Application of extended DLVO theory .4. Derivation of flotation rate equation from first principles

A flotation model was developed by considering both hydrodynamic and surface forces involved in the process, The hydrodynamic forces were determined using a stream function and then used for estimating the kinetic energies that can be used for thinning the water films between bubbles and particles. The kinetic energies were compared with the energy barriers created by surface forces to determine the probability of adhesion. The surface forces considered included ion-electrostatic, London-van der Waals, and hydrophobic forces. Due to the insufficient information available on the hydrophobic forces for bubble-particle interactions, contributions from the hydrophobic force were back-calculated from the values of the flotation rate constants determined experimentally with methylated silica spheres, The results show that the hydrophobic force constants (K-132) for bubble-particle interaction are larger than those (K-131) for particle-particle interactions but smaller than that (K-232) for air bubbles interacting with each other in the absence of surfactants, The K-132 values determined in the present work are close to the geometric means of K-131 and K-232, suggesting that the combining rules developed for dispersion forces may be useful for hydrophobic forces. The flotation rate equation derived in the present work suggests various methods of improving flotation processes. (C) 1996 Academic Press, Inc.