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Effect of Ball Mill Parameters’ Variation on the Particles of a Mechanical Activation-Assisted Leaching: A Hydrometallurgical Mechanics

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Abstract

The economic and technical values of the hydrometallurgical or leaching processing are a function of its reaction rates and these reaction rates are enhanced by mechanical activation (MA) in hydrometallurgical processing. This study presents a novel derived theoretical model for MA-assisted leaching in investigating the effects of ball mill parameters on the particle sizes (retained and recovered). This theoretical model is based on chemical reaction controlled shrinking core model kinetics in which the particles of the ore/mineral were subjected to milling by a spherical ball before the leaching/dissolution process. For the MA hydrometallurgical process, the key parameters for the mechanical device are the rotating speed \(\left(\omega \right)\); diameter \(\left(d\right)\) of the milling/grinding ball; and its weight \(\left(M\right)\). The developed theoretical equation was evaluated using experimental results obtained from literature and statistical tools were employed for their plot analysis. It was discovered that the milling speed and diameter of the ball have a great influence on the MA leaching process with an optimum speed of 600 \({rpm}\) and diameter of 10 \(\mathrm{mm}\) (r0 = 22.0 \({\mu m}\)) yielding values \({r}_{{retained}}^{600{rpm}}=0.76{ \mu m}\) and \({r}_{{reacted}}^{600{rpm}}=21.24{ \mu m}\) when compared with non-MA traditional method with values \({r}_{{retained}}=2.10{ \mu m}\) and \({r}_{{reacted}}=\) 19.90 \({\mu m}\) which cannot be computed considering speed and diameter variations. However, the values obtained for smaller particle sizes of the retained particles were approximately zeros: a proof by the developed model that MA has no effect on the leaching process for extremely smaller particle sizes as obtained for all the ball diameters used. The developed model thus provides a more economical way of predicting appropriate grinding and leaching parameters combination which eliminates MA-assisted leaching process drawbacks. The milling time can be considered in the derivation for future research direction.

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Data Availability

All the data generated or analyzed in the course of this study are included in this published article (and its Supplementary Information files).

Abbreviations

\(M\) :

Mass of the ball in kg

\({w}_{b}\) :

Angular velocity of the ball in rad/s

\(f\) :

Is the frequency of rotation in rev/min

\({E}_{a}\) :

Is the apparent activation energy in kJ/mol

\(k\) :

Is the maximum breakage rate factor

\(t\) :

Is the leaching time (s)

\(R\) :

Is the Universal gas constant equals 8.314 J/K/mol

\(\propto\) :

Is the fraction reacted

\({K}^{r}\) :

Is the apparent reaction rate constant (s−1)

\(T\) :

Is the leaching temperature in Kelvin

\({K}_{o}\) :

Is the frequency factor per second

\({r}_{b}\) :

Is the mill-ball radius in mm

\({r}_{o}\) :

Is the initial particle size in mm

\({r}_{reacted}\) :

Is the reacted or recovered particle radius in mm

\(r\) :

Is the radius of the particle in the solution

\({r}_{retained}\) :

Is the unrecovered particle radius in mm

\({r}_{a}\) :

Is the ash core radius in the gas film

\({r}_{i}\) :

Is the unreacted core in the gas film

NB:

Is the amount of particle B in mole

V:

Is the volume of the particle in cm3

\({\rho }_{B}\) :

Is the solid molar density in mol/cm3

CAg:

CAs, CAc concentration of gas-phase reactants in mol/cm3

MAAH/MAAL:

Mechanical activation-assisted hydrometallurgy/leaching

\({X}_{s}\) :

Is the dissolution particle size

MA:

Is mechanical activation

\({X}_{i}\) :

Is the initial particle size

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Acknowledgements

We would like to appreciate the valuable contributions of the Editors and the anonymous reviewers. Also, O.S. Odebiyi appreciates the Chinese Government Scholarship support for his Ph.D. research and the grants from the funding bodies.

Funding

This work was supported by the National Key R&D program of China under Grant No. 2020YFC1909703 and S&T Program of Hebei under Grant No. 21284402Z.

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Authors and Affiliations

  1. CAS Key Laboratory of Green Process and Engineering, Institute of Process Engineering, National Engineering Laboratory for Hydrometallurgical Cleaner Production Technology, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Oluwasegun Samuel Odebiyi, Hao Du, Biao Liu & Shaona Wang

  2. University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Oluwasegun Samuel Odebiyi, Hao Du, Kayode Hassan Lasisi & Mary Otuosorochukwu Nnyia

  3. Institute of Urban Environment, Chinese Academy of Sciences, Xiamen, 361021, People’s Republic of China

    Kayode Hassan Lasisi

  4. Department of Mechanical Engineering, Faculty of Engineering, University of Lagos, Akoka, Yaba Lagos, Lagos, 101012, Nigeria

    Charlse Chukwuemeka Nwakanma

  5. CAS Key Laboratory of Standardization and Measurement for Nanotechnology, National Center for Nanoscience and Technology, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Mary Otuosorochukwu Nnyia

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  1. Oluwasegun Samuel Odebiyi
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  4. Biao Liu
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Contributions

O.S.O. conceptualized and investigated the research finding, methodology development, formal analysis and validation of the mathematical derivation and data, statistical software coding for validation, writing original draft, and writing–reviewing and editing of the original draft. H.D. investigated and technically analyzed the derivation methodology, validated the derivation and data, supervised the project, and was a major contributor in writing–reviewing and editing the manuscript. K.H.L. was a major contributor in validating data and writing–editing and reviewing the manuscript. S.W. supervised, validated data, and was a major contributor in writing–editing, and reviewing the manuscript. B.L. supervised the project, validated the derivation, and was a major contributor in writing–editing and reviewing the manuscript. C.C.N. was a major contributor in coding and software validation of the mathematical derivation. M.O.N. was a major contributor in writing–editing and reviewing the manuscript and analyzed the particle size. All the authors read and approved the final manuscript.

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Correspondence to Oluwasegun Samuel Odebiyi.

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Odebiyi, O.S., Du, H., Lasisi, K.H. et al. Effect of Ball Mill Parameters’ Variation on the Particles of a Mechanical Activation-Assisted Leaching: A Hydrometallurgical Mechanics. Mater Circ Econ 3, 23 (2021). https://doi.org/10.1007/s42824-021-00030-6

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