Dynamic wetting and dewetting of viscous liquid droplets/films on viscoelastic substrates

当液体形态在（粘）弹性衬底上移动时，衬底中最大变形点（即三相接触线处）和移动界面处的摩擦力是理解能量耗散和脱湿边缘形状的关键，并且预计会影响spinodal脱湿模式的选择。与液体基材不同，固体粘弹性基材的局部变形总是对基材的状态产生全局影响，所产生的应变是永久性的。本研究旨在建立两层系统的数学模型和数值算法，将流体动力和粘弹性边界值问题与适当的界面条件相结合，包括在脱湿实验尺度上相关的分子间相互作用，以预测固体粘弹性基底上简单液体脱湿的旋模选择和破裂过程以及动力学和边缘形状。基材的弹性性能将桥接三个数量级下降到约1kpa。特别是对于非常柔软的基质，我们期望通过引入额外的非线性弹性熵贡献以及通过向软聚合物凝胶的总自由能中添加混合自由能来捕获诸如脱混之类的效应。与此同时，同样的问题将通过实验来解决，探索纳米级聚苯乙烯薄膜从聚二甲基硅氧烷网络中脱湿，通过原子力显微成像。将这些实验结果作为系统变化的粘弹性特性的函数进行定量比较，将允许对潜在的物理过程进行详细和基本的理解，并确认或证伪仍然在文献中讨论的高度有争议的效应。除此之外，这涉及到所考虑的实验系统中所谓的Shuttleworth效应的存在，以及同一材料的非交联分子的交联弹性体基质的潜在分离，这在刚性衬底和这里将考虑的长度尺度中尚未观察到。

When a liquid morphology moves over a (visco)elastic substrate, friction forces in the substrate both at the point of largest substrate deformation, i.e. at the three-phase contact line and at the moving interface are key to understanding energy dissipation and shapes of dewetting rims and are expected to impact the mode selection of spinodal dewetting. Unlike liquid substrates, the local deformation of a solid viscoelastic substrate always has a global impact on the state of the substrate and the resulting strains are permanent. This proposal aims at developing mathematical models and numerical algorithms for two-layer systems that couple the hydrodynamic and viscoelastic boundary value problem with appropriate interface conditions including intermolecular interactions that become relevant at the scales of the dewetting experiments, to predict the spinodal mode selection and rupture process and the dynamics and rim shapes of simple liquids dewetting from solid viscoelastic substrates. The elastic properties of the substrate will bridge three orders of magnitude down to about 1 kPa. In particular for the very soft substrates, we expect effects such as demixing that will be captured by the introduction of additional entropic contributions to the possibly non-linear elasticity and by adding a mixing free energy to the total free energy of the soft polymer gel. In parallel, the same questions will be tackled experimentally exploring nanoscopic thin polystyrene films dewetting from polydimethylsiloxane networks imaged by atomic force microcopy. A quantitative comparison of these experimental results as functions of systematically varied viscoelastic properties shall allow for a detailed and fundamental understanding of the underlying physical processes and to confirm or to falsify effects that are still discussed highly controversially in literature. Besides others, this concerns the existence of the so called Shuttleworth effect for the considered experimental system and the potential demixing of cross-linked elastomer matrix from non-cross-linked molecules of the same material, which was not yet observed for stiff substrates and the length scales that will be considered here.