Figure 6. Schematic representation of air bubble-water-solid particle system equilibrium force balance .
The contact angle may be altered by the addition of reagents prior to the flotation process. There are many factors that determine the success of floating a hydrophobic particle within a flotation cell: bubble diameter, turbulence within the cell, velocity of rising air bubbles, contact angle, collision efficiency, attachment efficiency, and stability efficiency. Several of these key parameters are influenced by the mixing that occurs within the flotation cell.
The schematic of a flotation cell is shown in Figure 7. Mechanically agitated flotation cells utilize an impeller to provide the agitation necessary for breaking air into bubbles and dispersing them throughout the cell while suspending solids long enough for bubble-particle agglomerates to form. It also creates the micro-turbulence necessary to facilitate bubble-particle collision. Air enters the cell through a concentric pipe surrounding the impeller shaft. The rotating impeller tips create a high-shear zone where air is broken up into a dispersion of bubbles. The bubble formation is shown in Figure 8. The bubbles are flung outwards from the impeller tips and scattered throughout the solid-liquid mixture (slurry) within the cell.
Figure 7. Schematic of a mechanical flotation cell 17].
The power dissipation per unit mass (mean energy dissipation, ε) influences the size of the bubbles . ε can be calculated with [7, 19]
P: power (W)
ρSL: density of the slurry (kg/m3)
V: volume of the slurry (kg/m3)
N: impeller rotational speed (rps)
D: impeller diameter (m)
k: geometric constant for a given impeller. Derived from the impeller swept volume.
The energy dissipation at the tip of the impeller is ~20 times greater than the average for the entire flotation cell [7, 19].
Figure 8. Schematic diagram of formation of bubbles in mechanical cells (after Grainger Allen, 1970; courtesy of Transactions of the Institute of Metallurgy, UK) .
The frequency of bubble-particle collisions, Z, determines the flotation rate for a system. An increase in dissipation rate leads to a greater frequency of collisions and therefore a higher flotation rate .
Impeller Rotational Speed
The effect of impeller speed is highly dependent on particle size; therefore, it is advantageous to separate fine and coarse material prior to the flotation step.
For fine particles a high impeller rotational speed causes greater energy dissipation. The collision frequency increases and this increase in collisions results in a higher flotation rate.
The opposite is observed overall for coarse particles. Higher rotational speeds increase the impeller tip speed and turbulence within the cell. An increase in tip speed causes bubble velocity to rise which in turn lowers the contact time between bubbles and particles. An increase in turbulence causes coarse particle-laden bubbles to readily burst and particle detachment to occur. These two factors contribute to a reduced flotation rate for coarse particles. In Figure 9 the bubble size is given as a function of Jg.
The bubble size within the collection zone is not affected by impeller rotational speed .
Figure 9. Sauter mean bubble diameter in the first lead rougher cell as a function of Jg, for surveys on different days with different impeller rotational speeds .
Power input may be used to increase flotation rate up to a certain point. As power input to the impeller is increased, the attachment rate increases until a certain maximum flotation rate is reached. At this point, any further increase in power input results in a large decrease in attachment rate and consequently an increase in overall detachment rate .
Most impellers are up-pumping and consist of a flat, circular disc with blades fitted concentrically to the disk’s lower section. The shape of the blade varies from cylindrical to half-spherical depending on the process. The submergence of the impeller depends on cell type/geometry and method of air introduction to the cell . Typical flow patterns, impellers and rotators for a flotation cell are given in Figures 10 and 11, respectively.
Figure 10. Typical flow patterns in a mechanical flotation cell (courtesy of Outokumpu Mintec Oy, Finland) .
Figure 11. Shapes of different impellers and stators. (A) Bateman; (B) Dorr-Oliver; (C) Outokumpu; (D) Wemco (courtesy of Bateman Process Equipment, Dorr-Oliver, Outokumpu Mintec Oy and Baker Process, respectively) .