## 3 Flotation Behavior
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Minerals** & **Particle Size/\(\mu\)m** & **Folation Results** \\ \hline calcite [1] & 180–250 125–150 75–125 45–75 & The calcite particles with rougher surfaces had a larger theoretical ultimate recovery than the smoother ones in all granularity ranges. \\  & 45–75 & The rougher magnesite and quartz particles exhibited a higher flotation recovery in the wide range of selected sodium oleate (NaOL) concentrations and at each pH value, but the effect of surface roughness on flotation was diminished with increasing NaCl concentrations. \\  & The flotation recovery of hematite particles arrived at 88.0\% and 75.9\% with the NaOL concentration by 125 mg/L when the Ra value was 8.5 nm and 2.1 nm, respectively. \\  & The flotation recovery increased from about 76\% to 85\% by increasing the Ra value from about 0.667 nm to 1.350 nm in the presence of kerosene, and the difference in flotation recovery was decreased with the increase in kerosene amounts. \\  & The flotation recoveries of rougher malachite were around 12\% higher than that of smoother ones. \\  & The flotation recovery of rougher cassiterite was 39.07\% higher than that of smoother ones. \\  & The dry-ground samples exhibited relatively rougher surfaces, higher flotation recovery, and faster flotation kinetics than wet-ground products. \\  & When increasing the surface roughness values of the abraded particles from 2.3 \(\mu\)m to 3.3 \(\mu\)m, the flotation recoveries increased from 29\% to 81\% at a low collector concentration of 10\({}^{-6}\) M. \\  & A smoother surface led to an improvement in the floatability of quartz, calcite, talc, and barite; and talc particles that reported to the concentrates were smoother than those that reported to the tailings. \\  & The barite and pyrite particles with a lower surface roughness and acuteness had better floatability and better concentrate grades. \\  & The wet-ground particles were characterized by more irregular shape factors and smoother coal surfaces and, thus, presented higher flotation recoveries compared to the dry-ground ones. \\  & The floatability of fine molybden particles was significantly reduced due to the creation of very rough surfaces. \\  & The flotation recovery of smoother ground chalcopyrite was approximately 16\% higher than the rougher ones. \\  & The flotation recovery of wet-ground spodumene particles with smoother surfaces was higher than that of dry-ground ones with rougher surfaces in all granularity ranges. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._The contradictory results are related to the fact that some studies ignore the effect of particle sizes on flotation recovery and fail to divide the particles into narrow sizes ranges. Additionally, most scholars have neglected the significant influence of particle shapes on flotation behavior, even when particles have been sorted into narrow sizes. Some investigations have combined the factors of surface roughness and particle shape to examine their effects on flotation recovery, but the results remain inconsistent. For example, [PERSON] et al. [51; 93; 95] found that talc and quartz particles with a higher angularity and roughness exhibited better floatability. In contrast, [PERSON] and [PERSON] et al. [46; 66; 96] reported that barite and pyrite particles with a lower surface roughness and acuteness had better floatability and concentrate grades. [PERSON] [99] observed that the particles produced through autogenously grinding had a lower surface roughness and compactness than those produced through conventional milling, resulting in better concentrate grades. Similarly, [PERSON] et al. [100] showed that autogenously ground particles, with a lower surface roughness and acuteness, achieved a higher flotation recovery and better concentrate grades. For eliminating the potential effects of particle sizes and shapes, numerous studies have been conducted to investigate the effect of surface roughness on flotation recovery.