Modelling the effect of surfactant on droplet breakup in a turbulent flow

In many industrial applications oil drops suspended in water are broken down by turbulent fluid motion, assisted by the addition of surfactants. In this paper, we develop a model for the interaction between droplet breakup and surfactant behaviour in a homogeneous turbulent flow. We derive equations for the evolution of droplet size distribution, surfactant concentration and surface tension. Our resulting model is analysed using both asymptotic and numerical methods. We find that the large-time behaviour is highly dependent on the history of the drop-surfactant interaction, and identify distinct phases in the breakup dynamics. The model is then used to investigate how increasing the concentration of surfactant promotes enhanced droplet breakup and thus increases the proportion of smaller droplets. We also explore varying the method of surfactant addition, and find that there may be advantages to adding the surfactant gradually rather than all at once. These results can be used to optimise surfactant application in industrial processes.