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，电动输运受到了极大的关注。电动流动已经成为微纳米系统中最重要的非机械技术之一，并被广泛地用于流动控制，包括泵浦、分离和混合。基于连续介质Poisson-Boltzmann方程和Navier-Stokes方程的电渗现象的建模和模拟已经被用来解释许多实验观测结果，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与亚微米或离子(分子)尺寸相当的尺寸时，连续介质假设就会被打破，分子效应就不能被忽略。基于分子的方法已经被用来模拟纳米尺度通道中的电渗流。然而，由于计算成本较高，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(例如，几纳米)的区域。能够耦合物质表面附近离子的分子动力学模拟(分子尺度)和体区(微米尺度)的连续泊松-玻尔兹曼模拟的多尺度模拟是解决这一难题的有效途径。这项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纳流体动力学，并开发新的多尺度建模算法，其中包括原子区和连续区中的长程库仑相互作用。这种方法的显著特点是，MD只模拟了界面附近场中的一小部分带电粒子，而在传统的基于粒子网格的方法中，必须跟踪空间中的所有粒子。该方案的研究目标包括：(I)发展一种新颖的多尺度(混合)方法，将分子动力学模拟和连续介质方法相结合来模拟微纳系统中的电动流动；(Ii)研究多尺度效应对电动流动的影响；(Iii)研究微纳米尺度电动流动的流动机制和特性，包括泵浦、分离和混合。电动现象是许多芯片实验室概念的基础。动电流动在生物芯片、燃料电池等微纳米系统中有着重要的应用。这项研究将为模拟微纳系统中的电动流动提供必要的数学基础，并发展多尺度的数值方法来模拟电动流动。该项目开发的算法将可供社区使用，并可扩展到纳米技术的许多研究中，例如纳米机器及其与带电生物分子的接口。将开发一个高效的并行程序，并且可以很容易地被研究界使用。拟议的研究还将为参与该项目的博士后、研究生和本科生提供跨学科培训，并将数值分析、科学计算、连续介质流体力学、纳米力学和电动力学的基础材料纳入普通课程。

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.