The use of compressed exponentials for kinetic modelling of batch flotation

Different first-order models have been used to characterize flotation kinetics due to their simple interpretation and mathematical treatment. However, these representations are not applicable to flotation responses that do not present decreasing recovery rates over time. Some erratic kinetic responses present close to S-shaped dependency as a function of time, indicating a delayed separation. These trends can be modelled by a variety of approaches; however, compressed exponentials of the type exp(−a t ^b), with b ≥ 1, are attractive due to the fact that the classical first-order model is a special case. This work analyses size-by-size batch kinetic responses of Cu and Pb minerals in their separation from a complex ore, showing the transition towards deterministic first-order rate constants in the coarser size classes, finally obtaining compressed exponentials in the −212 +150 μm fraction [R = R_∞(1-exp(−a t ^b)), with R_∞ the maximum recovery]. As the derivatives of these exponentials are zero at t = 0, this result indicates the delayed nature of the separation of coarse particles for this process.