Effects of surfactant on the critical velocity of bubble collisions for bubble coalescence

The determination of the critical collision velocity for bubble coalescence plays a crucial role in predicting bubble size distribution within bubble column reactors through population balance modeling. In this study, experimental measurements in surfactant-laden systems demonstrate that even trace amounts of surfactant significantly reduce the critical velocity. We propose the Marrucci number-a dimensionless parameter derived from the Marrucci film drainage model-as a fundamental metric for quantifying surfactant effects. This parameter is formally defined as the ratio between the film drainage resistance caused by the Marangoni effect and the driving force resulting from capillary pressure. Furthermore, we developed a novel correlation for critical velocity by establishing a quantitative relationship between the critical Weber number and the Marrucci number. This correlation successfully predicts critical velocities in ethanol solutions and shows potential applicability to other systems, such as propanol solutions.