On the motion of inertial particles by sound waves

Abstract

This paper describes the numerical simulation of the motion of a heavy spherical particle in an acoustic wave using the equation of motion for a point particle. Our results agree well with the recent experimental data of Gonzàlez, Hoffmann, and Gallego [“Precise measurements of particle entrainment in a standing-wave acoustic field between 20 and 3500 Hz,” J. Aerosol Sci. 31, 1461–1468 (2000)]. Our simulations cover a range of particle relaxation number, τ* = ωτ, where τ is the particle relaxation time and ω is the angular acoustic frequency from 0.06 to 10, particle to fluid density ratios, ρp/ρf, from 2500 to 2, and moderate acoustic velocity amplitudes. The results show that the Stokes force controls particle motion for τ* < 1 and ρp/ρf > 25. Within this regime it is appropriate to consider the Basset, pressure gradient, and virtual mass forces as “higher order” corrections to the Stokes force. The magnitude of the Basset force exceeds that of the Stokes force for ρp/ρf ⩾ 25 and τ* ⩾ 4. All the forces in the particle equation of motion should be accounted for when simulating particle motion in an acoustic wave for ρp/ρf < 25.