APPLICATION OF EXTENDED DLVO THEORY .4. DERIVATION OF FLOTATION RATE-EQUATION FROM FIRST PRINCIPLES

A flotation model was developed by considering both hydrodynamic and s urface forces involved in the process, The hydrodynamic forces were de termined using a stream function and then used for estimating the kine tic energies that can be used for thinning the water films between bub bles and particles. The kinetic energies were compared with the energy barriers created by surface forces to determine the probability of ad hesion. The surface forces considered included ion-electrostatic, Lond on-van der Waals, and hydrophobic forces. Due to the insufficient info rmation available on the hydrophobic forces for bubble-particle intera ctions, contributions from the hydrophobic force were back-calculated from the values of the flotation rate constants determined experimenta lly with methylated silica spheres, The results show that the hydropho bic force constants (K-132) for bubble-particle interaction are larger than those (K-131) for particle-particle interactions but smaller tha n that (K-232) for air bubbles interacting with each other in the abse nce of surfactants, The K-132 values determined in the present work ar e close to the geometric means of K-131 and K-232, suggesting that the combining rules developed for dispersion forces may be useful for hyd rophobic forces. The flotation rate equation derived in the present wo rk suggests various methods of improving flotation processes. (C) 1996 Academic Press, Inc.