Abstract
Two numerical methods based on the Finite Element Method are presented for calculating the secondary acoustic radiation force between interacting spherical particles. The first model only considers the acoustic waves scattering off a single particle, while the second model includes re-scattering effects between the two interacting spheres. The 2D axisymmetric simplified model combines the Gor’kov potential approach with acoustic simulations to find the interacting forces between two small compressible spheres in an inviscid fluid. The second model is based on 3D simulations of the acoustic field and uses the tensor integral method for direct calculation of the force. The results obtained by both models are compared with analytical equations, showing good agreement between them. The 2D and 3D models take, respectively, seconds and tens of seconds to achieve a convergence error of less than 1%. In comparison with previous models, the numerical methods presented herein can be easily implemented in commercial Finite Element software packages, where surface integrals are available, making it a suitable tool for investigating interparticle forces in acoustic manipulation devices.
Highlights
Acoustic radiation forces generated by standing wave fields are widely used for manipulation, trapping, patterning, and sorting of microparticles and cells [1,2,3,4]
The theoretical investigation of the primary acoustic radiation force on microparticles due to an external acoustic field was introduced by King [5], who calculated the acoustic radiation force on a small rigid sphere in an ideal fluid for both traveling and standing plane wave fields
In 2015, a weighted residue method was combined with the multipole expansion series for calculating the interparticle forces between spherical particles in an ideal fluid [28]
Summary
Acoustic radiation forces generated by standing wave fields are widely used for manipulation, trapping, patterning, and sorting of microparticles and cells [1,2,3,4]. Desired arrangement of particles in layers [15] or chains [16] is suspected to occur due to the secondary radiation force [17] Special cases of this force were investigated thoroughly: the seminal work by Bjerknes [18] on bubble-bubble interactions was followed by other theoretical studies [19,20,21,22] and validated experimentally [23]. A general theoretical model both for compressible and rigid particles, with no restriction on interparticle distance, was presented by Silva and Bruus recently [26] They followed a monopole-dipole description of the secondary force potential; this analytical formula being valid for particle sizes much smaller than the wavelength. To alleviate this restriction, numerical approaches have been developed for determining interparticle forces. Analytical methods, in contrast, are limited to small particle sizes and objects of simple geometry
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