Interparticle acoustic radiation force between a pair of spherical particles in a liquid exposed to a standing bulk acoustic wave

Abstract

We elucidate the interparticle force between a pair of particles suspended in a liquid exposed to a standing bulk acoustic wave. A three-dimensional model based on the perturbation technique and tensor integral method is employed to predict the interparticle force by subtracting the time-averaged primary radiation force due to the scattering effect from the time-averaged total radiation force due to combined scattering and re-scattering effects. The results show that irrespective of the sizes of particles at the nodal plane, interparticle force Fs* is attractive and symmetric and scales with the product of wavenumber (k) and interdistance (δx) as Fs*∼kδx−4. By studying the interparticle force between a pair of particles located out of the nodal plane, we unravel that the interparticle force is independent of their positions and depends on the horizontal (parallel to the nodal plane) and vertical interdistances. Our results reveal interparticle force changes from attractive to repulsive at a critical interdistance, attributed to the competition between time-averaged second-order pressure and velocity terms. We found that for a pair of particles parallel to the nodal plane, the interparticle force is independent of their distance from the nodal plane. Considering the total radiation force as the sum of the interparticle force, axial primary force, and drag force, we demonstrate a methodology for experimental quantification of the interparticle force. The interparticle force predicted from the model shows good agreement with experimental data (within 5%). Our study sheds light on interparticle forces that will facilitate more accurate estimation of forces on particles in an acoustic field.

Mechanistic Insights and Therapeutic Delivery through Micro/Nanobubble-Assisted Ultrasound

“…This mechanical force is called acoustic radiation force (ARF), which includes primary forces and secondary forces [ 76 ]. The primary forces act on single particles [ 77 ], but secondary forces are the forces that occur between particles [ 78 ]. Besides, the primary forces mainly push the particles to migrate in the sound field, while secondary forces mainly cause the aggregation and dispersion of particles [ 79 , 80 ].…”

Acoustofluidics 24: theory and experimental measurements of acoustic interaction force

“…[5][6][7][8]15 The acoustic interaction force has been studied theoretically, [4][5][6]8,15,37 numerically, 7,11,21,38 and experimentally. 9,10,12,37,[39][40][41] For a pair of objects, the acoustic interaction force has a component that acts in the centre-tocentre direction, inducing attraction or repulsion similar to electrostatic forces between charges. In addition, it can have a component in the tangential direction, which induces coupled rotational motion.…”

“…The change of interaction force with respect to relative distance (d) between a source n and target q, as shown in Fig. 2(a), can be derived for the special case of a pair of identical particles along or normal to the propagation direction of a plane wave, 6 corresponding to the direction of the pressure gradient, and has been shown 6,40 to be inversely proportional to (kd). 4 Furthermore, in this force potential formulation, the fully coupled scattering effects, up to the monopole-dipole approximation, are included in the calculation of the scattered fields of other objects, i.e., p n and v n in eqn (28), while α q and β q only depend on the density and compressibility ratios.…”

“…4 Furthermore, in this force potential formulation, the fully coupled scattering effects, up to the monopole-dipole approximation, are included in the calculation of the scattered fields of other objects, i.e., p n and v n in eqn (28), while α q and β q only depend on the density and compressibility ratios. 15 At large interparticle distances, the effect of re-scattering is negligible 6,40 and the scattered fields from neighbouring object n can be calculated directly from α n , β n and the external fields p 0 and v 0 .…”

Inter-Particle Effects with a Large Population in Acoustofluidics

“…Unlike the well-established primary ARF theory of solid particle, enrichment of the deep physics for the secondary ARF, either in theoretical models or in fundamental experiments, is still on the way [36,37]. Most of the related studies focus on the acoustic interaction effects of pulsating bubbles, in which the force is treated as a body force, far from the traditional theoretical framework of ARF [38][39][40].…”