Resonance and surfactant effects on the interaction of a rising bubble and a sedimenting particle in an oscillating fluid

This paper considers the interaction of a rising bubble and a sedimenting fine particle in a liquid with a soluble surfactant subjected to the gravity field, forced flow, and vibrations. The frequency of vibrations is close to the resonance value. The particle motion trajectories are calculated, taking into account its inertia, fluid viscosity, Basset force, buoyancy force, and the mean force acting on the particle due to the inhomogeneity of the pulsating field. The collision efficiency is evaluated, and the cross sections of the sedimenting particles captured by the rising bubble are found. It is demonstrated that even at low vibration intensity but in the presence of a weak surfactant effect, a significant increase in the probability of particle–bubble collision and in the capture cross section can be achieved. The obtained results can be used to intensify the flotation processes by ultrasonic treatment.