Compound droplets are excellent analogs of complex biological entities such as vesicles or cells. Despite significant advancements toward understanding the morphological evolution of a compound droplet in an incipient flow, the specific role of interfacial rheology toward dictating the same remains unaddressed. Here, we bring out non-trivial implications of interfacial rheology on the deformation of a compound drop subject to an imposed flow. The interfacial viscosity, in effect, interacts with the flow-induced non-uniform surfactant distribution to alter the droplet morpho-dynamics in a rather engaging manner. We employ a closed-form analytical approach to delineate the relative roles of advective and diffusive transport. In the paradigm of diffusion-dominated interfacial transport, viscous interfacial stress arrests the droplet deformation, thus enhancing its stability. However, for large values of the interfacial dilatational viscosity, the drop deformation increases with the interfacial shear viscosity. On the contrary, in the paradigm of surface convection-dominated surfactant transport, the interfacial rheology does not have any significant effect on either the shape deformation or the emulsion rheology. These results may pave a way toward explaining several unique features of complex fluid–fluid interfaces encountered in nature and biology.

中文翻译：

---

线性流中复合下降的界面粘度决定的形态动力学

复合液滴是复杂生物实体（如囊泡或细胞）的极好类似物。尽管在理解初始流动中复合液滴的形态演变方面取得了重大进展，但界面流变学在决定相同形态方面的具体作用仍未得到解决。在这里，我们提出了界面流变学对受强加流动影响的复合液滴变形的重要影响。实际上，界面粘度与流动诱导的非均匀表面活性剂分布相互作用，以一种相当吸引人的方式改变液滴形态动力学。我们采用封闭形式的分析方法来描述平流和扩散传输的相对作用。在扩散主导的界面传输范式中，粘性界面应力阻止了液滴变形，从而增强其稳定性。然而，对于较大的界面膨胀粘度值，液滴变形随着界面剪切粘度的增加而增加。相反，在表面对流主导的表面活性剂传输范式中，界面流变对形状变形或乳液流变没有任何显着影响。这些结果可能为解释自然界和生物学中遇到的复杂流体-流体界面的几个独特特征铺平道路。界面流变对形状变形或乳液流变没有任何显着影响。这些结果可能为解释自然界和生物学中遇到的复杂流体-流体界面的几个独特特征铺平道路。界面流变对形状变形或乳液流变没有任何显着影响。这些结果可能为解释自然界和生物学中遇到的复杂流体-流体界面的几个独特特征铺平道路。