We study spreading of a droplet, with insoluble surfactant covering its capillary surface, on a textured substrate. In this process, the surfactant-dependent surface tension dominates the behaviors of the whole dynamics, particularly the moving contact lines. This allows us to derive the full dynamics of the droplets laid by the insoluble surfactant: (i) the moving contact lines, (ii) the evolution of the capillary surface, (iii) the surfactant dynamics on this moving surface with a boundary condition at the contact lines and (iv) the incompressible viscous fluids inside the droplet. Our derivations base on Onsager's principle with Rayleigh dissipation functionals for either the viscous flow inside droplets or the motion by mean curvature of the capillary surface. We also prove the Rayleigh dissipation functional for viscous flow case is stronger than the one for the motion by mean curvature. After incorporating the textured substrate profile, we design a numerical scheme based on unconditionally stable explicit boundary updates and moving grids, which enable efficient computations for many challenging examples showing significant impacts of the surfactant to the deformation of droplets.
当表面活性分子在液体界面释放时，它们的扩散动力学由Marangoni流控制。虽然这样的马兰戈尼蔓延调查在不同的限制，精确的解决方案仍然很少。在这里，我们考虑沿深流体层的界面的不溶性表面活性剂的蔓延。对于二维Stokes流，最近表明，非线性输运问题可以精确地映射到复杂的Burgers方程[Crowdy，SIAM J. Appl. Math. 81，2526（2021）]。我们首先提出一个非常简单的推导这个方程。然后，我们提供了完全明确的解决方案，并发现，不同的初始表面活性剂分布-脉冲，孔，或周期性的-结果在不同的传播行为。在得到基本解的基础上，我们还讨论了表面扩散的影响。我们确定的情况下，传播可以被描述为一个有效的扩散过程，但观察到这种近似是不普遍有效的。最后，简要地考虑了具有轴对称的三维流动的情况。我们的研究结果应该提供参考解决方案的马兰戈尼蔓延，可以用荧光或光开关表面活性剂进行实验测试。
Dynamic Wettability Modulation of Textured, Soft and LIS Interfaces Using Electrowetting
School of Mechanical Sciences, Indian Institute of Technology (IIT) Goa（印度理工学院果阿分校机械科学学院）；Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur（印度理工学院卡拉格普尔分校机械工程系）
Droplet impact of emulsions on inclined microstructured surfaces
Facultad de Ingeniería, Universidad Nacional Autónoma de México（墨西哥国立自治大学工程学院）；Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México（墨西哥国立自治大学材料研究所）
