Numerical Determination of the Secondary Acoustic Radiation Force on a Small Sphere in a Plane Standing Wave Field

Gergely Simon, Marco A. B. Andrade, Marc Phillipe Yves Desmulliez, Mathis O. Riehle, Anne Bernassau

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)
34 Downloads (Pure)


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.

Original languageEnglish
Article number431
Issue number7
Early online date29 Jun 2019
Publication statusPublished - Jul 2019


  • 2D and 3D modeling
  • Scattering effects
  • Secondary acoustic radiation force

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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