Localised inducement of bubble surface mobility due to motion of a nearby particle

Bubbles found in nature or in industrial systems are often presumed to have immobile surfaces (i.e. a 'no-slip' boundary condition), due to surfactant adsorption. Even trace amounts of surfactants in the bulk liquid can result in effective immobilisation, because of the preferential partitioning of surfactants at the interface. In froth flotation, used to separate valuable minerals from waste 'gangue', interaction of bubbles with particles is modelled to predict the possibility of achieving attachment. The modelling often presumes a completely immobile bubble surface — although the alternative limiting condition of a fully mobile bubble surface ('full slip' boundary condition) is occasionally investigated. From recent experimental observations of a particle falling onto a submerged bubble it was concluded that the interface was partially mobile. A closer inspection of the data revealed that a transition from the immobile to (partially) mobile state may be occurring locally. It is known that flow of liquid over the surface of a rising bubble can sweep adsorbed surfactants to the rear of the bubble, forming a 'stagnant cap'. A similar principle could apply, locally, as liquid is squeezed out of the gap between a bubble and an approaching particle. In flotation the particles are often much smaller than the bubbles. The gas–liquid interface can then be approximated as a plane, and analytical solutions for the flow field are known. I derived from these the shear stresses at the bubble's surface in bipolar co-ordinates, for both parallel and perpendicular components of the particle's motion. Both cases attained shear stresses much greater than those required to form a stagnant cap. The tangential particle motion induced stresses that would be sufficient to sweep surfactant out of the interaction zone, thereby locally enhancing the surface mobility. These new findings quantitatively support the existence of a transition of bubble surface mobility, mediated by motion of a nearby particle, and strongly dependent upon the particle's trajectory.