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计划，以调查微观尺度的物种混合。 我们将特别研究由外部施加的电场驱动的时间周期电渗引起的混合，从而消除了对机械泵送部件的需要。 几个电场配置之间的快速切换将被用来创建不同的流场，从而增加物种间的接触面积和/或混乱的混合。 混合的数值模拟需要鲁棒的算法，使色散和扩散误差最小化。 为了满足这一需求，我们将使用Mortar元素和约束近似方法开发谱元素算法。 我们的方法将允许H型和P型不一致性的所有流动功能，包括薄的双电层的有效分辨率。除了三维Navier-Stokes和物种输运方程求解器之外，我们还将开发必要的算法来计算粒子轨迹，庞加莱截面以及表征混沌混合和混合效率所需的其他工具。Mortar元素和约束近似方法的实施也将允许这两个schemes.In湍流的情况下，在微观尺度上的流体混合的精度和计算效率之间的详细比较需要很长的混合长度和很长的时间。 这在设计用于微流体装置的有效混合器方面产生了重大挑战，所述微流体装置例如用于检测用于医疗、制药和国家安全应用的生物和化学试剂的微全分析系统。 利用时间周期电渗允许设计新的混合策略，通过增加种间接触面积来增强扩散混合，或者诱导混沌混合。 该项目将使人们能够更好地理解和表征电致混沌和扩散混合。 这项研究将促进新的微流体混合概念的发展，这可以在设计用于微流体和纳米流体应用的新型高效微混合器中实现。

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.