Numerical calculation of interaction forces between bubbles and particles based on the spatiotemporal evolution of wetting film

The bubble-particle interaction, including bubble-particle collision, attachment, and detachment, directly affects flotation efficiency as the basic unit of froth flotation. Among them, bubble-particle attachment is accompanied by the thinning and/or rupture of the wetting film between bubble and particles. Clarifying the interaction forces during the thinning of the wetting film is of great theoretical significance to regulate the flotation recovery of difficult-to-float coal/ore. The spatiotemporal profiles of the wetting film between hydrophilic/hydrophobized silica surface and an air bubble were investigated using the dynamic wetting film apparatus (DWFA). The bubble-particle interaction forces were calculated based on the wetting film thinning kinetics. Furthermore, the synergistic effect of hydrodynamic and surface forces on the wetting film thinning was analyzed. The results show that the wetting film between the hydrophilic silica and the bubble remains stable, eventually showing a “U” profile with a central thickness of 121.0 nm. However, for the hydrophobized silica surface, the wetting film is unstable and ruptures rapidly at 0.93 s, with a critical wetting film of 157.8 nm at the center. The interaction force results indicate that the hydrodynamic force is the most significant contributor to the wetting film drainage when the bubble-particle separation is far and the sample is driven by the motor approaching the bubble at 6 μm/s. When the separation is reduced to approximately 300 nm, surface forces come into play. Due to the low drainage rate of the wetting film between silica and bubbles, and the long time required, the motor stops driving before the wetting film reaches an equilibrium. The hydrodynamic force decreases and the surface force increases, so the repulsive disjoining pressure dominates the wetting film slowly drain to equilibrium. The hydrodynamic force between hydrophobized silica and bubble continuously increases, and as the separation distance decreases, the surface force such as an attractive van der Waals force or hydrophobic force enhances, inducing the rupture of the wetting film. Therefore, for silica with weak surface hydrophobicity, its strong repulsive interaction with bubbles is not conducive to bubble-particle attachment. The improvement of its surface hydrophobicity by surface modification contributes to the rupture of the wetting film as well as to increasing the attachment probability, which is attributed to the attractive disjoining pressure between the hydrophobized surface and the bubble.