Analysis of dynamic interactions in a bubble-particle system in presence of an acoustic field

Use of an acoustic field in flotation is known to improve mineral recovery. However, studies in this area are rather limited and in general there is a lack of a mechanistic description of the collision and collection efficiency of particles in presence of an external acoustic field. This study aims to contribute to this knowledge gap by developing a simplified 3D numerical model of single bubble-particle interactions based on a discrete element method (DEM) based approach. Volume mode oscillatory behaviour of the bubble was modelled within the theoretical spherical shape limit (0.1 ≤ Bo ≤ 0.5) using 1D Rayleigh-Plesset equation in a quiescent liquid medium and one-way coupled to particle motion obtained through DEM. Interaction dynamics were simulated for various operating conditions involving three parameters, namely oscillation amplitude ratio (ε ≤ 0.1), excitation frequency (below and above resonance frequency) and bubble-particle surface-to-surface distance (~1.0 to 10.6% of bubble radius). Regime maps were constructed to establish suitable combinations of these three operating parameters to represent the collision and attachment behaviour of a particle with the oscillating bubble. While conventional flotation models predict particle collision efficiency based on the nearest streamline adjacent to the bubble surface, application of an acoustic field on a bubble was shown to incur collision with a particle in the far field away from the interface due to oscillatory motion. It was noted that although such collisions occurred in the below-resonance-frequency regime (~35 to 79Hz), particle attachment did not occur due to weakening of the attractive capillary force. In the above-resonance-frequency regime (3.61-14.4kHz), however, particle attachment was predicted and attachment probability increased in the vicinity of the bubble resonance frequency.