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迷人的表现形式和应用潜力。薄弹性片上的液滴呈现透镜的形状，其可通过施加到片上的张力来调节。这种效应可用于构造微光学透镜。及时控制软衬底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一个重要过程。覆盖着光开关表面活性剂的液滴的蒸发提供了以亚液滴精度将溶质（如油墨颜料）定位在基板上的可能性，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和现象学表达式，如Cox-Voinov定律来描述接触线动力学。最近，我们已经实现了我们的边界元方法的刚性基板的时空润湿性图案的计算机代码，我们将扩展到处理不同的topics.First，我们将研究的液滴的定向运输的行波变形的光响应材料的表面上，并确定最佳的运输条件。其次，我们解决动态润湿的弹性片材，我们描述的二维弹性Skalak模型和Helfrich哈密顿弯曲。我们进行了彻底的研究，在不同的张力下的透镜状液滴和调查durotaxis，液滴移动到较软的部分的表。第三，我们将施加张力，该张力随时间变化并且沿着片材边缘，以探索受控液滴运动的可能性，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，对于刚性基板，我们看看蒸发液滴，其中由光开关表面活性剂确定的表面张力随照射光而局部变化。所产生的马兰戈尼电流在液滴内诱导涡流，其捕获溶质并最终将它们以设计的图案存款在基板上。

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.