Numerical methods for the moving contact line problem

接触线是流体界面与固体表面的相交处。长期以来，这一研究领域一直受到相互冲突的理论和关于如何对问题进行建模的不确定性的困扰。主要的困难源于这样一个事实，即经典流体力学（具体地说，Navier-Stokes方程与无滑移边界条件）预测在移动接触线的粘性应力的不可积的奇异性。本计画将利用宏观热力学、微观分子动力学及数值模拟等方法，系统地研究移动接触线问题。基于热力学原理和分子动力学模拟，推导了接触线的“第一性原理”模型。新的数值方法将开发的接触线模型，并将被应用到研究问题的实际和理论的利益，包括接触线动力学的异质表面。通过数值计算和渐近分析，研究了接触线模型在滑移长度趋于零时的渐近行为。接触线是由两个流体相和一个固体相组成的三相的交点。两个流体相可以是两种不混溶的流体，例如水和油，或者是相同物质的两个相，例如水的液相和气相。固相通常是流体的容器。因此，接触线也是两个流体相之间的界面的边界，因此是界面现象的普遍存在的部分。接触线也出现在许多应用中，例如涂布、印刷、石油生产和许多微流体装置中。移动接触线问题的主要困难源于这样一个事实，即经典流体动力学预测的能量耗散的无限速率，这仅仅意味着接触线不能移动。在这个项目中，PI将根据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。将开发新的数值方法，并将其应用于研究实际感兴趣的问题，如非均匀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.