Acoustic radiation force for multiple particles over a wide size-scale by multiple ultrasound sources

Abstract

In recent years, the manipulation of microparticles by ultrasound transducer arrays becomes possible. However, the contributions of rescattered waves among the particles have not to be taken into account in designs. The theoretical results are typically valid for small particles. This study considers the acoustic forces exerted by time-harmonic waves on large particles. The theory accounting for the scattering effect is developed for multiple sources (or transducers) and multiple particles of various sizes, levitated in an inviscid fluid. The external waves from multiple sources are expanded by equivalent plane wave series with the translation addition theorem. The multiple scattering field and the acoustic force can then be expressed under the plane wave series structure. The key to predicting the particle trajectory is the updating of the coordinate information of moving particles. The computed acoustic pressure field and the acoustic forces by this semi-analytical method are first validated by the full-field finite element simulation with a few particles. It is then used to calculate the more complex and interesting cases of multiple particles of various sizes manipulated by multiple transducers in the air. It is found that, in general, the contribution of scattering wave becomes significant when the size parameter ka>2, and it increases quadratically with the amplitude parameter of the transducers. A typical example also shows that the scattering force overtakes the gradient force when the source amplitude for a large particle is two times higher than that for a neighboring particle.