Numerical analysis of a single solid spherical particle falling in an ultrasonic standing wave field

The velocities of particle falling in a standing wave field through a verti cal pipes filled with a stagnant liquid in are analyzed numerically for Rey nolds number (Re) < 1, for a wide range of pipe diameters. The equations of motion of a spherical particle in a viscous fluid are solved based on the Basset-Boussinesq-Ossen (BBO) equation to clarify the falling velocities in an infinite stagnant fluid. and two-dimensional hydrodynamic equations bas ed on the cubic-interpolated pseudo-particle (CIP)-combined and unified pro cedure (C-CUP) method to clarify the effects of the walls of pipes. The vel ocity of a particle is periodically changed due to the influence of the rad iation force of the standing wave. The average terminal velocity in a stand ing wave field is lower than that for which there is no ultrasonic field. A s the particle diameter approaches the pipe diameter. the velocity of the p article approaches zero due to the influence of the pipe wall. The C-CUP me thod effectively simulates the behavior of a particle failing through a liq uid-filled pipe in the standing wave field.