The liquid flow force on a particle in the bubble-particle interaction in flotation

In this paper the problem of calculating the liquid flow force on a particle in interaction with an air bubble with a mobile surface in flotation as a function of the separation distance was solved. The force equation was obtained by first deriving the disturbed flow confined between the surfaces. The model for the force includes the separation distance between the bubble and the particle, the particle size, the bubble's Reynolds number, the bubble rise velocity, and the polar position of the particle on the bubble surface. The proposed equations provide an exact solution to the situation where the particle and the bubble are very close together. The attractive flow force and the surface forces are of similar orders of magnitude. Consequently, the models presented in this paper should provide a better estimate for calculating the forces on particles interacting with air bubbles in mineral flotation and other separation operations involving colloidal interactions.