## 5 Bubble-Particle Interaction
### Bubble-Particle Interaction Force  
With the introduction of micro-force measurement equipment, we can now directly measure the adhesion force between bubbles and particles [43]. This method provides a clearer understanding of how surface roughness affects the wettability and floatability of mineral and material particles, especially when compared to simply measuring the time of attachment. The results show that the surface roughness of particles significantly affects the adhesion/detachment force between air bubbles/water droplets and particles (Figure 14). [PERSON] et al. [54] found that the detachment force of air bubbles on a rough hydrophilic glass bead was lower than that on a smooth hydrophilic bead. In contrast, the detachment force for bubbles on a rough hydrophobic glass bead was higher than that on a smooth hydrophobic bead. Similarly, [PERSON] et al. [30] observed that reducing the surface roughness of coal particles decreased the repulsive force during the bubble-particle attachment process, while increasing the adhesive force during bubble-particle detachment, which is more favorable for flotation. The maximum adhesion forces between air bubbles and coal surfaces with roughness values of 2.51 \(\upmu\)m, 0.77 \(\upmu\)m, 0.31 \(\upmu\)m, and 0.12 \(\upmu\)m were approximately 53 \(\upmu\)N, 150 \(\upmu\)N, 180 \(\upmu\)N, and 218 \(\upmu\)N, respectively. [PERSON] et al. [117] reported similar results, that the maximum adhesion forces between water droplets and coal surfaces were 111.70 \(\upmu\)N, 125.48 \(\upmu\)N, and 136.42 \(\upmu\)N at surface roughness values of 0.23 \(\upmu\)m, 0.98 \(\upmu\)m, and 2.79 \(\upmu\)m, respectively. In contrast, the maximum adhesion forces between air bubbles and coal surfaces were 97.14 \(\upmu\)N, 42.76 \(\upmu\)N, and 17.86 \(\upmu\)N for the same roughness values. Further work by [PERSON] et al. [39; 120] confirmed these findings, indicating that surface roughness decreased the adhesion force between air bubbles and hydrophilic surfaces, as well as between water droplets and hydrophobic surfaces. They found that the normalized maximum adhesion force for air bubble attachment on the natural magnesite surface decreased from about 97 mN/m (Rq = 2 nm) to 46 mN/m (Rq = 240 nm) [120]. Additionally, they reported that the maximum adhesion force for water droplets on hematite surfaces decreased from 0.467 mN to 0.349 mN as the surface roughness increased from 3 nm to 145 nm after interacting with 125 mg/L of NaOL at a pH of 9 (Figure 14b,c) [39]. [PERSON] et al. [58] further confirmed that an increasing nanoscale roughness weakened the adhesive forces between air bubbles and hydrophilic surfaces. Specifically, the maximum adhesion force decreased more profoundly, from about 170 \(\upmu\)N to 51 \(\upmu\)N for hematite and from 174 \(\upmu\)N to 38 \(\upmu\)N for pyrite as the Rq value increased from 3 to 4 nm to 250 to 260 nm (Figure 14d,e). [PERSON] et al. [167; 168] demonstrated that a stronger detachment force and larger detachment time are required to separate the rough particles from the attached bubbles, compared to smoother particles. This is due to larger values of the three-phase contact perimeter for rough particles, indicating a stronger adhesion force and shorter induction time. [PERSON] et al. [84] found that the adhesion forces of water droplets on glass intensified from 25.4 \(\upmu\)N to 29.0 \(\upmu\)N and then to 35.8 \(\upmu\)N as the surface roughness of the natural glass increased, which is attributed to the stable wetting film. Conversely, the adhesion forces of water droplets on hydrophobic glass beads decreased from 249.2 uN to 234.4 uN and then to 183.6 uN with the increasing surface roughness. Finally, [PERSON] et al. [59] reported that the snap-in force of water droplets on hematite surfaces increased from about 0.41 mN to 0.51 mN as the Rq value rose from 3 nm to 145 nm.