Numerical study of the motion of a solid particle in the field of ultrasonic standing wave - Sboev, Ivan Olegovich; Lyubimova, Tat′yana Petrovna; Rybkin, Konstantin Anatol′yevich (Computational Continuum Mechanics, 2026)
This numerical study examines the dynamics of a solid particle in a viscous fluid within a closed cavity under the influence of an ultrasonic standing wave. The study comprises two stages. First, the distribution of acoustic pressure in the quiescent fluid is calculated, ignoring disturbances induced by the particle or the flow. Two ultrasonic source configurations are considered: a planar ultrasonic vibrator extending throughout the entire lower boundary and a finite-size ultrasonic source. For a planar vibrator, the distribution of acoustic pressure  of a harmonic plane wave is derived analytically from the one-dimensional Helmholtz equation. For finite-size sources, the same equation is numerically solved using the finite element method to account for the complex structure of the acoustic field and edge effects near the ultrasonic source.  At the second stage, the computed pressure distribution is used to determine the spatial distribution of the Gor'kov  potentials and the resulting acoustic radiation force, acting on the spherical particle of a specified size. The particle trajectory in the field of the ultrasonic standing wave is determined by solving numerically the equation of particle motion, taking into account the contributions from the added mass, acoustic radiation force, and drag force. The drag coefficient for the Reynolds numbers ranging from 0.1 to 0.8×10³ is calculated using the Schiller-Naumann correlation. Numerical simulations are conducted for different initial positions of the particle. The calculated data are consistent  with the known concept of the solid particle motion in the field of  ultrasonic standing wave, according to which a solid particle under the influence of the acoustic radiation forces tends to get into the region of the Gor'kov potential minimum, involving the standing wave nodes. Numerical simulation of the solid particle motion in the field of ultrasonic standing wave induced by the finite - size  ultrasonic radiator allowed us to describe the displacement of the particle in the direction perpendicular to the direction of wave propagation observed in experiments.
Keywords: ultrasonic standing wave; acoustic pressure distribution; Gorkov's potential; acoustic radiation force; drag force; particle dynamics; numerical simulation