Numerical methods for the moving contact line problem

动接触线问题的数值方法

• 批准号: 1114827
• 负责人: Eric Vanden-Eijnden
• 金额: $ 17.97万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-10-01 至 2015-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1114827&HistoricalAwards=false
• 关键词: Numerical; methods; moving; contact; line

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.

当流体界面与固体表面的交点是接触线。长期以来，这个研究领域一直困扰着有关如何建模问题的理论和不确定性。主要难度源于以下事实：经典的流体动力学（具体来说，具有无滑动边界条件的Navier-Stokes方程）预测了在移动接触线处的粘性应力的不可融合奇点。在这个项目中，移动接触线问题应在宏观热力学，微观分子动力学和数值模拟的帮助下进行系统地研究。基于热力学和分子动力学模拟的原理，得出了``第一原理''接触线模型。将为接触线模型开发新的数值方法，并将应用于研究实践和理论兴趣的问题，包括异质表面上的接触线动力学。接触线模型的渐近行为作为滑移长度占零，将在数字和渐近分析的帮助下研究。这两个流体相可以是两种不混溶的流体，例如水和油，也可以是相同物质的两个阶段，例如水的液相和蒸气相。固相通常是流体的容器。因此，接触线也是两个流体相之间界面的边界，因此是界面现象的无处不在的部分。在许多应用中，例如涂料，印刷，石油生产和许多微富集设备，也会出现接触线。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了无限的能量耗散速率，这仅意味着接触线无法移动。在该项目中，PI将根据热力学原理和分子动力学模拟得出第一原则接触线模型。将开发新的数值方法，并将应用于研究实际兴趣的问题，例如异质表面上的接触线动力学。