Numerical methods for the moving contact line problem

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Contact lines arises as the intersection of fluid interfaces with solid surfaces. For a long time, this area of study has been plagued with conflicting theories and uncertainties regarding how the problem should be modeled. The main difficulty stems from the fact that classical hydrodynamics (specifically, the Navier-Stokes equation with the no-slip boundary condition) predicts a non-integrable singularity for the viscous stress at the moving contact line. In this project, the moving contact line problem is to be systematically studied with the help of macroscopic thermodynamics, microscopic molecular dynamics, and numerical simulations. A ``first-principle'' contact line model is derived based on principles of thermodynamics and molecular dynamics simulations. Novel numerical methods will be developed for the contact line model, and will be applied to study problems of both practical and theoretical interests, including the contact line dynamics on heterogeneous surfaces. The asymptotic behavior of the contact line model as the slip length goes to zero will be investigated with the help of numerics and asymptotic analysis.A contact line is the intersection of three phases, ofter two fluid phases and a solid phase. The two fluid phases can either be two immiscible fluids such as water and oil, or two phases of the same substance, such as the liquid and vapor phase of water. The solid phase is usually the container for the fluids. For this reason, the contact line is also the boundary of the interface between the two fluid phases, and is therefore an ubiquitous part of interfacial phenomena. Contact lines also arise in many applications such as coating, printing, oil production, and in many micro-fluidic devices. The main difficulty of the moving contact line problem stems from the fact that classical hydrodynamics predicts an infinite rate of energy dissipation which simply implies that contact lines cannot move. In this project, the PI will derive a first-principle contact line model based on thermodynamics principles and molecular dynamics simulations. Novel numerical methods will be developed and will be applied to study problems of practical interests, such as the contact line dynamics on heterogeneous surfaces.