Microflotation of fine particles in the presence of a bulk-insoluble surfactant

A theoretical description of the flotation of semiBrownian spherical particles by small spherical bubbles containing a surface active substance is presented. The surfactant is considered to be insoluble in the bulk and to have small deviations in surface coverage. Collection efficiencies between the surfactant covered bubbles and the rigid particles are calculated with allowance for gravity, Brownian motion, and van der Waals attraction for a variety of bubble Péclet numbers and particle-to-bubble size ratios. The hydrodynamic problem was decomposed into axisymmetric and asymmetric parts, and pairwise hydrodynamic mobility functions were calculated for different degrees of bubble surface mobility. The effect of the adsorbed surfactant is characterized by the dimensionless surface retardation parameter, A=MaPes, a product of the Marangoni and surface Péclet numbers. A=0 corresponds to a bubble with a freely mobile interface. For the limiting case of A→∞, the axisymmetric problem reduces to that of a bubble with a rigid interface. In the asymmetric problem, however, higher transversal mobilities occur for the case of A→∞ than for those of a rigid bubble. This fact results in lower collection efficiencies for A→∞ than for rigid bubbles, in some cases by as much as 80%. In general, the maximum influence of the bubble surface mobility on the collection efficiency occurs in the range where bulk convective and diffusive effects are comparable; in these cases, the collection efficiencies may vary by more than an order of magnitude for the range of possible values assumed by the surface retardation parameter.