Detachment of particles from bubbles in a turbulent motion

In the flotation process for separating minerals from ores, a key step is the collection of hydrophobic particles by bubbles. In mechanical cells, turbulence is necessary to bring bubbles and particles together and improve the rate of flotation of fine particles. However, it is known that when the turbulent field is too strong, as evidenced by high values of the energy dissipation rate, coarse particles can detach from the bubbles, leading to a reduction in recovery as the particle size increases beyond a certain value. Schulze (1982) constructed a theory which postulated that particles would break away from bubbles when the centrifugal detachment force induced on a particle as it rotates about the centre of a turbulent eddy, exceeds the forces of attachment due to surface tension. Thus if a dimensionless Bond number is defined as the ratio of the detachment forces to the attachment forces, particles will detach when the Bond number Bo > 1. This theory has not previously been tested. This investigation is concerned with the behaviour of particles attached to bubbles, that are allowed to rise into the turbulent region surrounding an impeller rotating in a stirred vessel. Schulze’s theory has been closely examined, and some minor errors have been detected and corrected. Experiments have been conducted in which the Bond number is calculated in terms of the power input into the cell, the particle size and shape, the contact angle, and the sizes of the bubble and the particle. It has been observed that the particles do not detach at a single Bond number. Rather, as the energy input increases, the fractional detachment of particles increases, but there is no sharp cutoff value at which all particles detach. When interpreting the results, a value of the Bond number Bo₅₀ at which 50% of the particles, detach has been found to follow Schulze’s theory in broad terms. Experiments were performed in which the bubble-laden particles were introduced into the tank at different radial distances from the centre. The energy dissipation rate diminishes quite quickly with increasing radial distance, as has been reported by various workers in the literature. The literature values were used, to calculate the appropriate Bond number at the different locations. All the components of the Bond number, such as the energy dissipation rate, the bubble and particle sizes, and the contact angle have been varied independently, to investigate their effect. In general, the results fall within the range predicted by Schulze’s theory, providing the correct value of the local energy dissipation rate is used.