Numerical Analysis of a Single Solid Spherical Particle Falling in an Ultrasonic Standing Wave Field

Abstract

The velocities of particle falling in a standing wave field through a vertical pipes filled with a stagnant liquid in are analyzed numerically for Reynolds 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 based on the cubic-interpolated pseudo-particle (CIP)-combined and unified procedure (C-CUP) method to clarify the effects of the walls of pipes. The velocity of a particle is periodically changed due to the influence of the radiation force of the standing wave. The average terminal velocity in a standing wave field is lower than that for which there is no ultrasonic field. As the particle diameter approaches the pipe diameter, the velocity of the particle approaches zero due to the influence of the pipe wall. The C-CUP method effectively simulates the behavior of a particle falling through a liquid-filled pipe in the standing wave field.