Demonstration of a minimum in the recovery of nanoparticles by flotation: Theory and experiment

The flotation of nano- and submicron particles does not follow the conventional collection theory based on the interception and collision mechanisms, which predicts extremely low collection efficiency for particles smaller than 10-μm10-μm. Brownian diffusion and colloidal forces strongly influence the collection of such particles by air bubbles in flotation. In this paper, a theoretical model is presented for predicting the collection efficiency of nanoparticles. The theory incorporates mass transfer by Brownian diffusion, microhydrodynamics of particles in the vicinity of a slip surface of rising air bubbles, and colloidal interactions that come into effect at small separation distances. The governing equation was solved numerically using the Crank–Nicolson method with variable step size. A finite difference scheme with mesh refinement in the vicinity of the air bubble surface was used to discretise the stiff partial differential equation for the particle concentration. The mesh refinement produced correct numerical solutions without oscillation in the particle concentration distribution, which otherwise occurred due to the stiffness of the differential equation and coarseness of the numerical mesh. Predictions from the model were compared with experimental results obtained with a small laboratory column cell, in which colloidal silica particles with diameters in the range 40–160nm were floated using fine bubbles of typical average diameter 150μm. The particle concentration in the pulp was about 1% by weight. Cetyltrimethyl ammonium bromide and Dowfroth 250 were used as the flotation collector and frother, respectively. Both the theory and experiment show significant effect of the electrical double-layer and non-DLVO hydrophobic attractive forces on the collection of nanoparticles by air bubbles. The theoretical and experimental results show the collection efficiency to have a minimum at a particle size in the order of 100nm. With larger particles, the interception and collision mechanisms predominate, while the diffusion and colloidal forces control the collection of particles with a size smaller than the transition size.