In this talk, I will present a hybrid Arbitrary-Lagrangian-Eulerian(ALE)-Phase-Field method for the direct numerical simulation of multiphase flows where fluid interfaces, moving rigid particles, and moving contact lines coexist. Practical applications include Pickering emulsions, froth flotation, and biolocomotion at fluid interface. An ALE algorithm based on a Galerkin finite element method and an adaptive moving mesh is used to track the moving boundaries of rigid particles. A phase-field method based on the same moving mesh is used to capture the fluid interfaces; meanwhile, the Cahn-Hilliard diffusion automatically takes care of the stress singularity at the moving contact line when a fluid interface intersects a solid surface. To fully resolve the diffuse interface, mesh is locally refined at the fluid interface. All the governing equations, i.e., equations for fluids, interfaces, and particles, are solved implicitly in a unified variational framework. As a result, the hydrodynamic forces and moments on particles do not appear explicitly in the formulation and an energy law holds for the whole system. The three-phase flow is essentially free of parasitic currents if the surface tension term is properly formulated. In the end I will present some results on the water entry problem and the capillary interaction between floating particles (a.k.a. the Cheerios effect), with a focus on the effect of contact-line dynamics.

Pengtao Yue received B.S. in applied and theoretical mechanics in 1997 and Ph.D. in fluid mechanics in 2002, both from the University of Science and Technology of China. After graduation, he came to the Levich Institute at the City College of New York as a postdoctoral associate. In 2004, he moved to Vancouver, Canada and continued his postdoctoral research at the University of British Columbia. In 2008, he became a faculty member in the Department of Mathematics at Virginia Tech and he has been working there ever since. Pengtao Yue is interested in numerical simulations of  interfacial flows, contact-line dynamics, and complex fluids. Currently he focuses on the wetting dynamics on floating particles and multi-component systems.