The effect of the bubble and particle size distributions on the kinetic rate constant

"The bubble size distribution plays a fundamental role in flotation kinetics. Nowadays it is possible to measure the bubble size distribution, gas holdup and superficial gas velocity by using specialized equipment developed for this purpose. In this article a methodology is presented for estimating the kinetic rate constant using a known particle and bubble size distributions. The attachment and detachment probabilities were modelled from three matrixes. The first matrix represents particle size distribution, the second was named the probability matrix, and the third is the bubble size distribution. Using laboratory data, it has been possible to estimate the flotation rate constant as a function of operating conditions and both the bubble and particle size distributions. The model tested at laboratory scale achieved a quadratic correlation coefficient equal to 0.97. This methodology could be used in the operation and control of the flotation, when in the near future we have industrial equipment that allows in-line measurement, in real time, of gas dispersion and bubble size distribution. knowing particle size distribution, it will be possible to manipulate the operating flotation cell conditions, in order to modify the bubble size distribution and find the bubble distribution that maximizes flotation kinetics. Furthermore, knowing the bubble size distribution, the grinding operator will be able to look for the particle size distribution that produces the maximum flotation kinetics. In order to do this, the operator will have to modify the solids percentage fed to the hydrocyclone cluster, modify the apex/vortex ratio, etc. Finally, this article shows that the maximum flotation speed is reached when the particle size distibution slope is equal to the bubble size distribution slope."