Particle retention during bubble deformation and breakup in flotation Systems: A numerical investigation in shear flow

This study presents a numerical investigation of the deformation, breakup, and particle-retention behavior of particle-laden bubbles subjected to shear flow. A coupled Eulerian–Lagrangian framework employing the Volume-of-Fluid (VOF) method together with the isoAdvector interface reconstruction algorithm is developed to simultaneously resolve gas–liquid interface dynamics and particle transport. Particle attachment to the bubble surface is modeled using a hydrophobic interaction force, enabling the simulation of particle retention and detachment during bubble deformation and breakup. The effects of Capillary number, density ratio, and viscosity ratio on bubble morphology and particle retention are investigated. The results show that increasing the Capillary number changes the deformation regime from stable elongation to complete breakup. The maximum particle-retention ratio of approximately 42% is obtained at Ca = 0.5 after 2 s, whereas increasing the Capillary number to 1.0 reduces the retention ratio to approximately 29% because of breakup-induced particle detachment. As the density ratio increases from 0.001 to 2.0, the number of attached particles at t = 0.5 s increases from 23 to 40, although stronger breakup subsequently reduces long-term attachment stability. Increasing the viscosity ratio from 9.06 × 10⁻ 3 to 1 decreases the number of retained particles at t = 0.5 s from 34 to 28 owing to enhanced interface oscillations and particle migration. Bubble breakup is identified as the primary mechanism governing particle detachment through interfacial deformation and transient flow disturbances. The developed framework provides a robust computational tool for predicting particle-retention behavior in flotation and related gas–liquid–solid separation processes.