One dimensional transport equations for CE systems by asymptotic homogenization

描述（由申请人提供）：微流体领域的研究最近受到创建微总量分析系统（mu-TAS）或更通俗地称为“芯片实验室”的最终目标的推动。毛细管电泳（CE）通道是任何此类系统的重要组成部分，许多努力集中在改进其设计，以最大限度地提高分离效率和重现性。描述分离过程的物理方程的数值解是设计人员可用的最重要的现代工具之一。计算研究有助于在实际制造原型之前缩小可能的设计解决方案，从而节省时间和成本。本方案寻求将数值方法和渐近方法结合起来求解CE通道中的流体流动和物种输运方程，从而将计算成本降低许多数量级。基于观察，这类物理问题的特征是一个小参数：微通道的特征宽度与特征长度之比。这个小参数的存在使基础方程变得“僵硬”，因此难以求解。然而，人们可以利用这种刚度，通过使用“渐近均匀化”，从本质上把三维问题简化为只有一个空间维度的问题，并且只有很小的精度损失。作为概念的证明，将创建一个基于web的计算设计工具，远程用户可以在其上实时运行计算。这是可能的，因为用一维非刚性系统取代偏微分方程的三维刚性系统大大减少了计算工作量。

DESCRIPTION (provided by applicant): Research in the area of Microfluidics has lately been driven by the ultimate goal of creating a micro-total analysis system (mu-TAS) or more colloquially the 'Lab On a Chip'. The Capillary Electrophoresis (CE) channel is an essential component of any such system and much effort is focussed upon improving its design so as to maximize separation efficiency and reproducibility. Numerical solution of the equations describing the physics of the separation process is one of the most important modern tools available to the designer. Computational studies help save time and cost by helping to narrow down the possible design solutions prior to actual fabrication of prototypes. This proposal seeks to combine numerical approaches and asymptotic methods towards the solution of the fluid flow and species transport equations in CE channels so as to reduce the computational cost by many orders of magnitude. It is based on the observation that the physical problems in this class are characterized by a small parameter: the ratio of the characteristic width to the characteristic length of the micro-channel. The presence of this small parameter renders the underlying equations "stiff and hence difficult to solve. One can however take advantage of this stiffness by using "asymptotic homogenization" to essentially reduce the three dimensional problem to one that has only one space dimension with only a very small loss of accuracy. As a proof of concept, a web based computational design tool will be created on which remote users can run computations in real time. This is possible because of the massive reduction of computational effort that results from the replacement of a 3D stiff system of partial differential equations by a 1D non-stiff system. RELEVANCE: An approach is being proposed for reducing by many orders of magnitude the computational effort involved in the numerical simulation protocols used in computer aided design of microfluidic systems. The availability of such design tools increases the probability that the effort to create practical "Lab On a Chip" devices would succeed. The emergence of such devices would have an enormous impact on human health as they would enable biochemical analyses (such as DNA sequencing) that currently take months or years to be completed in minutes.