Modelling and model validation of particle stability and detachment from the particle-laden surface

Abstract

Particle-bubble aggregates in flotation are characteristic of particle-laden bubbles and surfaces, but the available theories focus on the stability and detachment of single particle that resides lonely at the free surface. There is no modelling attempt to quantify the particle stability and detachment from the laden surfaces that can be relevant to flotation. Here, we developed a model that considers the particle tenacity (maximum adhesion force) at the particle-laden surface by solving the Young-Laplace equation (YLE) using the superposition approximation method. The vertical position of the target particle was calculated by considering the additive effect on the position by other nearby particles at the laden surface, based on the linearised YLE. Using the numerical results, a semi-empirical model for the particle tenacity was developed for engineering calculation exercises and assessed against the data of film flotation experiments. Application of the model to the case of changing contact angle was also established. The tenacity of particles at the laden surface was shown to be higher than at the free surface due to the lateral capillary attraction. This is the first model to quantify the particle stability and detachment from the particle-laden surface that can be useful for flotation.