Correlation between Flotation and Rheology of Fine Particle Suspensions
Abstract
:1. Introduction
2. Flotation
2.1. Fine Particle Flotation
2.2. Challenges in Fine Particle Flotation
3. Rheology
3.1. Rheology of Fine Particle Suspensions
3.2. Zeta Potential of Fine/Colloidal Particles
4. Correlation between Rheology and Flotation
Researcher  Type of Modeling Approach  Aims and Challenges  Findings and Limitations 

Schubert and Bischofberger, 1978 [187]  N/A 


Schubert and Bischofberger, 1998 [188]  N/A 


Schubert, 1999 [228]  ${Z}_{BP}=5{n}_{p}{n}_{b}{d}_{pb}^{2}\sqrt{\overline{{\upsilon}_{p}^{\prime}{}^{2}+{\upsilon}_{b}^{\prime}{}^{2}}}$ (8) 


Pyke et al., 2003 [104]  ${E}_{c}={E}_{csu}{\mathrm{sin}}^{2}{\theta}_{t}exp\left\{\left[3{K}_{3}\left(\mathrm{ln}\frac{3}{{E}_{csu}}1.8\right)\frac{4\left(\frac{2}{3}+\frac{{\mathrm{cos}}^{3}{\theta}_{t}}{3}\mathrm{cos}{\theta}_{t}\right)}{{\mathrm{sin}}^{4}{\theta}_{t}}\right]\mathrm{cos}{\theta}_{t}\right\}$ (9) 


${E}_{a}=\frac{{\mathrm{sin}}^{2}{\theta}_{a}}{{\mathrm{sin}}^{2}{\theta}_{t}}$ (10)  
${E}_{s}=1exp\left(1\frac{1}{{B}_{0}^{*}}\right)$ (11)  
$\frac{d{N}_{p}}{dt}=2.39\frac{{G}_{fr}}{{d}_{b}{V}_{cel}}\left[\frac{0.33{\u03f5}^{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{1ex}{$9$}\right.}{d}_{b}{}^{\raisebox{1ex}{$7$}\!\left/ \!\raisebox{1ex}{$9$}\right.}}{{\upsilon}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$3$}\right.}}{\left(\frac{\mathrm{\Delta}{\rho}_{b}}{{\rho}_{fl}}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{1ex}{$3$}\right.}\frac{1}{{\upsilon}_{b}}\right]\times {E}_{C}{E}_{a}{E}_{s}{N}_{p}$ (12)  
Shabalala et al., 2011 [149]  N/A 


Genc et al., 2012 [217]  N/A 


Patra et al., 2012 [150] 

 
Xu et al., 2012 [225]  ${R}_{t}={R}_{max}\left(1\mathrm{exp}\left(kt\right)\right)$ (13) 


Forbes et al., 2014 [57]  $f\left(t\right)=\eta +\phi .{\mathit{e}}^{\left({k}_{f}t\right)}+\left(1\phi \eta \right).{\mathit{e}}^{\left({k}_{s}t\right)}$ (14) 


Cruz et al., 2015 [230]  N/A 


Wang et al., 2016 [224]  N/A 


Zhang and Peng, 2015 [226]  $EN{T}^{con:tail}=\frac{\frac{{M}_{gangue}}{{M}_{water\text{}con}}}{\frac{{M}_{gangue}}{{M}_{water\text{}tail}}}$ (15) 


${R}_{ent}=\frac{1R}{1{R}_{w}}EN{T}^{con:tail}{R}_{w}$ (16)  
Zhang et al., 2015 [223]  N/A 


Farrokhpay et al., 2016 [192]  N/A 


Wang et al., 2015 [221]  N/A 


Basnayaka et al., 2017 [227]  $R={R}_{\infty}\left[1\frac{\left(1{e}^{{k}_{max}t}\right)}{{k}_{max}t}\right]$ (17) 


Chen et al., 2017 [193]  N/A 


Farrokhpay et al., 2018 [222]  N/A 


Liu et al., 2018 [229]  N/A 


Li et al., 2020 [220]  N/A 


5. Summary and Future Perspectives
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
${A}_{H}$  Hamaker constant 
${B}_{0}^{*}$  Bond number 
${d}_{b}$  Bubble diameter 
$\frac{d{N}_{p}}{dt}$  Rate of removal of particles by bubbles 
${d}_{p}$  Particle diameter 
${d}_{pb}$  $\frac{{d}_{p}+{d}_{b}}{2}$ 
$e$  Elementary charge 
${E}_{a}$  Attachment efficiency 
${E}_{c}$  Collision efficiency 
${E}_{csu}$  Sutherland collision efficiency 
${e}_{G}$  Entrainment factors for nonfloatable minerals 
${e}_{M}$  Entrainment factors for floatable minerals 
$EN{T}^{con:tail}$  Degree of entrainment 
${E}_{s}$  Stability efficiency 
$f\left(t\right)$  Fraction of chalcopyrite remaining unrecovered after time t 
${F}_{EDL}$  Electrical double layer force 
${F}_{M}$  Intercept on the mineral recovery axis 
${F}_{VDW}$  Van der Waals force 
${G}_{fr}$  Gas flowrate 
$H$  Interparticle separation distance 
$k$  Flotation rate constant 
${k}_{B}$  Boltzmann constant 
${k}_{f}$  Rate coefficient of the fast floating chalcopyrite 
${k}_{max}$  Maximum flotation rate constant 
${k}_{s}$  Rate coefficient of the slow floating chalcopyrite 
${M}_{gangue}$  Mass of gangue minerals 
${M}_{watercon}$  Mass of water in concentrate 
${M}_{watertail}$  Mass of water in tailings 
${n}_{o}$  Number concentration of ions 
${n}_{B}$  Bubble number concentration 
${n}_{P}$  Particle number concentration 
${N}_{p}$  Number density of particles 
$R{R}_{t}$  Overall recovery of mineral (%) 
${R}_{ent}$  Recovery by entrainment 
${R}_{G}$  Recoveries of nonfloatable particles 
${R}_{M}$  Recoveries of floatable particles 
${R}_{w}$  Recovery of water in the cell (%) 
${R}_{\infty}{R}_{max}$  Flotation recovery at an infinite time 
$t$  Time 
$T$  Absolute temperature 
${\upsilon}_{b}$  Bubble velocity 
${V}_{cel}$  Flotation cell volume 
${W}_{water}$  Weight of recovered water in given time 
$z$  Ionic valence 
${Z}_{BP}$  Number of collisions per unit volume and time 
$\epsilon $  Dielectric constant 
$\u03f5$  Turbulent dissipation energy 
${\epsilon}_{0}$  Permittivity of free space 
$\kappa $  Debye–Huckel reciprocal length 
$\eta $  Fraction of nonfloating chalcopyrite 
${\rho}_{p}$  Particle density 
${\rho}_{fl}$  Fluid density 
$\mathrm{\Delta}{\rho}_{b}$  ${\rho}_{p}{\rho}_{fl}$ 
$\upsilon $  Kinematic viscosity 
${\upsilon}_{b}^{\text{'}}$  Rootmeansquare values of the turbulent velocity fluctuations of the bubble 
${\upsilon}_{p}^{\text{'}}$  Rootmeansquare values of the turbulent velocity fluctuations of the particles 
${\tau}_{y}$  Shear yield stress 
${\tau}_{\mathrm{y}\left(\mathrm{max}\right)}$  Maximum shear yield stress 
$\phi $  Fraction of fastfloating chalcopyrite 
${\theta}_{a}$  Adhesion angle 
${\theta}_{t}$  Maximum possible collision angle of particle on bubble (angle of tangency) 
$\zeta $  Zeta potential 
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Researcher  Approach Adopted  Findings 

Ahmed and Jameson (1985) [43]  Bubble size reduction  The flotation rate constant of fine particles (<50 µm) increased up to five hundredfolds (1 × 10^{−4} to 5 × 10^{−2} s^{−1} at 300 rpm). 
Yoon and Luttrell (1986) [106]  Bubble size reduction  Particle–bubble attachment probability increased with a decrease in the induction time and maximum particle–bubble probability (0.92) was recorded at 350 µm bubble size at 10 msec induction time. 
Hewitt et al. (1995) [121]  Bubble size reduction  Smaller bubbles have higher attachment efficiencies than do larger bubbles for all particle sizes over a wide range of contact angles and ionic strengths. 
Song et al. (2001) [120]  Use of potassium amyl xanthate (PAX) for the formation of flocs of galena and sphalerite  The floc flotation of galena and sphalerite fines (<20 µm) can reach floatability of 100%, in comparison with conventional flotation obtaining floatability of about 40%. For galena and sphalerite, the optimum floc size was 38 µm and 45 µm, respectively. 
Rubio et al. (2007) [122]  Treatment of the copper/molybdenum sulfide ore (0.94% Cu and 0.05% Mo) using emulsified oil extender flotation.  Copper and Molybdenum recovery of fine (37–5 μm) and ultrafine (<5 μm) increased around 4% to 5% and 3% to 5% respectively as compared with a “standardized” mill laboratory procedure. 
Otsuki and Yue (2017) [36]  Adoption of CGAassisted flotation to a complex gold ore  Higher gold recovery (94.33%) and grade (75.42 g/t) was achieved with the CGA process as compared with the recovery (92.44%) and grade (36.63 g/t) in flotation without CGA, especially in the fine particle fraction (between 38–53 µm). 
Arriagada et al. (2020) [123]  Use of hydrophobized glass bubbles (HGB)  HGB addition increased the flotation kinetics rate constant by 1.4 times and the maximum recovery from 64 to 90% (considering a firstorder kinetics model). 
Farrokhpay et al. (2020) [124]  Use of nanobubbles  When microbubbles were used, much less collector (about half) was needed to achieve the same or even slightly higher recovery. The quartz flotation recovery increased from 88 to 92% with the use of microbubbles. 
Zhou et al. (2020) [125]  Use of nanoscale bubbles generated by hydrodynamic cavitation (HC)  The separation efficiencies of conventional flotation and flotation of ultrafine coal pretreated via HC increased from 2.62 to 3.62, respectively. 
Zhang et al. (2021) [126]  Use of nanobubbles  The rutile treated with nanobubbles showed higher recovery (93%) as compared with the conventional bubbles, i.e., 86%. 
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Sajjad, M.; Otsuki, A. Correlation between Flotation and Rheology of Fine Particle Suspensions. Metals 2022, 12, 270. https://doi.org/10.3390/met12020270
Sajjad M, Otsuki A. Correlation between Flotation and Rheology of Fine Particle Suspensions. Metals. 2022; 12(2):270. https://doi.org/10.3390/met12020270
Chicago/Turabian StyleSajjad, Mohsin, and Akira Otsuki. 2022. "Correlation between Flotation and Rheology of Fine Particle Suspensions" Metals 12, no. 2: 270. https://doi.org/10.3390/met12020270