Effect of detachment velocity on the dynamic contact angles between bubble and glass plate with different contact angles

In recent years, researchers have been dedicated to improving the understanding of detachment mechanisms to achieve efficient recovery of coarse particles. Traditional bubble detachment models are mostly based on quasi-static conditions and do not adequately account for the effect of detachment velocity. However, in practical flotation processes, there exist significant variations in particle detachment velocities, and the effect of these variations on detachment has not yet been systematically investigated. To address this, a customized bubble-glass plate detachment measurement system was employed to study the effect of detachment velocity on the dynamic contact angle during detachment. The classical Hoffman model for dynamic contact angle was modified, and a new formula for calculating dynamic capillary force incorporating contact angle hysteresis was developed. The results show that an increase in bubble detachment velocity enhances the contact angle hysteresis effect, which promotes the formation of a reverse capillary neck at the bottom of the bubble, leading to an increase in the residual bubble volume after detachment. This trend becomes more pronounced with increasing substrate hydrophobicity. By introducing and modifying the classical Hoffman model, a functional relationship between the dynamic contact angle and the capillary number was fitted and validated. Furthermore, a dynamic capillary force formula accounting for contact angle hysteresis was derived. The model predictions exhibit strong agreement with experimental results, not only validating its effectiveness in describing interfacial mechanical behavior during dynamic bubble detachment but also extending traditional capillary force models to dynamic detachment conditions.