Fig. 6. Conventional flotation model illustrating the effect of bubble size on collision and adhesion probabilities during the flotation process.

a Collision probability between a bubble with a 20–100 µm radius and particles ranging from 1–50 µm in size. b Adhesion probabilities between a bubble with a 20–100 µm radius and particles ranging from 1–50 µm in size. c Collision probabilities between a bubble with a 0–1000 nm radius and particles ranging from 1–50 µm in size. d Adhesion probabilities between a bubble with a 0–1000 nm radius and particles ranging from 1–50 µm in size. Inset figures depict the collision (a, c) and adhesion (b, d) of particles and bubbles without (a, b) and with (c, d) the presence of NBs.