Forces arising during bubble–particle interaction

In numerous natural and industrial situations, including froth flotation, particles and bubbles interact, and sometimes attachment is achieved. Through direct experimental observation of a particle dropping onto a stationary bubble, we have described particle–bubble interaction and attachment at low Reynolds numbers. Increased understanding can be gained by comparison to numerical modelling predictions. Our modelling incorporated: • Stokes drag; • inertia and added mass; • buoyancy; and • microhydrodynamic resistances, due to flow of liquid between the bubble and the approaching or retracting particle. The governing differential equation was resolved into radial and tangential components, and solved numerically to produce predictions of particle trajectories, and velocities, which can be used to predict the likelihood of attachment, and the 'induction period' for attachment. These can be compared to the experimental results. Even greater insight is obtained by explicitly evaluating the force components. The evolution of these forces over time reveals which mechanism is controlling the interaction at various stages. It also provides a basis for inclusion or neglect of other terms in the governing equation (e.g. Basset force). We simulated the interaction for a variety of approach trajectories, with different particle densities. We also simulated cases in which particles approach at elevated speeds, as could occur in a real system where particles are accelerated by turbulent eddies toward a bubble that is enveloped by a laminar boundary layer. We found that increasing the initial velocity does not necessarily decrease the induction period, as deceleration can occur rapidly, before the particle is very close to the bubble. Particles impinging on the bubble away from the bubble's apex exhibited longer induction periods. If a repulsion of chemical origin prevents attachment, then low-energy particles 'slide' off the bubble, while high-energy particles could 'bounce' off the bubble's surface.