The bounce behavior of a freely rising oil droplet in water under the horizontal wall constraint

Abstract

The interaction problem of a freely-rising oil droplet in water due to the horizontal wall constraint is solved numerically. The motion equation, water film drainage equation, and Young-Laplace equation are coupled to establish a dimensionless mathematical model for describing the bounce behavior of oil droplets in water. In addition to buoyancy and flow resistance, the motion equation also introduces added mass force and film induced force caused by interaction with the wall. Further analysis shows that the coupling model conforms to the dynamics characteristics of a damped vibration system from the perspective of vibration. Based on the analysis of vibration parameters, We found that the bounce behavior of oil droplets is directly related to the oil-water system's Eo number and Oh number, in addition to the size dependence. Moreover, the bounce pattern diagram with (G, Oh) as the control parameter provides a suitable identification for the transition law of the bounce number of oil droplets under the horizontal wall constraint. The findings of this study facilitate quantifying the processes of oil droplet adhesion, coalescence, and spreading and provide a sub-model reference for the description of complex oil-water systems.