Multiscale Modeling and Simulations of Micro- and Nano-Scale Electrokinetic Flows

近年来，随着生物mems和生物nems应用以及燃料电池技术的发展，电动运输受到了广泛的关注。电动流动已成为微纳米系统中最重要的非机械技术之一，并已被积极用于泵送、分离和混合等流动控制。基于连续体泊松-玻尔兹曼方程和纳维-斯托克斯方程的电渗透现象建模和模拟已被用于解释许多实验观察结果，并指导微全分析系统的设计。然而，当流动系统的特征尺寸达到亚微米级或离子（分子）级时，连续介质假设就失效了，分子效应不可忽视。基于分子的方法已被用于模拟纳米级通道中的电渗透流动。然而，由于计算成本高，分子动力学模拟只能探测非常有限的时间（例如，几十纳秒）和长度尺度（例如，几纳米）域。能够耦合材料表面离子分子动力学模拟（分子尺度）和体区连续泊松-玻尔兹曼模拟（微米尺度）的多尺度模拟是解决这一难题的有效途径。本研究的重点是发明一种新的多尺度方法来模拟电动系统中的微观和纳米流体动力学，并开发新的多尺度建模算法，将原子和连续体区域的远程库仑相互作用结合起来。该方法的显著特点是仅模拟界面附近场中的一小部分带电粒子，而传统的基于粒子网格的方案必须跟踪空间中的所有粒子。本课题的研究目标包括：(i)开发一种创新的多尺度（混合）方法，将分子动力学模拟与连续介质方法相结合，模拟微纳米系统中的电动力学流动；（ii）研究了电动流动的多尺度效应；(3)研究泵送、分离和混合等微纳米尺度电动流动的流动机制和特征。电动现象是许多芯片实验室概念的基础。电动力流在微纳米系统，如生物芯片或燃料电池中有许多重要的应用。所提出的研究将为微纳米系统中电动力流动的建模提供必要的数学基础，并为模拟电动力流动提供多尺度数值方法。该项目开发的算法将可供社区使用，并且可以扩展到许多纳米技术的研究中，例如纳米机器及其与带电生物分子的界面。一个高效的并行程序将被开发出来，并且可以很容易地被研究界使用。本研究亦将为参与本研究的博士后、研究生和本科生提供跨学科的训练，并将数值分析、科学计算、连续流体力学、纳米力学和电动力学的基础材料纳入一般课程。

With the growing interests in bio-MEMS and bio-NEMS applications and fuel cell technologies, electrokinetic transport has received great attention in recent years. Electrokinetic flows have become one of the most important non-mechanical techniques in micro- and nano-systems and have been actively used for flow-controls, including pumping, separating and mixing. Modeling and simulations of electroosmotic phenomena based on the continuum Poisson-Boltzmann equation and the Navier-Stokes equations have been used to explain many experimental observations and guided the design of Micro-Total Analysis System. However, when the characteristic size of the flow system reaches the size comparable to submicron or the ion (molecule) size, the continuum assumption breaks down and the molecular effects cannot be ignored. Molecular-based methods have been used to model electroosmotic flows at nanoscale channels. However, because of the high computational cost, molecular dynamics simulations can only probe a very limited time (e.g., tens of nanoseconds) and lengthscale (e.g., a few nanometers) domain. The multiscale simulation capable of coupling molecular dynamics simulation of ions near material surfaces (molecular scale) and the continuum Poisson-Boltzmann simulation for the bulk region (micron scale) is an efficient way to solve this difficulty. The important thrust of the proposed research is to invent a new multiscale method to simulate micro- and nano-fluid dynamics in electrokinetic systems and to develop new algorithms for multiscale modeling that incorporate long-range Coulomb interactions in both atomistic and continuum regions. The distinguished feature in this approach is that only a small portion of the charged particles in the field near interfaces are simulated in MD, while in traditional particle-mesh based schemes all particles in the space must be followed. The research objectives in this proposal include: (i) develop an innovative multiscale (hybrid) method coupling molecular dynamics simulation with continuum method to simulate electrokinetic flows in micro and nano systems; (ii) investigate the multiscale effects on the electrokinetic flow; (iii) Investigate the flow mechanisms and characteristics of the micro- and nano-scale electrokinetic flows, including pumping, separation and mixing. Electrokinetic phenomena are the basis of many lab-on-a-chip concepts. The electrokinetic flow has many important applications in micro and nano systems, such as bio-chip or fuel cells. The proposed research will provide the mathematical foundations necessary for modeling the electrokinetic flows in micro- and nano-systems and develop multiscale numerical methods for simulating the electrokinetic flow. The algorithms developed in the project will be available to the community and can be extended for many studies of nano-technologies, such as nano-machines and their interface with charged biomolecules. A highly efficient parallel program will be developed and can be easily used by the research community. The proposed research will also provide an interdisciplinary training to postdocs, graduate and undergraduate students involved in the project, and bring basic material on numerical analysis, scientific computing, continuum fluid mechanics, nanomechanics and electokinetics into the general curriculum.