Particle-Bubble Attachment in Mineral Flotation

Influence of surface active substances on bubble motion and collision with various interfaces

Bubble motion as a function of distance from a point of its detachment and phenomena occurring during the bubble approach and collision with liquid/gas and liquid/solid interfaces in pure water and solutions of various surface active substances are described and discussed. It is showed that presence of surface active substance has a profound influence on values of the terminal velocity and profiles of the local velocity. At low solutions concentrations there are three distinct stages in the bubble motion: (i) a rapid acceleration, (ii) a maximum velocity value followed by its monotonic decrease, and (iii) attainment of the terminal velocity, while at high concentrations (and in pure water) there are only stages (i) and (iii). It is showed that the bubble terminal velocity decreases rapidly at low surfactant concentration, but there can be found some characteristic concentrations (adsorption coverage's) above which the velocity almost stopped to decrease. Immobilization of the bubble surface resulting from adsorption of the surface active substances (surface tension gradients inducement) causes over twofold lowering of the bubble velocity. Presence of the maximum on the local velocity profiles is an indication that a stationary non-uniform distribution of adsorption coverage (needed for immobilization the bubble interface) was not established there. When the rising bubble arrives at liquid/gas interface or liquid/solid interface there can be formed either foam or wetting film or three-phase contact (TPC). It is showed that prior to the foam and/or wetting film formation the bubble colliding with the interfaces can bounce backward and simultaneously its shape pulsates rapidly with a frequency over 1000 Hz. It is rather unexpected that even in the case of the free surface the bubble's shape and consequently its surface area can vary so rapidly. It shows straightforward that on such a rapidly distorted interface the adsorption coverage can be very different from that at equilibrium. This fact should be taken into account more appropriately in the discussion of the mechanism of formation and stabilization of various dispersed systems (e.g. foams, emulsions). Bubble collision with solids and formation of the three-phase contact is a necessary condition for flotation separation. It is rather common understanding that immediate attachment should occur in the case of hydrophobic surface, while there should be no attachment in the case of the hydrophilic ones. It is reported that even in the case of such hydrophobic solid surface as Teflon, the bubble attachment did not need to occur at first collision and in distilled water the bubble can bounce a few times without attachment. Presence of frother facilitates the bubble attachment to hydrophobic solid surface. Time scale of the TPC formation is very short, of an order of single ms. It was observed that presence of a micro-bubble at the solid surface facilitated drastically an attachment of the colliding bubble. Roughness of Teflon surface increases probability of the bubble attachment-most probably-as a result of higher probability of micro- and/or nano-bubbles presence at the solid surface.

Movement of fine particles on an air bubble surface studied using high-speed video microscopy

A CCD high-speed video microscopy system operating at 1000 frames per second was used to obtain direct quantitative measurements of the trajectories of fine glass spheres on the surface of air bubbles. The glass spheres were rendered hydrophobic by a methylation process. Rupture of the intervening water film between a hydrophobic particle and an air bubble with the consequent formation of a three-phase contact was observed. The bubble-particle sliding attachment interaction is not satisfactorily described by the available theories. Surface forces had little effect on the particle sliding with a water film, which ruptured probably due to the submicrometer-sized gas bubbles existing at the hydrophobic particle-water interface.

Bubble particle heterocoagulation under turbulent conditions

An analytical model that enables the calculation of the flotation rate constant of particles as a function of particle size with, as input parameters, measurable particle, bubble, and hydrodynamic quantities has been derived. This model includes the frequency of collisions between particles and bubbles as well as their efficiencies of collision, attachment, and stability. The generalized Sutherland equation collision model and the modified Dobby-Finch attachment model developed previously for potential flow conditions were used to calculate the efficiencies of particle-bubble collision and attachment, respectively. The bubble-particle stability efficiency model includes the various forces acting between the bubble and the attached particle, and we demonstrate that it depends mainly on the relative magnitude of particle contact angle and turbulent dissipation energy. The flotation rate constants calculated with these models produced the characteristic shape of the flotation rate constant versus particle size curve, with a maximum appearing at intermediate particle size. The low flotation rate constants of fine and coarse particles result from their low efficiency of collision and low efficiencies of attachment and stability with gas bubbles, respectively. The flotation rate constants calculated with these models were compared with the experimental flotation rate constants of methylated quartz particles with diameters between 8 and 80 micro m interacting with gas bubbles under turbulent conditions in a Rushton flotation cell. Agreement between theory and experiment is satisfactory.