FLOTATION RATES OF FINE, SPHERICAL-PARTICLES AND DROPLETS

Flotation rates of fine, spherical particles or droplets by a spherica l, rising bubble or drop have been computed for conditions relevant to microflotation. The buoyancy-driven motion of the rising drop (or bub ble) is characterized by small Reynolds, and large Peclet numbers. Par ticular attention is given to suspended droplets (or particles) much s maller than the rising drop; dilute conditions are assumed. Two comple mentary regimes are considered: (1) convective capture dominated by th e buoyancy-driven, relative motion between a collecting drop and small er, dispersed droplets, and (2) capture dominated by diffusive transpo rt of small droplets within a boundary layer on the surface of a large r collecting drop. The first regime is relevant for the flotation of m icron-size and larger droplets; the second is relevant for submicron s izes. A scaling analysis reveals three distinct mechanisms for droplet capture by a larger rising drop. According to the scaling analysis, f lotation rates depend strongly on the size of the dispersed droplets, the size of the collecting drops, and the mobility of the collecting d rop interface; a bubble with a free surface is a more efficient collec tor than a viscous drop, and a collector with an interface immobilized by surfactant is least efficient. The scaling analysis predicts that flotation rates depend weakly on the strength of van der Waals forces, and are insensitive to the viscosity or density of the dispersed drop lets; flotation rates of droplets and particles are very similar. The scaling predictions are illustrated by dimensionless flotation rates c omputed by a trajectory analysis in regime (1), and by mass transport formulae for regime (2). Detailed pairwise, hydrodynamic and van der W aals interactions are incorporated into the analysis of the first regi me, but not the second where they are shown to be unimportant by scali ng arguments. The droplet size that is most difficult to float and its flotation rate are predicted by scaling and estimated numerically.