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全分析系统（mu-TAS）或更通俗地说“芯片实验室”的最终目标的驱动。毛细管电泳（CE）通道是任何此类系统的重要组成部分，并且许多努力都集中在改进其设计上，以便最大限度地提高分离效率和再现性。描述分离过程物理过程的方程的数值解是设计者可用的最重要的现代工具之一。计算研究通过在实际制造原型之前帮助缩小可能的设计解决方案来帮助节省时间和成本。该建议旨在将联合收割机数值方法和渐近方法结合起来，以解决CE通道中的流体流动和物质输运方程，从而将计算成本降低许多数量级。这是基于观察，在这一类的物理问题的特点是一个小参数：特征宽度的比例的特征长度的微通道。这个小参数的存在使得基本方程“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”，基本上减少了三维问题，只有一个空间维度，只有一个非常小的损失的准确性。作为概念验证，将创建一个基于网络的计算设计工具，远程用户可以在其上运行真实的计算。这是可能的，因为大量减少的计算工作，结果从一个三维刚性系统的偏微分方程的一维非刚性系统的替代。 相关性：提出了一种方法，用于减少许多数量级的计算工作中所涉及的计算机辅助设计的微流体系统中使用的数值模拟协议。这种设计工具的可用性增加了创建实用的“芯片实验室”设备的可能性。这些设备的出现将对人类健康产生巨大影响，因为它们将使目前需要数月或数年的生化分析（如DNA测序）在几分钟内完成。

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.