Representation of Kinetics Models in Batch Flotation as Distributed First-Order Reactions

• Main Authors: Luis Vinnett, Kristian E. Waters
• Format: Article
• Language: English
• Published: MDPI AG 2020-10-01
• Series: Minerals
• Subjects: flotation kinetics; batch flotation; first-order model; flotation rate distribution
• Online Access: https://www.mdpi.com/2075-163X/10/10/913

Four kinetic models are studied as first-order reactions with flotation rate distribution <i>f</i>(<i>k</i>): (i) deterministic nth-order reaction, (ii) second-order with Rectangular <i>f</i>(<i>k</i>), (iii) Rosin–Rammler, and (iv) Fractional kinetics. These models are studied because they are considered as alternatives to the first-order reactions. The first-order representation leads to the same recovery <i>R</i>(<i>t</i>) as in the original domain. The first-order <i>R</i>_∞-<i>f</i>(<i>k</i>) are obtained by inspection of the <i>R</i>(<i>t</i>) formulae or by inverse Laplace Transforms. The reaction orders of model (i) are related to the shape parameters of first-order Gamma <i>f</i>(<i>k</i>)s. Higher reaction orders imply rate concentrations at <i>k</i> ≈ 0 in the first-order domain. Model (ii) shows reverse J-shaped first-order <i>f</i>(<i>k</i>)s. Model (iii) under stretched exponentials presents mounded first-order <i>f</i>(<i>k</i>)s, whereas model (iv) with derivative orders lower than 1 shows from reverse J-shaped to mounded first-order <i>f</i>(<i>k</i>)s. Kinetic descriptions that lead to the same <i>R</i>(<i>t</i>) cannot be differentiated between each other. However, the first-order <i>f</i>(<i>k</i>)s can be studied in a comparable domain.