The Effects of Vibrations on Particle Motion Near a Wall in a Semi-Infinite Fluid Cell

Abstract

The effects of small vibrations on a particle-fluid system relevant to material processing such as crystal growth in space have been investigated experimentally and theoretically. An inviscid model for a spherical particle of radius, R0, suspended by a thin wire and moving normal to a cell wall in a semi-infinite liquid-filled cell subjected to external horizontal vibrations, was developed to predict the vibration-induced particle motion under normal gravity. The wall effects were studied by varying the distance between the equilibrium position of the particle and the nearest cell wall, H. The method of images was used to derive the equation of motion for the particle oscillating in an inviscid fluid normal to the nearest cell wall. The particle amplitude in a semi-infinite cell increased linearly with the cell vibration amplitude as expected from the results for an infinite cell, however, the particle amplitude also changed with the distance between the equilibrium position of the particle and the nearest wall. The particle amplitude was also found to increase or decrease depending on whether the cell vibration frequency was below or above the resonance frequency, respectively. The theoretical predictions of the particle amplitudes in the semi-infinite cell agreed well with the experimental data, where the effect of the wall proximity on the particle amplitude was found to be significant for (H∕R0<2) especially near the resonance frequency. Experiments performed at high frequencies well above the resonance frequency showed that the particle amplitude reaches an asymptotic value independent of the wire length.