Simplified empirical and phenomenological evaluation of relation between particle size and kinetics of flotation

Abstract A relation between the kinetics of flotation and particle size is complex, therefore different flotation ranges for ultrafine, fine, medium and coarse particles, are usually considered. Our data on kinetics of froth flotation and particle size of metahydrophobic shale as well as experimental data of other authors for different materials were analyzed to find a general pattern of the relation between a flotation rate constant and a particle size, and the most suitable mathematical formulas relating these two parameters. The tried formulas included Nernst-, Zuniga-, direct proportionality-type as well as one Tomlinson-Fleming formula and two Arrhenius-type equations. It was found that the best approximation was provided by the Tomlinson-Fleming relation in the form of k = Bdn, where k is the first order flotation rate constant, d particle size, while B and n are process empirical constants. Values of the particle size kinetic power n were calculated and discussed in the light of the efficiency of particle capture by a bubble. Also a modified Arrhenius equation k = Hexp(−E/RT(log(d/do))), where E is the activation energy, T absolute temperature, R gas constant, as well as H and standard particle size do = 1 μm are constants, was suitable for experimental data evaluation, while other empirical equations provided worse fittings.