Vol.:(0123456789) 1 3 Materials Circular Economy (2021) 3:23 https://doi.org/10.1007/s42824-021-00030-6 ORIGINAL PAPER Efect of Ball Mill Parameters’ Variation on the Particles of a Mechanical Activation‑Assisted Leaching: A Hydrometallurgical Mechanics Oluwasegun Samuel Odebiyi 1,2  · Hao Du 1,2  · Kayode Hassan Lasisi 2,3  · Biao Liu 1  · Shaona Wang 1  · Charlse Chukwuemeka Nwakanma 4  · Mary Otuosorochukwu Nnyia 2,5 Received: 9 June 2021 / Revised: 2 September 2021 / Accepted: 5 September 2021 © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2021 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 efects 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 () ; diameter (d) of the milling/grinding ball; and its weight (M) . 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 infuence on the MA leaching process with an optimum speed of 600 rpm and diameter of 10 mm (r 0 = 22.0 m ) yielding values r 600rpm retained = 0.76m and r 600rpm reacted = 21.24m when compared with non-MA traditional method with values r retained = 2.10m and r reacted = 19.90 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 efect 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. Keywords Mechanics · Circular economy · Hydrometallurgy · Odebiyi-Hao · Mechanical activation · Particle size Abbreviations/Nomenclatures 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 ∝ 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 * Oluwasegun Samuel Odebiyi samodebiyi@ipe.ac.cn Hao Du hdu@ipe.ac.cn 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 2 University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 3 Institute of Urban Environment, Chinese Academy of Sciences, Xiamen 361021, People’s Republic of China 4 Department of Mechanical Engineering, Faculty of Engineering, University of Lagos, Akoka, Yaba Lagos, Lagos 101012, Nigeria 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