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

当液体形态在（粘）弹性基底上移动时，在基底中的摩擦力在最大基底变形的点处，即在三相接触线处和在移动界面处是理解能量耗散和去湿边缘的形状的关键，并且预计将影响失稳去湿的模式选择。与液体基底不同，固体粘弹性基底的局部变形总是对基底的状态具有全局影响，并且所产生的应变是永久的。 该提案旨在开发数学模型和数值算法的两层系统耦合的流体动力学和粘弹性边界值问题与适当的界面条件，包括分子间的相互作用，成为相关的尺度上的去湿实验，预测的旋节模式选择和破裂过程和动力学和边缘形状的简单液体去湿固体粘弹性基板。基底的弹性性质将桥接三个数量级，低至约1kPa。特别是对于非常软的基板，我们预期的效果，如分层，这将被捕获通过引入额外的熵贡献的可能的非线性弹性，并通过添加混合自由能的总自由能的软聚合物凝胶。在平行，同样的问题将解决实验探索纳米级的聚苯乙烯薄膜去湿从聚二甲基硅氧烷网络原子力显微镜成像。这些实验结果作为系统变化的粘弹性性能的函数的定量比较，应允许一个详细的和基本的物理过程的理解，并确认或证伪的影响，仍然是在文献中讨论的高度争议。除此之外，这涉及所考虑的实验系统的所谓的Shuttleworth效应的存在以及交联弹性体基质与相同材料的非交联分子的潜在分层，这对于刚性基底和这里将考虑的长度尺度尚未观察到。

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.