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

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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.