Dynamic wetting on deforming substrates, elastic sheets, and under evaporation: A study with the boundary element method

柔性和可切换基板的动态润湿具有许多令人着迷的表现和潜在的应用。薄弹性薄片上的液滴呈透镜形状，可通过施加在薄片上的张力来调节。这种效应可以用来制造微光学透镜。及时控制软基板的表面变形可以移动微米大小的液滴，这是芯片实验室设备的基本过程。覆盖有可调光表面活性剂的液滴的蒸发提供了以亚液滴精度在基材上定位溶质（如油墨颜料）的可能性，这与印刷技术的进步有关。在我们的项目中，我们计划解决这些问题，以实现基本和彻底的理解。我们将使用边界元法（BEM）来确定液滴内的流场，并使用Cox-Voinov定律等现象学表达式来描述接触线动力学。最近，我们已经在计算机代码中实现了具有时空润湿性模式的刚性衬底的BEM方法，我们将扩展到处理不同的主题。首先，我们将研究液滴在光响应材料表面的行波变形的定向输运，并确定最佳输运条件。其次，我们讨论了弹性片上的动态润湿，我们用二维弹性Skalak模型和Helfrich汉密尔顿弯曲量来描述。我们对不同张力下的透镜状液滴进行了深入的研究，并研究了液滴移动到薄片较软部分的趋向性。第三，我们将施加张力，张力随时间和沿薄片边缘变化，以探索控制液滴运动的可能性，也使用电润湿。我们将在这里与P. Huber（汉堡）合作，他们可以制造弹性纳米多孔硅片，并计划进行相应的实验。最后，对于刚性基质，我们观察蒸发液滴，其中由可光切换表面活性剂决定的表面张力随着辐照光局部改变。由此产生的马兰戈尼电流在液滴内引发漩涡，从而捕获溶质，并最终以设计的图案沉积在基底上。

Dynamic wetting of flexible and switchable substrates has many fascinating manifestations and potential for applications. Droplets on thin elastic sheets assume the shape of a lens, which is tunable by tension forces applied to the sheet. This effect can be used to construct micro-optical lenses. Controlling the surface deformations of soft substrates in time allows to move micron-sized droplets, an essential process for lab-on-a-chip devices. The evaporation of droplets covered with light-switchable surfactants offers the possibility to position solutes such as ink pigments on a substrate with subdroplet precision, which is relevant for technological advances in printing.In our project we plan to address these topics in order to achieve a fundamental and thorough understanding. We will use the boundary element method (BEM) to determine the flow field within the droplet and phenomenological expressions such as the Cox-Voinov law to describe the contact-line dynamics. Recently, we have implemented our BEM approach for rigid substrates with spatio-temporal wettability patterns in a computer code, which we will extend to deal with the different topics.First, we will study the directed transport of droplets by traveling-wave deformations on the surface of light-responsive materials and determine conditions of optimal transport. Second, we address dynamic wetting on elastic sheets, which we describe with the two-dimensional elastic Skalak model and the Helfrich Hamiltonian for bending. We perform a thorough study of the lens-shaped droplets under varying tension forces and investigate durotaxis, where the droplet moves to softer parts of the sheet. Third, we will apply tension forces, which vary in time and along the sheet edge to explore the possibility of controlled droplet motion, also using electrowetting. We will collaborate here with P. Huber (Hamburg), who can fabricate elastic nanoporous silicon sheets and plans to perform corresponding experiments. Finally, for rigid substrates we look at evaporating droplets, where the surface tension determined by light-switchable surfactants is locally changed with irradiated light. The resulting Marangoni currents induce vortices within the droplet, which trap solutes and ultimately deposit them on the substrate in designed patterns.