A Nonconforming Spectral Element Method for Electroosmotically Induced Microfluidic Mixing

在这个项目中，我们将开发一个全面的理论和数值研究程序来研究微尺度的物种混合。我们将特别研究由外加电场驱动的时间周期电渗透引起的混合，从而消除对机械泵送部件的需求。在几种电场构型之间的快速切换将被用来创建不同的流场，从而导致物种间接触面积的增加和/或混沌混合。混合的数值模拟需要健壮的算法来最小化色散和扩散误差。为了满足这一需求，我们将使用迫击炮单元和约束近似方法来开发非协调谱元素算法。我们的方法将允许h型和p型不整合，以有效地分辨所有流动特征，包括薄的电双层。除了三维Navier-Stokes和物种输运方程解算器外，我们还将开发必要的算法来计算粒子轨迹、庞加莱截面和其他表征混沌混合和混合效率所需的工具。在没有湍流的情况下，流体在微观尺度上的混合需要很长的混合长度和很长的时间。这对用于医疗、制药和国家安全应用的生物和化学制剂检测的微流控设备(如微型全分析系统)的高效混合器的设计带来了重大挑战。利用时间周期电渗透可以设计新的混合策略，这些策略要么通过增加物种间接触面积来增强扩散混合，要么诱导混沌混合。该项目将加强对电渗透诱导的混沌和扩散混合的理解和表征。这项研究将有助于发展新的微流控混合概念，可应用于微纳米流体应用的新型高效微混合器的设计中。

In this project, we will develop a comprehensive theoretical and numerical research program to investigate the micro-scale species mixing. We will particularly study mixing induced by time-periodic electroosmosis that is driven by externally applied electric fields, hence eliminating the need for mechanical pumping components. Rapid switching between several electric field configurations will be utilized to create different flow fields, resulting in increased interspecies contact area and/or chaotic mixing. Numerical simulations of mixing require robust algorithms that minimize the dispersion and diffusion errors. To address this need, we will develop nonconforming spectral element algorithms using the Mortar element and constrained approximation methods. Our approach will allow both h-type and p-type nonconformities for efficient resolution of all flow features, including the thin electric double layers. In addition to the three-dimensional Navier-Stokes and species transport equation solvers, we will develop necessary algorithms to calculate the particle trajectories, Poincare sections, and other tools required to characterize the chaotic mixing and mixing efficiency. Implementation of both the Mortar element and constrained approximation methods will also allow detailed comparisons between the accuracy and computational efficiency of these two schemes.In the absence of turbulence, mixing of fluids on micro-scales requires very long mixing lengths and long times. This creates significant challenges in design of efficient mixers for micro-fluidic devices, such as micro-total-analysis-systems, utilized in detection of biological and chemical agents for medical, pharmaceutical, and national security applications. Utilization of time-periodic electroosmosis allows design of new mixing strategies that either enhance diffusive mixing by increasing the interspecies contact area, or induce chaotic mixing. This project will enable enhanced understanding and characterization of electroosmotically induced chaotic and diffusive mixing. The research will facilitate development of new micro-fluidic mixing concepts, which can be implemented in design of new efficient micro-mixers for micro- and nano-fluidic applications.