Simulation of bubble–particle attachment process and estimation of attachment probability using a coupled smoothed particle hydrodynamics–discrete element method model

• The bubble (B)–particle (P) attachment process was examined using a coupled SPH–DEM. • The sliding time and the B–P attachment probability were estimated. • The model embodied complex interactions between B and P. • New attachment and net probability models were proposed based on simulation results. • The B–P interactions can be decoupled into hydrodynamic and thermodynamic effects. The bubble–particle attachment is an important step in determining the success of recovery in froth flotation. In this study, the bubble–particle attachment process was investigated using a coupled smoothed particle hydrodynamics (SPH)–discrete element method (DEM) model. The effects of particle inertia and the drag of fluid flow on the particle motion were examined. The sliding time was determined for different particle sizes, densities, and bubble sizes, and the simulated sliding time was compared with the analytical solution and our own experimental results using a high-speed camera. As the particle size and density increased, the sliding time decreased. However, this value was independent of the bubble size. The induction time was calculated as a function of the particle size and contact angle from an empirical model, and it was used to determine the attachment and net probabilities in a dynamic simulation. Based on the SPH–DEM simulation results, novel probability models were developed for bubble–particle interactions. Both attachment and net probabilities could be decoupled into hydrodynamic and thermodynamic effects, given that the collision probability was also derived as a single function of the particle Stokes number. The developed probability models embodying the mutual influence of bubbles and particles can be extended to macroscopically describe flotation cells and evaluate cell performance including particle recovery.