## 5 Bubble-Particle Interaction
### Bubble-Particle Attachment
Figure 10: Bubble–article attachment processes [146]. and [PERSON] et al. [160] suggested that the surface roughness accelerated the formation of the critical thickness of the liquid film. The presence of air entrapped in rough surfaces facilitated the quicker rupture of the liquid film, thus increasing the attachment efficiency and enhancing the particle flotation. [PERSON] [35] observed that the induction time decreased from 15.1 ms to 7.9 ms as the surface roughness of the glass beads increased from about 0.44 \(\upmu\)m to 0.76 \(\upmu\)m (produced through the etching method). A similar trend was obtained by [PERSON] et al. [84], who found that the induction time of hydrophobic glass particles was shortened from 863 ms to 12 ms as the surface roughness increased from about 0.418 \(\upmu\)m to 1.565 \(\upmu\)m. Furthermore, [PERSON] et al. [81] found that the induction time of low-rank coal particles increased from 93 ms to 133 ms when the roughness decreased from about 1.15 to 1.08 during the grinding process. Conversely, [PERSON] et al. [61], [PERSON] [83], and [PERSON] et al. [116] reported findings that contradicted these trends. They concluded that the shorter attachment times and stronger attachment patterns of bubbles occurred on smooth coal surfaces compared to rough surfaces. This was attributed to entrapped water in the grooves of rough surfaces, which prevented the bubble-coal particle attachment. The induction times were 1750 ms, 1000 ms, and 2.5 ms for Ra values of 2.40 \(\upmu\)m, 0.84 \(\upmu\)m, and 0.34 \(\upmu\)m, respectively (Figure 12a) [61]. The attachment times between the bubbles and coal surfaces were about 4000 ms and 29 ms for Ra values of 2.6 \(\upmu\)m and 0.2 \(\upmu\)m, respectively (Figure 12c) [83]. [PERSON] et al. [161] concluded that nanoscale asperities reduced the bubble-surface attachment strength. [PERSON] et al. [118] observed an increase in the contact time of air bubbles on coal surfaces from 156 ms to 215 ms as the Ra value increased from 2.5 \(\upmu\)m to 6.02 \(\upmu\)m. [PERSON] et al. [30] showed that the bubble-particle attachment time increased alongside the increase in surface roughness. [PERSON] et al. [120] reported that the stability of the water film on the natural magnesite surface increased with a greater surface nano-roughness, with induction times increasing from 5.3 ms to 8.0 ms and then to 12.0 ms as the Rq value increased from 42 nm to 69 nm and subsequently to 240 nm, respectively (Figure 12d). Figure 12: (**a**) Induction time of coal samples with different Ra value under natural conditions (insets are snapshots of TPC line after bubble retracted to original position) [61]; (**b**) induction time test of cooking coal and anthracite [116]; (**c**) attachment times between bubbles and coal surfaces with various roughness [83]; and (**d**) images of air bubbles in water during interactions with magnesite surfaces of different roughness [120]. [PERSON] et al. [127; 128; 155; 156] observed that increasing the surface roughness from below 1 \(\upmu\)m to 100 \(\upmu\)m (achieved using abrasive papers) significantly reduced the time required for the TPC (Thin Liquid Film) formation and bubble attachment from approximately 84 ms to just 2.5 ms (Figure 13). They concluded that a greater surface roughness increases the diameter and perimeter of the TPC, resulting in lower bubble detachment rates compared to smooth surfaces. [PERSON] et al. [150] reported that the time for the TPC formation and bubble attachment on rough fluorite surfaces ranged from 5 to 45 ms, while it exceeded 150 ms for smooth surfaces. [PERSON] et al. [151] found that the time for the TPC line formation (t\({}_{\text{TPC}}\)) on a rough polystyrene (PS) surface in pure water was 72 ms, compared to 127 ms for the smoother side. Furthermore, when the concentration of tri (propylene glycol) butyl ether was 5 \(\times\) 10\({}^{-4}\) M, the t\({}_{\text{TPC}}\) decreased for both smooth and rough PS surfaces, measuring 22 ms and 42 ms, respectively. [PERSON] et al.