Numerical study of interparticle radiation force acting on rigid spheres in a standing wave

Acoustic radiation force can be used to move micro-sized particles, such as cells, in microfluidic devices. Although the number of particles in a microfluidic device is large, typically 2.5% (weight/volume), the acoustic force acting on a particle is commonly calculated using an analytical formula for a single particle in infinite medium. The interparticle forces are typically ignored as these are not easily accounted for and calculated with simple closed-form solutions. Based on the isothermal theory for an ideal fluid, a numerical scheme is hereby proposed to calculate the total radiation force, including the interparticle forces. The method uses the multipole series expansion and the weighted residual method to solve the governing Helmholtz equation with the necessary boundary conditions on the particle surface. The effect of different parameters on the primary and interparticle forces is studied using the proposed numerical scheme. It is shown that, near the pressure node, the interparticle forces are dominant and configurations of the spheres are determined by the interparticle forces. The proposed numerical scheme can be used for various sizes of spherical particles.