Influence of Marangoni stress on the variation in number of coalescence cascade stages

The present work is an experimental and theoretical study on surfactant-laden liquid drop impact on a liquid pool. When the drop breaks into a secondary droplet after impinging, then it is called partial coalescence. If this happens successively in self-similar manner then it is called coalescence cascade. Three different types of surfactants, cationic, anionic, and non-ionic, are used as drop fluid and water as the liquid pool. Here we report how the surfactant types and concentrations affect the number of stages in coalescence cascade. The experimental outcome revealed that the number of stages in cascade decreases with increasing surfactant concentration. Also, we determine that drop viscosity, density, and size play a crucial role while comparing the stages of cascade among three types of surfactants. We also perform scaling analysis to determine the contribution of inertial and surface forces in the cascade. A theoretical analysis using lubrication approximation has also been carried out to justify the experimental observations. The coalescence process is actually triggered by the drainage of entrapped air between the drop and pool. The theoretical analysis reveals that the faster air drainage rate and acceleration induces a strong Marangoni stress for necking and quick pinch off. Finally, it is shown that Marangoni flow, originated due to the surface tension difference between the drop and pool, is responsible for partial coalescence and a number of coalescence stages in cascade.