Coupling Flotation Rate Constant and Viscosity Models
In a flotation process, the particle–bubble and particle–particle interactions are key factors influencing collection efficiencies. In this work, the generalized Sutherland equation collision model and the modified Dobby–Finch attachment model for potential flow conditions were used to calculate the...
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| Format: | Article |
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MDPI AG
2022-02-01
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| Series: | Metals |
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| Online Access: | https://www.mdpi.com/2075-4701/12/3/409 |
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| author | Mohsin Sajjad Akira Otsuki |
| author_facet | Mohsin Sajjad Akira Otsuki |
| author_sort | Mohsin Sajjad |
| collection | DOAJ |
| description | In a flotation process, the particle–bubble and particle–particle interactions are key factors influencing collection efficiencies. In this work, the generalized Sutherland equation collision model and the modified Dobby–Finch attachment model for potential flow conditions were used to calculate the efficiencies of particle–bubble collision and attachment, respectively, for a flotation particle size of 80 μm. The negative effects of increase in the suspension viscosity due to the presence of fine particles on the flotation performance of fine particles have been reported, but there is no overarching model coupling the suspension viscosity and the flotation performance in the literature. Therefore, our study addressed this very important research gap and incorporated the viscosity model as a function of solid concentration, shear rate, and particle size into a flotation rate constant model that was proposed and conducted for the first time. This is quite a unique approach because the previously developed flotation rate constant model has never been coupled with a suspension rheology model taking into account the solid particle concentration and shear rate, although they are very important flotation variables in practice. The effect of the presence of ultra-fine/fine particles on the viscosity of the suspension and the flotation efficiencies and rate constant of flotation particle size of 80 μm were also investigated in order to better understand the mechanism of the problematic behavior of ultra-fine/fine particles in flotation. This coupling study started with the simplest case: flowing suspensions of inert, rigid, monomodal spherical particles (called hard spheres). Even for hard spheres, the effect of shear rate and particle size which produces deviation from the ideal case (constant viscosity at constant temperature regardless of shear rate) was clearly identified. It was found that the suspension viscosity increases with the decrease in fine/ultra-fine particle size (i.e., 1 µm–8 nm) and at higher solid particle concentration. Then, the colloidal particle suspensions, where interparticle forces play a significant role, were also studied. The suspension viscosity calculated for both cases was incorporated into the flotation efficiencies and rate constant models and discussed in terms of the effects of the presence of ultra-fine and fine particles on the flotation kinetics of flotation particle size of 80 μm. |
| first_indexed | 2024-03-09T13:20:54Z |
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| institution | Directory Open Access Journal |
| issn | 2075-4701 |
| language | English |
| last_indexed | 2024-03-09T13:20:54Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Metals |
| spelling | doaj.art-f1bd91bdef784e15b423eae0630dca4d2023-11-30T21:30:45ZengMDPI AGMetals2075-47012022-02-0112340910.3390/met12030409Coupling Flotation Rate Constant and Viscosity ModelsMohsin Sajjad0Akira Otsuki1Ecole Nationale Supérieure de Géologie, GeoRessources UMR 7359 CNRS, University of Lorraine, 2 Rue du Doyen Marcel Roubault, BP 10162, 54505 Vandœuvre-les-Nancy, FranceEcole Nationale Supérieure de Géologie, GeoRessources UMR 7359 CNRS, University of Lorraine, 2 Rue du Doyen Marcel Roubault, BP 10162, 54505 Vandœuvre-les-Nancy, FranceIn a flotation process, the particle–bubble and particle–particle interactions are key factors influencing collection efficiencies. In this work, the generalized Sutherland equation collision model and the modified Dobby–Finch attachment model for potential flow conditions were used to calculate the efficiencies of particle–bubble collision and attachment, respectively, for a flotation particle size of 80 μm. The negative effects of increase in the suspension viscosity due to the presence of fine particles on the flotation performance of fine particles have been reported, but there is no overarching model coupling the suspension viscosity and the flotation performance in the literature. Therefore, our study addressed this very important research gap and incorporated the viscosity model as a function of solid concentration, shear rate, and particle size into a flotation rate constant model that was proposed and conducted for the first time. This is quite a unique approach because the previously developed flotation rate constant model has never been coupled with a suspension rheology model taking into account the solid particle concentration and shear rate, although they are very important flotation variables in practice. The effect of the presence of ultra-fine/fine particles on the viscosity of the suspension and the flotation efficiencies and rate constant of flotation particle size of 80 μm were also investigated in order to better understand the mechanism of the problematic behavior of ultra-fine/fine particles in flotation. This coupling study started with the simplest case: flowing suspensions of inert, rigid, monomodal spherical particles (called hard spheres). Even for hard spheres, the effect of shear rate and particle size which produces deviation from the ideal case (constant viscosity at constant temperature regardless of shear rate) was clearly identified. It was found that the suspension viscosity increases with the decrease in fine/ultra-fine particle size (i.e., 1 µm–8 nm) and at higher solid particle concentration. Then, the colloidal particle suspensions, where interparticle forces play a significant role, were also studied. The suspension viscosity calculated for both cases was incorporated into the flotation efficiencies and rate constant models and discussed in terms of the effects of the presence of ultra-fine and fine particles on the flotation kinetics of flotation particle size of 80 μm.https://www.mdpi.com/2075-4701/12/3/409complex orecritical raw materialscollection efficiencyparticle–bubble interactionsolid concentrationshear rate |
| spellingShingle | Mohsin Sajjad Akira Otsuki Coupling Flotation Rate Constant and Viscosity Models Metals complex ore critical raw materials collection efficiency particle–bubble interaction solid concentration shear rate |
| title | Coupling Flotation Rate Constant and Viscosity Models |
| title_full | Coupling Flotation Rate Constant and Viscosity Models |
| title_fullStr | Coupling Flotation Rate Constant and Viscosity Models |
| title_full_unstemmed | Coupling Flotation Rate Constant and Viscosity Models |
| title_short | Coupling Flotation Rate Constant and Viscosity Models |
| title_sort | coupling flotation rate constant and viscosity models |
| topic | complex ore critical raw materials collection efficiency particle–bubble interaction solid concentration shear rate |
| url | https://www.mdpi.com/2075-4701/12/3/409 |
| work_keys_str_mv | AT mohsinsajjad couplingflotationrateconstantandviscositymodels AT akiraotsuki couplingflotationrateconstantandviscositymodels |