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

This study examines four kinetic models as first-order reactions with flotation rate distribution f (k): deterministic nth-order reaction, second-order with Rectangular f (k), Rosin–Rammler, and Fractional kinetics. The objective is to explore alternatives to first-order reactions, demonstrating that the first-order representation leads to the same recovery R(t) as in the original domain. The methodology includes obtaining the first-order R∞-f (k) either by inspecting the R(t) formulae or through inverse Laplace Transforms. Results reveal that reaction orders of the deterministic model correlate with the shape parameters of first-order Gamma f (k)s, where higher reaction orders suggest rate concentrations at k ≈0. Model analysis shows that the second-order model generates reverse J-shaped first-order f (k)s, the Rosin–Rammler model exhibits mounded first-order f (k)s under stretched exponentials, and the fractional kinetics model ranges from reverse J-shaped to mounded first-order f (k)s with derivative orders below 1. Despite the different kinetic descriptions leading to similar R(t), first-order f (k)s can still be further investigated in a comparable domain.