Theory of flotation of small and medium-size particles

The paper describes a theory of flotation of small and medium-size particles less than 50μ in radius) when their precipitation on a bubble surface depends more on surface forces than on inertia forces, and deformation of the bubble due to collisions with the particles may be neglected. The approach of the mineral particle to the bubble surface is regarded as taking place in three stages corresponding to movement of the particles through zones 1, 2 and 3. Zone 3 is a liquid wetting layer of such thickness that a positive or negative disjoining pressure arises in this intervening layer between the particle and the bubble. By zone 2 is meant the diffusional boundary layer of the bubble. In zone 1, which comprises the entire liquid outside zone 2, there are no surface forces. Precipitation of the particles is calculated by considering the forces acting in zones 1, 2 and 3. The particles move through zone 1 under the action of gravity and inertia. Analysis of the movement of the particles under the action of these forces gives the critical particle size, below which contact with the bubble surface is impossible, if the surface forces acting in zones 2 and 3 be neglected. The forces acting in zone 2 are ‘diffusio-phoretic’ forces due to the concentration gradient in the diffusional boundary layer. The concentration and electric field intensity distribution in zone 2 is calculated, taking into account ion diffusion to the deformed bubble surface. An examination is made of the ‘equilibrium’ surface forces acting in zone 3 independent of whether the bubble is at rest or in motion. These forces, which determine the behaviour of the thin wetting intervening layer between the bubble and the mineral particle and the height of the force barrier against its rupture, may be represented as results of the disjoining pressure forces acting on various parts of the film. The main components of the disjoining pressure are van der Waals forces, forces of an iono-electrostatic nature and forces related to structural changes in the boundary layers. A quantitative examination of the first two kinds of forces makes it possible (by neglecting the forces of the third kind) to obtain the condition of disappearance of the force barrier, i.e. of unhindered rupture of the wetting film and formation of a wetting perimeter. When this condition is fulfilled the kinetics of flotation recovery depends only on stages 1 and 2. Calculation of the forces acting in zone 2 and of their influence on the velocity of precipitation of the particles is given separately for small particles, the size of which does not exceed the thickness of the diffusional boundary layer, and for relatively large (‘medium’) particles, whose size is greater than the thickness of the diffusional boundary layer. The possibility and rate of precipitation of small particles are determined by diffusio-phoretic relationships in the concentration and electric fields of the diffusional boundary layer. A formula is derived for the resultant velocity of precipitation of small particles on a bubble surface under the action of gravity and diffusio-phoretic forces (in the absence of a force barrier in zone 3), and this serves as a basis for calculating the effectiveness of precipitation and the critical particle size below which contact is impossible at certain values of the cationic and anionic components of the ζ-potential (even for hydrophobic particles). The paper then deals with the specific forces of a diffusio-electric nature, which arise when the particle acquires or surpasses the ‘average’ size of zone 2, in the process of desorption of the flotation reagent from its surface, its diffusion to the bubble surface and adsorption on it. It is shown that these forces favour thinning of the liquid layer between the bubble and particle surfaces, the viscous resistance of which in their absence cannot be overcome in a number of cases during the ‘contact’ time. ‘Medium’-sized particles, and under certain conditions small particles as well, pass through stage 2 ‘unhindered’, and then flotation efficiency depends on the forces acting in zone 3. In particular, there may be cases where the main controlling factor is the ζ-potential.