We present a theoretical expression for the acoustic interaction force between small spherical particles suspended in an ideal fluid exposed to an external acoustic wave. The acoustic interaction force is the part of the acoustic radiation force on one given particle involving the scattered waves from the other particles. The particles, either compressible liquid droplets or elastic microspheres, are considered to be much smaller than the acoustic wavelength. In this so-called Rayleigh limit, the acoustic interaction forces between the particles are well approximated by gradients of pair-interaction potentials with no restriction on the interparticle distance. The theory is applied to studies of the acoustic interaction force on a particle suspension in either standing or traveling plane waves. The results show aggregation regions along the wave propagation direction, while particles may attract or repel each other in the transverse direction. In addition, a mean-field approximation is developed to describe the acoustic interaction force in an emulsion of oil droplets in water.
Most studies investigating the acoustic radiation force upon a target are based on symmetry considerations between the object and the incident beam. Even so, this symmetry condition is not always fulfilled in several cases. An expression for the radiation force is obtained as a function of the beam-shape and the scattering coefficients of an incident wave and the object, respectively. The expression for the radiation force caused by a plane wave on a rigid sphere is used to validate the formula. This method represents a theoretical advance permitting different interpretations and predictions concerned to the acoustic radiation force phenomenon.
The subject of this paper is to present a theory for the dynamic radiation force produced by dual-frequency ultrasound beams in lossless and nondispersive fluids. An integral formula for the dynamic radiation force exerted on a three-dimensional object by a dual-frequency beam is obtained stemming from the fluid dynamics equations. The static radiation force due to a monochromatic wave appears as a particular case of this theory. Dependence of the dynamic radiation force to nonlinear effects of the medium is analyzed. We calculate the dynamic radiation force exerted on solid elastic spheres of two different materials by a low-amplitude dual-frequency plane wave. The static and dynamic radiation forces exhibited approximately same magnitude. Resonance patterns observed in the dynamic radiation force are similar to those present in the static radiation force.
Different types of particle and/or cell patterning in acoustic cavities produced by the radiation force of ultrasonic standing waves have been observed. However, most explanations of this phenomenon are constrained to particles much smaller than the wavelength (i.e., the so-called Rayleigh regime). Here, we present a theoretical model for acoustic trapping and patterning of particles/cells in a rectangular cavity beyond the Rayleigh regime. A simple closed-form expression of the radiation-force potential for particles of virtually any size immersed in a fluid is obtained. Particles with a size comparable to one wavelength (Mie particles) can be trapped in acoustic potential wells, whose stability is quantified by the trap stiffness. Our findings reveal that an acoustic trap can occur at a pressure node, antinode, and midpoint (i.e., a point midway between two nodes). These locations depend on the acoustic parameters of the particle and surrounding fluid (density, longitudinal, and shear speed of sound) and the ratio of particle size to wavelength. We also investigate the effects of the secondary radiation forces on trapping stability. We determine the possible acoustic patterns formed with polystyrene particles and osmotically swollen red blood cells (SRBCs). The conditions that may lead to one particle/cell per acoustic well patterning are discussed. A set of patterning experiments is performed with an acoustofluidic rectangular device, operating at 6.5-MHz frequency, using polystyrene particles with diameters of 10 μm (Rayleigh particles) and 75 μm (Mie particles) immersed in distilled water. The obtained experimental results are consistent with our theoretical predictions. The present study can help in designing acoustofluidic devices with the ability to spatially arrange larger, or more closely spaced particles, cells, and other microorganisms .
In this paper, the acoustic interaction forces and torques exerted by an arbitrary time-harmonic wave on a set of N objects suspended in an inviscid fluid are theoretically analyzed. We utilize the partialwave expansion method with translational addition theorem and reexpansion of multipole series to solve the related multiple scattering problem. We show that the acoustic interaction force and torque can be obtained using the farfield radiation force and torque formulas. To exemplify the method, we calculate the interaction forces exerted by an external traveling and standing plane wave on an arrangement of two and three olive-oil droplets in water. The droplets' radii are comparable to the wavelength (i.e. Mie scattering regime). The results show that the acoustic interaction forces present an oscillatory spatial distribution which follows the pattern formed by interference between the external and re-scattered waves. In addition, acoustic interaction torques arise on the absorbing droplets whenever a nonsymmetric wavefront is formed by the external and re-scattered waves interference.
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