Highly accurate numerical simulation of wetting and dewetting on flexible substrates including Heat transfer

该项目的实质是数值模拟方法的发展。要分别模拟的具体物理是由优先计划2171(SPP 2171)中计划的实际实验激发的。特别是，要研究柔性表面发生润湿或去湿的实验。为此，在第一个供资阶段开发了相应的高精度数值工具箱，用于模拟由弹性固体以及液体和气相组成的三相系统。在该计划的第二个资助阶段，这些模拟技术将得到进一步改进和扩展，以涵盖更广泛的实验。特别是，现在要考虑蒸发效应。值得注意的是，模拟是对SPP 2171中实验的补充，可以说，它可以起到放大镜的作用：它提供了实验无法提供的见解。例如，模拟使确定由于技术限制而难以或不可能在实验中测量的量成为可能。计划对日益复杂的实验进行补充模拟。在一开始，将会有简单的液滴和液桥的配置。在进一步的课程中，将研究液滴在柔性衬底上的冲击行为。通过加热衬底进行蒸发也将被考虑。作为该项目的总结，最具挑战性的模拟是莱登弗罗斯特构型，即由自身蒸汽层支撑的蒸发液滴在加热的基质上方盘旋。模拟过程基于申请者开发的两相流数值方法。这些是两种不相容的流体的混合物，在这种情况下是印刷油墨和环境空气。这一设置现在由第三阶段补充，即柔性固体。如果空气、液体和固体相遇，这被称为三相接触线。该项目的数值数学基础是一种所谓的扩展间断Galerkin方法，该方法是专门为高精度模拟有接触线的三相流动而开发的。特别是气液界面以及三相接触线的跟踪精度更高。对于给定的问题，该方法必须与固体模拟方法相结合。此外，还必须对传热和蒸发进行建模。

The essence of this project is development of numerical simulation methods. The specific physics to be modeled, respectively simulated, is motivated by the practical experiments planned in the Priority Program 2171 (SPP 2171). In particular, experiments are to be investigated in which wetting or dewetting of flexible surfaces takes place. For this purpose, a corresponding high-precision numerical toolbox for the simulation of three-phase systems, consisting of a flexible solid as well as a liquid and a gaseous phase, was developed in the first funding phase. In the second funding phase of the program, these simulation techniques will be further improved and extended to cover a broader range of experiments. In particular, evaporation effects are now to be taken into account.It is important to note that simulation is a complement to the experiments in SPP 2171 here, as it can act as a magnifying glass, so to speak: it provides insights that experiment cannot. For example, simulations make it possible to determine quantities that are difficult or impossible to measure in experiments due to technical limitations.The complementary simulation of experiments of increasing complexity is planned. At the beginning there will be configurations with simple droplets and liquid bridges. In the further course, the impact behavior of droplets on flexible substrates will be investigated. Evaporation, by heating the substrate, will also be considered. The most challenging simulation, which concludes the project, is a Leidenfrost configuration, i.e. an evaporating droplet which, supported by its own vapor layer, hovers above a heated substrate.The simulation procedure is based on a numerical method for two-phase flows, developed by the applicants. These are mixtures of two immiscible fluids, in this case the printing ink and the ambient air. This setup is now supplemented by a third phase, i.e. a flexible solid. If air, liquid and solid meet, this is referred to as a three-phase contact line. The numerical-mathematical basis for this project is a so-called extended discontinuous Galerkin method, which was specially developed to simulate three-phase flows with contact lines with high accuracy. In particular, the interfaces between air and liquid, as well as the three-phase contact line can be followed with high accuracy. For the given problems, the method has to be combined with a simulation method for solids. Furthermore, the heat transfer as well as the evaporation have to be modeled.