Hybrid Numerical Methods for Three-Phase Flows with Moving Contact Lines

涉及固体和流体界面的多相流在许多应用中都很普遍，例如颗粒稳定乳液、浮选技术和流体界面上的动物运动。这些应用在采矿工业、微纳米技术、生物技术和环境科学中发挥着重要作用。例如，由于毛细力的作用，纳米颗粒可以在流体界面上自组装；这种效应可用于制造纳米结构材料。干水是一种由二氧化硅纳米颗粒稳定的空气中的水乳液，它已经证明了吸收二氧化碳的非凡能力，在对抗全球变暖的战争中具有潜在的用途。浮选技术是利用气泡去除悬浮颗粒的技术，在废水处理中得到了广泛的应用。该项目旨在开发用于详细研究这些复杂流动的数值工具，并解决应用中出现的基本问题。该项目还将为研究生提供从事跨学科研究的实践培训机会。该项目的目标是开发混合数值方法，用于直接数值模拟可变形流体界面，移动刚性颗粒和移动接触线共存的流动问题。采用非结构自适应运动网格上的任意拉格朗日-欧拉（ALE）算法来跟踪刚性粒子的运动边界。基于同一运动网格的两种界面捕获方法，即相场法和水平集法，将被开发用于捕获流体界面的变形和运动接触线。这些混合ALE界面捕获方法结合了这两个组件的优点：ALE方法提供了粒子表面的精确表示，这对于微妙的接触线条件至关重要；接口捕获方法很容易处理流体界面的拓扑转换。特别是，ale相场方法满足能量定律，并且基本上没有寄生电流。将开发有限元软件包来实现所提出的方法。这项工作将促进不同类型的移动边界问题的数值算法的发展，也丰富了对复杂系统中接触线动力学的理解。

Multiphase flows that involve both solid bodies and fluid interfaces are ubiquitous in many applications such as particle-stabilized emulsions, flotation technology, and animal locomotion at fluid interfaces. These applications play important roles in the mining industry, micro- and nanotechnologies, biotechnology, and environmental science. For example, nanoparticles may self-assemble on a fluid interface due to capillary forces; this effect can be used in the fabrication of nanostructured materials. Dry water, a water-in-air emulsion stabilized by silica nanoparticles, has demonstrated extraordinary capability to absorb carbon dioxide and is potentially useful in the war against global warming. Flotation techniques, where gas bubbles are used to remove suspended particles, have been widely used in wastewater treatment. This project aims to develop numerical tools for detailed studies of these complex flows and to resolve fundamental questions that arise in applications. The project will also provide hands-on training opportunities for graduate students to work in interdisciplinary research. The goal of this project is to develop hybrid numerical methods for the direct numerical simulation of flow problems where deformable fluid interfaces, moving rigid particles, and moving contact lines coexist. An arbitrary Lagrangian-Eulerian (ALE) algorithm on an unstructured adaptive moving mesh will be adopted to track the moving boundaries of rigid particles. Two interface-capturing methods based on the same moving mesh, namely the phase-field and the level set methods, will be developed to capture the deformation of fluid interfaces as well as the moving contact lines. These hybrid ALE-interface-capturing methods combine the advantages of both components: the ALE method provides an accurate representation of the particle surface, which is critical for delicate contact-line conditions; the interface-capturing methods easily handle the topological transitions of fluid interfaces. In particular, the ALE-phase-field approach satisfies an energy law and is essentially free of parasitic currents. Finite-element software packages will be developed to implement the proposed methods. This work will advance the development of numerical algorithms for different types of moving boundary problems and also enrich the understanding of contact-line dynamics in complex systems.