Dynamics of Unstable Thin Liquid Films and Coarsening

不稳定薄液膜和粗化的动力学

• 批准号: 0638481
• 负责人: Dejan Slepcev
• 金额: $ 9.27万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0638481&HistoricalAwards=false
• 关键词: Dynamics; Unstable; Thin; Liquid; Films

This project is devoted to investigating dynamical behavior of thin liquid films and, more generally, systems driven by energy reduction. Thin liquid films can be described by a single equation for the fluid height --- the thin-film equation. Intermolecular forces can destabilize fluid films and lead to complex dynamical behavior. In some systems, droplet configurations that form coarsen over time; the average size of droplets grows, while their number is decreasing. In others instabilities lead to singularity formation. We will investigate these processes using a combination of novel analytical techniques, asymptotic analysis and computational methods. We will also investigate formation and dynamics of interfaces in models of biological aggregation. Large-scale and long-time behavior will also be investigated. Unifying theme of the above systems is that they are driven by energy dissipation. We intend to both use and further develop modern analytical techniques that utilize the underlying geometric structure of these systems.The project will generate experimentally verifiable predictions about behavior of thin liquid films. With continuing miniaturization trends, applications in which thin liquid films play a role are becoming more widespread (industrial processes, microfluidic devices). Thus understanding the multitude of phenomena that thin films exhibit becomes ever more important. Systems driven by reduction of the energy are ubiquitous in nature. Many such systems share the common structure of the equation that describes them. We will use recent advances on geometry of such equations to gain direct insights into the syste

该项目致力于研究薄液膜的动力学行为，更一般地说，由能量减少驱动的系统。薄液膜可以用一个流体高度方程来描述-薄膜方程。 分子间力可以使流体膜不稳定并导致复杂的动力学行为。在一些系统中，形成的液滴配置随着时间的推移而变粗;液滴的平均大小增加，而它们的数量减少。在其他情况下，不稳定性导致奇点的形成。我们将调查这些过程中使用新的分析技术，渐近分析和计算方法相结合。 我们还将研究生物聚集模型中界面的形成和动力学。大规模和长时间的行为也将被调查。上述系统的统一主题是它们由能量耗散驱动。我们打算使用和进一步发展现代分析技术，利用这些系统的基本几何结构。该项目将产生实验验证的预测薄液膜的行为。随着持续的小型化趋势，其中薄液体膜发挥作用的应用变得越来越广泛（工业过程、微流体装置）。因此，了解薄膜所表现出的众多现象变得越来越重要。由能量减少驱动的系统在自然界中无处不在。许多这样的系统共享描述它们的方程的共同结构。我们将利用这些方程几何学的最新进展来直接了解这个系统。