effect of bubble/droplet morphology and slippage on attachment induction time in deoiling flotation process

a modified model has been analytically developed to describe the induction time of an elliptic air bubble in contact with an elliptic hydrophobic oil droplet. the role of hydrophobicity was revealed in the slippage of liquid over the surfaces of bubble and droplet. in this condition, the analytical relationships for pressure distribution and consequently hydrodynamic resistance force through the water film have been reported. the obtaining results were compared with the previous models and different orientations of approaching bubble and droplet have been investigated. it was found that the induction time is very sensitive to the orientation of bubble and droplet in collision. on the other hand, the role of slippage can be shown by the decrease in pressure and hydrodynamic resistance force in liquid film and also in induction time, in comparison with the case of drainage of a film confined between two particles under no-slip boundary conditions on their surfaces.