Structure Formation in Thin Liquid Films
Structure Formation in Thin Liquid Films
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DOI：
10.1007/978-3-211-69808-2_2
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发表时间：
2007
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影响因子：
--
通讯作者：
U. Thiele
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文献类型：
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作者：
U. Thiele
我们概述了一些最近的发展，在理论上描述的结构形成的液体薄膜。主要关注的是涉及在固体基底上的单层液体的系统，其可以使用膜厚度分布的演化方程来描述。我们回顾历史的主题，我们勾勒出重要的实验和理论结果和实际应用。在讨论了不同情况下的分类后，我们介绍了软物质薄膜研究的共同数学框架，即从Navier-Stokes方程推导出此类薄膜的一般演化方程。在主要部分中，我们首先介绍了不同的可能的几何形状和它们之间的过渡，即从均匀到不均匀的基板，或从水平到倾斜基板。然后，我们提出的物理问题所提出的各个系统和讨论的方法和结果：·去湿水平均匀的基板。我们调查的解决方案的结构及其后果的系统行为。对于初始薄膜破裂，我们区分了线性不稳定薄膜的成核主导和不稳定主导行为。·水平不均匀基底上的去湿。的控制方程的解决方案的结构分析作为一个功能的化学异质性的强度。我们描述了一个具有大范围多稳定性的钉扎-粗化转变，这意味着较大的滞后以及对初始条件和噪声的强烈依赖。·水平均匀衬底上的加热薄膜。我们讨论成核和下降的解决方案，并表明，它是可能的，以构建所有的下降的解决方案分离的干燥区域。计算分离压力可以研究液滴图案的粗化行为。·在倾斜的均匀基底上的滑动滴。使用一个模型，结合分离压力允许计算经常使用的adhoc参数的模型移动接触线从表面化学。对于加热的薄膜，分析了倾斜角增加时发生的从Cahn-Hilliard型到Kuramoto-Sivashinsky型动力学的转变。·讨论了液体脊的横向不稳定性，包括所有上述几何形状。特别注意的是这样的不稳定性的稳定，由于条纹状的不均匀性的休息脊在水平基板上，并在模式类型的急剧变化时，倾斜的基板。它的变化从一个对称的静脉曲张模式（水平基板）通过一个不对称的静脉曲张模式，并通过一个不对称的曲折模式去耦的正面和背面model.Finally，我们简短地讨论了扩展的薄膜研究超出了一个单一的演化方程的情况下。特别是，我们介绍了两个不同的模型的基础上描述的两层薄膜和化学驱动的自推进运动的液滴，分别去湿的动力学耦合演化方程。
We outline some recent developments in the theoretical description of structure formation in thin liquid films. The main focus is systems involving a single layer of liquid on a solid substrate that can be described using an evolution equation for the film thickness profile. We review the history of the subject and we sketch important experimental and theoretical results and practical applications. After discussing the classification of the different cases, we introduce the common mathematical framework for studies of thin films of soft matter, namely by deriving the generic evolution equation for such films from the Navier-Stokes equations. In the main part we first introduce the different possible geometries and the transitions between them, i.e. from homogeneous to inhomogeneous substrates, or from horizontal to inclined substrates. We then present the physical questions posed by the individual systems and discuss approaches and results for:• Dewetting on a horizontal homogeneous substrate. We investigate the solution structure and its consequences for the system behavior. For the initial film rupture we distinguish nucleation-dominated and instability-dominated behavior for linearly unstable thin films.• Dewetting on a horizontal inhomogeneous substrate. The solution structure of the governing equation is analysed as a function of the strength of a chemical heterogeneity. We describe a pinning-coarsening transition with a large range of multistability, implying a large hysteresis and strong dependence on initial conditions and noise.• Heated thin films on a horizontal homogeneous substrate. We discuss nucleation and drop solutions and show that it is possible to construct all drop solutions separated by dry regions. Incorporating a disjoining pressure allows to study the coarsening behaviour of the drop pattern.• Sliding drops on an inclined homogeneous substrate. Using a model that incorporates a disjoining pressure allows to calculate the frequently used adhoc parameters of models for moving contact lines from surface chemistry. The involved transition from a Cahn-Hilliard-like to a Kuramoto-Sivashinsky-like dynamics that occurs for increasing inclination angle is analyzed for heated films.• Transverse instabilities of a liquid ridge are discussed encompassing all the above geometries. Particular attention is given on the stabilization of such an instability due to stripe-like heterogeneities for a resting ridge on a horizontal substrate and on the drastic change in the mode type when inclining the substrate. It changes from a symmetric varicose mode (horizontal substrate) via an asymmetric varicose mode and via an asymmetric zigzag mode to decoupled front and back modes.Finally, we shortly discuss extensions of thin film studies beyond the case of a single evolution equation. In particular, we introduce two different models based on two coupled evolution equations describing the dynamics of dewetting of a two-layer thin film and the chemically driven self-propelled movement of droplets, respectively.