SIAM Journal on Applied Mathematics, Volume 81, Issue 1, Page 129-152, January 2021.
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 behavior in a homogeneous turbulent flow. We derive equations for the evolution of droplet size distribution, surfactant concentration, and surface tension. Our resulting model is analyzed using both asymptotic and numerical methods. We find that the large-time behavior is highly dependent on the history of the drop-surfactant interaction, and we 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 optimize surfactant application in industrial processes.

中文翻译：

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模拟表面活性剂对湍流中液滴破裂的影响

SIAM应用数学杂志，第81卷，第1期，第129-152页，2021年1月。
在许多工业应用中，悬浮在水中的油滴会由于湍流的运动而破裂，并需要添加表面活性剂。在本文中，我们建立了均匀湍流中液滴破裂与表面活性剂行为之间相互作用的模型。我们导出了液滴尺寸分布，表面活性剂浓度和表面张力的演化方程。我们使用渐近法和数值法对所得模型进行了分析。我们发现长时间行为高度依赖于液滴-表面活性剂相互作用的历史，并且我们确定了分解动力学中的不同阶段。然后，该模型用于研究增加表面活性剂的浓度如何促进增强的液滴破碎，从而增加较小液滴的比例。我们还探索了改变表面活性剂添加方法的方法，发现逐渐添加而不是一次全部添加表面活性剂可能具有优势。这些结果可用于优化工业过程中表面活性剂的应用。