We analyze the interface-interface interactions of a surfactant-covered double emulsion using the lattice Boltzmann method and study the interaction of the inner and outer interfaces and the local surfactant distribution under a uniaxial extensional flow. First, the capillary effects are analyzed. Upon surfactant application, the outer droplet deformation increases and the inner droplet deformation decreases. The concentrated surfactants on the outer interface increase deformation, and the inner droplet is affected by the inner flow. At a fixed Péclet number (Pe), the surfactant concentration at the outer interface increases with an increase in capillary number (Ca); however, such a tendency is difficult to identify at the inner interface. Next, the Pe effects are analyzed. With an increase in Pe, the deformation of the inner droplet decreases significantly. The local distribution of the surfactant considerably affects the double emulsion stabilization, which is analyzed in terms of internal flow. The interfacial tension gradient induced by the surfactant generates vortices internally, which is verified by applying the surfactant to each interface independently. The radius ratio affects droplet deformation and surfactant transport. The compression of the inner flow region increases the viscous force and decreases the interface velocity. Therefore, with an increase in radius ratio, the deformation increases, and the surfactant transport becomes slow.

中文翻译：

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表面活性剂覆盖的双乳状液在拉伸流中的界面行为

我们使用晶格玻尔兹曼方法分析了表面活性剂覆盖的双乳状液的界面相互作用，并研究了单轴拉伸流下内外界面的相互作用以及局部表面活性剂的分布。首先，分析毛细作用。在施用表面活性剂时，外部液滴变形增加并且内部液滴变形减小。外部界面上浓缩的表面活性剂会增加变形，内部液滴会受到内部流动的影响。在固定的佩克利数（Pe）下，外界面处的表面活性剂浓度随毛细管数（Ca）的增加而增加；但是，这种趋势很难在内接口处识别。接下来，分析Pe效应。随着Pe的增加，内部液滴的变形显着降低。表面活性剂的局部分布极大地影响了双重乳液的稳定性，这是根据内部流动来分析的。表面活性剂引起的界面张力梯度会在内部产生涡旋，这可以通过将表面活性剂单独应用于每个界面来验证。半径比影响液滴变形和表面活性剂传输。内部流动区域的压缩增加了粘性力并降低了界面速度。因此，随着半径比的增加，变形增加，并且表面活性剂的输送变慢。表面活性剂引起的界面张力梯度会在内部产生涡旋，这可以通过将表面活性剂单独应用于每个界面来验证。半径比影响液滴变形和表面活性剂传输。内部流动区域的压缩增加了粘性力并降低了界面速度。因此，随着半径比的增加，变形增加，并且表面活性剂的输送变慢。表面活性剂引起的界面张力梯度会在内部产生涡旋，这可以通过将表面活性剂单独应用于每个界面来验证。半径比影响液滴变形和表面活性剂传输。内部流动区域的压缩增加了粘性力并降低了界面速度。因此，随着半径比的增加，变形增加，并且表面活性剂的输送变慢。