A theoretical study of the feasibility of acoustical tweezers: Ray acoustics approach

Abstract

The optical tweezer has been found to have many biomedical applications in trapping macromolecules and cells. For the trapping mechanism, there has to be a sharp spatial change in axial optical intensity and the particle size must be much greater than the wavelength. Similar phenomenon may exist in acoustics. This work was undertaken to demonstrate theoretically that it is possible to acoustically trap particles near the focal point where most of the acoustic energy is concentrated if certain conditions are met. Acoustic force exerted on a fluid particle in ultrasonic fields is analyzed in a ray acoustics regime where the wavelength of acoustic beam is much smaller than the size of the particle. In order to apply the acoustical tweezer to manipulating macromolecules and cells whose size is in the order of a few microns or less, a prerequisite is that the ultrasound wavelength has to be much smaller than a few microns. In this paper, the analysis is therefore based on the field pattern produced by a strongly focused 100 MHz ultrasonic transducer with Gaussian intensity distribution. For the realization of acoustic trapping, negative axial radiation force has to be generated to pull a particle towards a focus. The fat particle considered for acoustic trapping in this paper has an acoustic impedance of 1.4 MRayls. The magnitude of the acoustic axial radiation force that has been calculated as the size of the fat particle is varied from 8lambda to 14lambda. In addition, both Fresnel coefficients at various positions are also calculated to assess the interaction of reflection and refraction and their relative contribution to the effect of the acoustical tweezer. The simulation results show that the feasibility of the acoustical tweezer depends on both the degree of acoustic impedance mismatch and the degree of focusing relative to the particle size.

Manipulation of particles in two dimensions using phase controllable ultrasonic standing waves

“…Initially, these 'acoustical tweezers' used opposing focused transducers to produce a trap at their, common, focal point (Wu 1991). More recent theoretical (Lee et al 2005;Lee & Shung 2006) and experimental (Lee et al 2009) work has demonstrated the feasibility of using a single focused transducer working at a high frequency (30 MHz) to trap particles much larger than a wavelength in diameter against a surface. Particle manipulation has been achieved by moving the transducer and hence the focal position.…”

Acoustic radiation force on a rigid cylinder in a focused Gaussian beam

“…The problem of acoustic radiation force on rigid and elastic spherical/cylindrical particles in an unfocused sound field has been the subject of many studies [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. The very first studies on acoustic radiation force are those by King [8], Embleton [21], Gor'kov [22] and Nyborg [23], in which, several theoretical models for the calculation of the radiation force on spherical particles in different acoustical fields had been developed [24].…”

“…While the experimental activities have been mainly concerned with the application of standing waves and Gaussian beams [1][2][3][4][5][6][7], a better understanding of the nature of the problem has been gained through the development of a number of mathematical models using King's derivation of the exerted radiation force and the standard wave decomposition method [8][9][10][11][12][13][14][15][16][17][18][19]. The problem of acoustic radiation force for Gaussian beams, on the other hand, has often been dealt with using ray acoustics method; see for example [20]. In the next paragraphs, we shall provide a review of these two methods and the application of Gaussian beams for acoustic manipulation of fine particles.…”

“…In some recent experimental and theoretical investigations [20,[41][42][43], it has been shown that Gaussian beams can effectively be used for axial and transverse entrapment of miro-and nano-scale particles. Preliminary analytical studies of Lee et al [20] and Lee and Shung [41] using ray acoustics approach also showed the feasibility of acoustic tweezing and trapping of arbitrarily located spherical objects using a highly focused high frequency Gaussian beam. These studies have shown that Gaussian beams can be used for trapping particles in both axial and transverse directions, although the latter is expectedly much easier.…”

Focused high frequency needle transducer for ultrasonic imaging and trapping

“…In addition, a focused needle ultrasonic transducer offers more flexibility in carrying out single beam acoustic trapping experiments given the extremely congested environment in the small area within which the experiments are performed. 4 For a miniaturized transducer, piezoelectric materials with high dielectric constant are more desirable since the electrical impedance of a transducer is inversely proportional to the dielectric constant of the piezoelectric material. 5 Comparing with other materials, Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 (PMN-PT) single crystal is a promising candidate to build small transducers because of its high dielectric constant (1000-5000).…”