Numerical methods for the moving contact line problem

接触线是流体界面与固体表面的交点。长期以来，这一研究领域一直受到相互矛盾的理论和关于如何对问题进行建模的不确定性的困扰。主要的困难是由于经典流体力学（特别是具有无滑移边界条件的Navier-Stokes方程）预测了运动接触线处粘性应力的不可积奇点。本课题将运用宏观热力学、微观分子动力学和数值模拟等方法对运动接触线问题进行系统研究。基于热力学原理和分子动力学模拟，导出了“第一性原理”接触线模型。我们将为接触线模型开发新的数值方法，并将应用于研究实际和理论问题，包括非均质表面上的接触线动力学。本文将运用数值和渐近分析的方法研究滑移长度趋于零时接触线模型的渐近行为。接触线是三相的交点，通常是两个流体相和一个固体相。这两种流体相既可以是两种不混溶的流体，如水和油，也可以是同一物质的两相，如水的液相和气相。固相通常是流体的容器。因此，接触线也是两相界面的边界，是界面现象中普遍存在的部分。接触线也出现在许多应用中，如涂层、印刷、石油生产和许多微流体装置。运动接触线问题的主要困难在于，经典流体力学预测能量耗散率为无穷大，这仅仅意味着接触线不能移动。在这个项目中，PI将基于热力学原理和分子动力学模拟推导出第一原理接触线模型。新的数值方法将被开发并应用于研究实际问题，如非均质表面上的接触线动力学。

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.