Coal flotation kinetics: Methods for estimating distribution of rate constants

To incorporate the effect of particle size and hydrophobicity on the distribution of flotation rate constants, the existing first-order models were modified. This was done by addition of a third parameter which enabled the width of the distribution to become independent of the mean flotation rate. The three-parameter models, which were so obtained from their two-parameter analogs, such as rectangular, triangular and sinusoidal, fitted the flotation rate data very well for a variety of experimental conditions. Separate estimates of the flotation rate constant distributions by microscopy and film flotation techniques agreed with the estimates from the three-parameter models. It was observed that the differences in the values of the model parameters and curve-fitting errors diminished upon modification. This eliminated the need for model discrimination among the first-order models.;Three methods of estimating the "true" distribution of flotation rate constants were evaluated for a variety of materials and experimental conditions using the modified first-order models. These methods generated estimates of the "true" distribution using the kinetics data from the total, size fractionated and size-specific gravity fractionated froth products. The estimates obtained using the total flotation products depended on the model utilized. Since the flotation rate constant distribution of a given material was a complex function of particle size and hydrophobicity, a single function should not be expected to produce a good estimate for a wide range of experimental conditions. The estimates using the narrow size fractions of the froth products were model independent. By this approach the effects of size and hydrophobicity on the flotation rate could be evaluated separately. Fractionation of the froth products into size and specific gravity fractions suffered from large analytical, sampling and statistical errors in addition to the extremely tedious experimental procedures. Kinetic analysis on narrow, non-overlapping size fractions was found to be a good compromise in estimating the "true" distributions of flotation rate constants.