The interaction acoustic radiation force in a standing plane wave applied to each small solid sphere in a two-particle system immersed in a viscoelastic fluid is studied in a framework based on perturbation theory. In this work, the first- and second-order perturbation theories are used in the governing equations with considering the upper-convected Maxwell model to obtain mathematical modeling. We use the finite element method to carry out simulations and describe the behavior of the viscoelastic fluid. The mathematical development is validated from three literature case studies: a one-particle system in a viscous fluid, a two-particle system in a viscous fluid, and a one-particle system in a viscoelastic fluid. The novelty of this study is to establish the acoustic interaction force between two spherical particles immersed in a viscoelastic fluid. The results show that the acoustic interaction force between two spheres is greater in a viscous fluid in comparison with the viscoelastic fluid with the same shear viscosity. This behavior is due to the relaxation time effect. It is also indicated that the acoustic interaction force between the particles decreases by the relaxation time and increases by the fluid's viscosity. A mathematical formula is proposed for the acoustic interaction force between particles located close to each other in a viscoelastic fluid.

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