Direct numerical simulation study of multi-dispersed particle-bubble turbulent collision frequency based on the lattice boltzmann method

Flotation is an important method for upgrading and impurity removal of fine mineral particles, but it faces the challenge of low recovery rates for micro-fine particles. Turbulence is a necessary condition to enhance the flotation of microfine particles, yet the mechanisms of multi-scale collisions and their control remain unclear. Particularly for multi-dispersed particle/bubble systems, there exists a gap between traditional flotation theories and modern industrial applications. The behavior of multi-dispersed particle-bubble collisions in turbulence is focused on, utilizing isotropic turbulent direct numerical simulation (DNS) combined with collision dynamics theory. By examining radial relative velocity and distribution functions, this study explores the characteristics of turbulent collisions under the effects of large-scale eddy transport and microscale eddy local enrichment, and the impact of size effects on the collision process. The research finds that the effects of polydispersity and inertia lead to significant discrepancies between the DNS results of point particles and the predictions of the classical Saffman & Turner model, highlighting the limitations of classical theories in predicting behaviors in polydisperse systems. These findings underscore the necessity for high-fidelity predictions of turbulence characteristics and ideal collision frequencies within polydisperse particle-bubble systems. Under the competitive and cooperative interactions between large-scale eddy transport and microscale eddy enrichment, increasing the turbulence dissipation rate and enlarging the diameters of very fine particles/bubbles prove to be effective strategies to enhance the ideal collision frequency of polydisperse particles and bubbles. Additionally, as the dispersion of particles/bubbles increases, the effect of large-scale eddy transport is enhanced, while the effect of microscale eddy enrichment is weakened. Therefore, there exists an optimal dispersion that achieves higher collision frequencies in polydisperse particle-bubble groups. This indicates that controlling the particle/bubble size distribution during the flotation process is crucial for improving separation efficiency. This study elucidates the mechanisms of particle-bubble collisions under the competitive and synergistic effects of large-scale eddy turbulence transport and microscale eddy enrichment, providing rich theoretical support for modern flotation theories of particle-bubble mineralization.