Theory and Calculation of Sound Induced Particle Interactions of Viscous Origin

In this paper a theoretical study is carried out to describe the hydrodynamic effect known as the acoustic wake effect and its influence on acoustic interactions between the particles of a suspension. The study presents a two-dimensional analysis of this hydrodynamic effect under Oseen flow conditions. The set of differential equations, which governs the acoustically induced dynamics of two close-by particles, is solved for an incident monochromatic plane wave. For the first time, a semi-analytical solution is derived to describe acoustic wake particle interactions in a two-dimensional plane, revealing attraction and repulsion patterns around the particles. A parametric study with the new model reveals strong attraction between the two interacting particles for line-of-center orientation angles from 0° to 45° with respect to the wave propagation direction. Only insignificant repulsion is found at angles close to 60°. Trajectories of interacting particles are calculated by means of analytical integration of the equations of motion. The resulting attraction patterns closely resemble experimental findings of Hoffmann [1], displaying the so-called tuning fork trajectories. Gravitational processes are shown to have an important effect on the shape of the particle trajectories as well as on the probability of "hit" or "miss" between two interacting particles.