The probability of particle capture by an isolated bubble rising through a suspension of particles has been determined using fundamental principles of fluid mechanics. This analysis has allowed the rate constant for flotation to be evaluated as functions of bubble sine, particle size, flotation column diameter, air flow rate and critical film rupture thickness. The last parameter is a measure of the hydrophobicity of the particles to be floated. Using the theoretically determined rate constant, a population balance model has been developed for the flotation of fine coal in a column. The model is capable of predicting the dynamic response of the flotation column to changes in a wide range of operational conditions. Model simulations have been found to be in reasonable agreement with experiments conducted using a bench-scale column. / Ph. D. / incomplete_metadata