A Nonconforming Spectral Element Method for Electroosmotically Induced Microfluidic Mixing

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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.