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

当液体形态在(粘性)弹性衬底上运动时，衬底中的摩擦力在衬底变形最大处，即三相接触线和运动界面上都是理解能量耗散和除湿轮缘形状的关键，并有望影响调幅节点除湿模式的选择。与液体衬底不同，固体粘弹性衬底的局部变形总是对衬底的状态产生全局影响，所产生的应变是永久性的。这一建议旨在开发两层系统的数学模型和数值算法，该系统将流体动力学和粘弹性边值问题与适当的界面条件(包括分子间相互作用)耦合在去湿实验的尺度上，以预测旋节模式的选择和破裂过程以及简单液体从固体粘弹性衬底上脱湿的动力学和边缘形状。衬底的弹性性能将连接三个数量级的桥梁，降至约1千帕。特别是对于非常软的衬底，我们预计将通过引入对可能的非线性弹性的额外熵贡献以及通过向软聚合物凝胶的总自由能添加混合自由能来捕捉诸如分离等效果。同时，同样的问题将通过原子力显微镜成像的聚二甲基硅氧烷网络的纳米级聚苯乙烯薄膜的实验研究来解决。将这些实验结果作为系统变化的粘弹性性质的函数进行定量比较，将允许详细和基本地了解潜在的物理过程，并确认或证伪在文献中仍有很大争议的影响。此外，对于所考虑的实验体系，这涉及到所谓的Shuttleworth效应的存在，以及从相同材料的非交联性分子中潜在地分离出交联型弹性体基质，这在刚性衬底和将在这里考虑的长度尺度上尚未观察到。

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.