Coupled dynamics of a thin lubricating film with hydrodynamic instabilities in a conjugated liquid layer

在最初资助的DI 1689/1-1项目的过程中，在温度梯度的驱动下，在液体层中产生了b<s:1>纳德-马兰戈尼（BM）细胞对流不稳定性。对流电池引起放置在层和支撑基板之间的薄的不混溶膜的界面变形。如果薄膜流体是可通过紫外线照射固化的聚合物，则可以固定变形。在放置在这样一个预先结构化的基材上的液体层中重新建立BM对流，会导致与用于构建基材的流动模式完全相同的流动模式，即流体体积中形成的水动力模式被“存储”在其边界并再次从中提取。这项后续建议的目的是更详细地阐述这一原则。本文将通过弱非线性分析和完整的数值模拟来探讨共轭液层系统的稳定性。随后，这种耦合自组织子系统的描述将在一个更通用的数学框架中进行转换，以识别一类导致整个系统紧急行为的耦合算子。这意味着它的动力学（即共轭层的动力学）可能在性质上不同于它的组分（即单个液体层）的动力学。不需要固化薄膜；只要暂时去除驱动温度梯度后液-液界面变平所需的特征时间远远大于较厚层中对流的衰减时间，薄膜对上层的模式保存作用就会继续发挥作用。这一性质将用于实验探索受BM对流影响的溶解/悬浮物质的对流-扩散动力学。从流体域的边界存储和检索流体动力模式对于更广泛的流动现象是可行的。为此，当在液体层和固体衬底之间放置一层薄薄的液体膜时，将对暴露于垂直振动的液体层中出现的法拉第不稳定性进行实验研究。与BM对流相比，法拉第不稳定性意味着线性振荡流，其剪切应力不一定导致液膜的时间平均变形。然而，薄膜的存在可能使共轭系统非线性，因此可以观察到时间平均变形。通过紫外光固化，这种变形可以存储在流体边界，并由轮廓仪进行分析，而其流体动力学“信息内容”可以在随后的实验中检索。通过这项工作，我们打算建立一个新的工程工具的基础，不仅可以调整某些流动的稳定性制度，而且还可以将某些流动特征“雕刻”到域边界中。我们称这种新原理为流体动力模式记忆。

In the course of the originally funded project DI 1689/1-1, the Bénard-Marangoni (BM) cellular convective instability, driven by a temperature gradient, was generated in a liquid layer. The convection cells cause interfacial deformations of a thin immiscible film placed between the layer and the supporting substrate. The deformations can be fixated if the film fluid is a polymer curable by irradiation with ultraviolet (UV) light. Re-establishing BM convection in a liquid layer placed on such a pre-structured substrate leads to a flow pattern which is exactly identical to the one used to structure the substrate, i.e. the hydrodynamic pattern formed in the fluid volume is 'stored' at its boundary and retrieved from it again. This follow-up proposal aims at elaborating on this principle in more detail. The stability regime of the conjugated liquid layer system will be probed by a weakly non-linear analysis as well as by full numerical simulations. Subsequently, the description of such coupled self-organizing subsystems will be cast in a more generic mathematical framework to identify a class of coupling operators which cause an emergent behavior of the full system. This means that its dynamics (i.e. of the conjugated layers) may be qualitatively different from that of its constituents (i.e. the individual liquid layers). Solidification of the film is not required; the pattern-conserving effect the thin film has on the upper layer remains functional as long as the characteristic time the liquid-liquid interface takes to flatten after a temporary removal of the driving temperature gradient is much larger than the decay time of the convection in the thicker layer. This property will be used to experimentally explore convection-diffusion dynamics of a dissolved/suspended species subjected to BM convection. Storing and retrieving a hydrodynamic pattern from the boundary of a fluid domain may be feasible for a broader class of flow phenomena. To this end, the Faraday instability emerging in a liquid layer upon exposure to vertical vibrations will be experimentally examined when a thin liquid film is placed between the liquid layer and the solid substrate. By contrast to BM convection, the Faraday instability implies linear oscillatory flow, whose shear stress does not necessarily cause a time-averaged deformation of the liquid film. Nevertheless, the presence of the film may render the conjugated system non-linear, so that a time-averaged deformation may be observed. Via solidification by UV light such deformations may be stored at the fluid boundary and analyzed by a profilometer, while its hydrodynamic 'information content' may be retrieved in a subsequent experiment. With this work we intend to establish the fundaments of a new engineering tool allowing not only to tune the stability regimes of certain flows, but also to 'engrave' certain flow characteristics into the domain boundary. We call this novel principle hydrodynamic pattern memory.