to King's derivation method, further mathematical models have been developed in standing wave, Gaussian beam, Bessel wave, Mathieu wave and plane wave field [12], [13], [14], [15], [16], [17], [18], [19], [34], [35], [36], [37], [38], [39], which have gained a better understanding of the nature of the problem. Hasegawa et al. [20], [21], [22] investigated the acoustic radiation pressure of an elastic particle, cylinder and spherical shell in the plane wave sound field and numerical calculations showed that the radiation force functions were affected distinctly by the material properties. Doinikov [23], [24], [25] developed the theory of the radiation force acting on a spherical particle in viscous media. Researches revealed that the forces acted on particles could be negative in the standing wave field of inviscid or viscid fluid [26], [27], [28]. Using boundary-layer theory [29], [30], models have been developed to analyze the suspension of a single small spherical particle (a thermoviscous fluid droplet or a thermoelastic solid particle), and it proves that the thermoviscousity theory leads to profound consequences for the radiation force. Miri [31] computed the radiation force on an air bubble, a hexane, a red blood and mercury fluid spheres in water by use of the partial wave series, and results showed that the dynamics of air bubble would be significantly altered on the axis of the wave beam. The radiation force on a shell or cylinder near the boundary is more complicated [32], [33]. Due to the interaction between plane waves and regulated object, pushing and pulling forces could be generated by controlling the particle size or acoustic frequency. However, it is difficult to generate a sufficiently large and stable pulling force.
Acoustic radiation force of a single spherical particle has been investigated experimentally and theoretically. The effects of the interaction between bubbles and particles in liquid, however, have been less thoroughly investigated in the literature. In actually, when ultrasonic wave propagates through the liquid, gas nuclei could develop into bubbles which might affect the motion of the neighboring particle. Therefore, it is necessary to investigate the influence on acoustic radiation force of particles caused by the oscillating bubble in the ultrasonic field. Based on the theory of acoustic scattering, the interaction between a particle and a bubble will be considered, and the acoustic radiation force acting on an elastic particle is derived in a plane wave field.
Section snippets
Scattering on an elastic particle with a plane wave
For simplicity, a system composed by a suspended elastic particle and a bubble in the unbounded ideal liquid is shown in Fig. 1. The outer radius of the particle and bubble are denoted by and respectively, and is their separate distance, as shown in Fig. 1. Two local spherical coordinates originate at their centers. An incident plane wave propagates along the positive direction of the polar x-axes.
In the local spherical coordinates, the velocity potential of incident
Acoustic radiation force on an elastic particle with a plane wave
In the unbounded ideal liquid, the acoustic radiation force function on the elastic particle surface can be written as [1], [2]where is pressure-flux, and are the radial and tangential vectors of the particle surface, respectively, is the speed of the surrounding fluid, is the surface of particle at its equilibrium position, the radial component of the particle velocity and tangential component
Numerical results and discussion
According to Eq. (22), the acoustic radiation force function on a floating particle neighboring a bubble is analyzed numerically in water. The parameters are set to = 1500 m/s, = 1000 kg/m3, and the others used in our calculations are listed in Table 1 [20].
The acoustical radiation force functions of single rigid particle, single elastic particle, a rigid particle-bubble system, and an elastic particle-bubble system are analyzed numerically by use of Eq. (22). To check
Conclusion
It is important to investigate acoustic manipulation of particles in complex liquid. In this paper, a coupled scattering model is proposed to investigate the sound scattering around a particle-bubble system. The sound scattering field around the elastic particle is described theoretically by considering the interaction between the two objects. The analytical solution of the acoustic radiation force is presented through King’s method for the elastic particle. Subsequently, it is very easy to
CRediT authorship contribution statement
Kangyi Feng: Conceptualization, Methodology, Formal analysis, Software, Writing - original draft, Writing - review & editing, Validation, Data curation. Chenghui Wang: Conceptualization, Methodology, Formal analysis, Writing - original draft, Writing - review & editing, Software, Validation. Runyang Mo: Conceptualization, Validation, Formal analysis, Writing - review & editing. Jing Hu: Conceptualization, Supervision, Formal analysis, Validation. Sai Li: Software, Validation, Resources, Funding
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the National Nature Science Foundation of China (Grant Nos. 11974232 and 11727813).
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