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相交时，就会出现接触线。长期以来，这一研究领域一直饱受相互矛盾的理论和关于如何建模问题的不确定性的困扰。主要困难源于经典流体动力学（特别是具有无滑移边界条件的纳维-斯托克斯方程）预测移动接触线处粘性应力的不可积奇点。本项目将借助宏观热力学、微观分子动力学和数值模拟对动接触线问题进行系统研究。 “第一原理”接触线模型是根据热力学和分子动力学模拟原理推导出来的。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，包括异质表面上的接触线动力学。将借助数值和渐近分析来研究接触线模型当滑移长度趋于零时的渐近行为。接触线是三相（通常是两个流体相和一个固相）的交点。两个流体相可以是两种不混溶的流体，例如水和油，也可以是同一物质的两个相，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界面的边界，因此是界面现象中普遍存在的部分。接触线还出现在许多应用中，例如涂层、印刷、石油生产以及许多微流体装置。移动接触线问题的主要困难源于这样一个事实：经典流体动力学预测能量耗散率是无限的，这简单地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。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，例如异质表面上的接触线动力学。