Dynamics of Unstable Thin Liquid Films and Coarsening

这个项目致力于研究薄膜液体的动力学行为，更广泛地说，研究由能量降低驱动的系统的动力学行为。液体薄膜可以用单一的流体高度方程来描述-薄膜方程。分子间作用力会破坏流体膜的稳定性，导致复杂的动力学行为。在某些系统中，形成的液滴构型随着时间的推移而变粗；液滴的平均尺寸增大，而液滴的数量却在减少。在另一些情况下，不稳定性会导致奇点的形成。我们将结合新的分析技术、渐近分析和计算方法来研究这些过程。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是由能量耗散驱动的。我们打算使用并进一步开发利用这些系统的基本几何结构的现代分析技术。该项目将产生关于薄膜液体行为的实验可验证的预测。随着持续的小型化趋势，薄膜在其中发挥作用的应用变得越来越广泛(工业过程、微流控设备)。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式的共同结构。我们将利用此类方程几何方面的最新进展来直接了解系统。

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