Numerical calculation of acoustic radiation forces acting on a sphere in a viscous fluid

In this work, a numerical scheme based on multipoles and Stokeslet is proposed for calculating the radiation force acting on a single rigid sphere in a viscous fluid. First-order velocity and pressure are obtained from the multipole series solution, and the volumetric force in the acoustic streaming is subsequently calculated from the first-order velocity and pressure. The acoustic streaming equations are solved using the Stokeslet method within a finite domain descretized by tetrahedral elements. The boundary conditions for streaming are imposed using the weighted residue method to obtain the unknown coefficients in the multipole series expansion for the second-order velocity potentials. The radiation forces obtained from this multipole-Stokeslet method match well with Doinikov's series solution, for a wide range of the sphere size. Compared to the complicated series solution, the multipole-Stokeslet method can be easily implemented without the evaluation of the semi-infinite integrals.