Numerical Study of Electrokinetic Bioparticle Transport Through Fluid-Structure-Electric Interaction

本提案旨在开发一种新的计算框架来模拟涉及复杂流体-结构-电相互作用的微流体装置中的电动生物颗粒传输。由于多物理场和多尺度现象的复杂性，必须解决几个重要的数值问题：(1)由于强流固耦合引起的数值刚度和收敛性挑战；(2)具有可变形运动边界的流动相互作用引起的尾迹、分离和涡流等非定常现象的解析；(3)强电-结构相互作用带来的收敛性和精度挑战。研究人员和她的团队建议使用晶格玻尔兹曼方程（LBE）来计算流体运动，因为它的精度（低耗散/低色散和更好的各向同性）和计算优势，包括其出色的并行可扩展性，不需要为压力场求解耗时的椭圆泊松型方程，以及易于在笛卡尔网格上表示复杂边界。选择浸入边界法（IBM）跟踪可变形的移动边界，因为它易于实现而无需重新网格划分以生成贴体网格。采用松弛法和多重网格法求解拉普拉斯方程表示的电场。本提案的中心主题是通过对这些方法进行更严格的数学表述并结合其数值分析，以及通过应用现有的数值算法与开发新的高效数值技术相结合，来提高LBE、IBM和多网格技术的能力。这项研究的主要动机之一来自芯片实验室（LoC）的应用，这对生物医学、制药和环境工业很重要。生物粒子输运的良好控制是LoC工作原理的基础。例如，通过微流体储层中的可变形性进行的电细胞分离可以使用所提出的数值框架进行演示，这将有利于对影响人类细胞生物力学特性的病原体（如疟疾中被寄生虫感染的红细胞）进行廉价的即时诊断。该项目将补充和推进目前微流体器件中粒子动力学的知识，并为未来生物颗粒操纵微器件的设计和电气控制奠定流体力学基础。此外，这项建议的研究将与本科和研究生教育计划密切结合。

This proposal aims to develop a new computational framework to simulate electrokinetic bioparticle transport in microfluidics devices involving complex fluid-structure-electric interactions. Due to the complicated nature of multi-physics and multi-scale phenomena, several important numerical issues have to be addressed: (1) Numerical stiffness and convergence challenges due to the strong fluid-structure interactions; (2) Resolution of unsteady phenomena such as wakes, separation and vortices induced by interactions of flows with deformable moving boundaries; (3) Convergence and accuracy challenges imposed by the strong electric-structure interactions. The investigator and her team propose to use the lattice Boltzmann equation (LBE) for the fluid motion because of its accuracy (low dissipation/low dispersion and better isotropy) and computational advantages including its excellent parallel scalability, absence of the need to solve a time consuming elliptic Poisson-type equation for the pressure field, and ease of representation of complex boundaries on Cartesian grids. The immersed boundary method (IBM) is chosen to track the deformable moving boundaries for its ease of implementation without re-meshing to generate the body-fitted mesh. Relaxation and multigrid methods are used to solve the electric field represented by Laplace equation. A central theme of this proposal is to advance the capability of LBE, IBM and multigrid techniques through a more rigorous mathematical formulation of these methods combined with their numerical analysis, as well as through the application of existing numerical algorithms in conjunction with the development of novel efficient numerical techniques.One of the main motivations for this study comes from the Lab-on-a-chip (LoC) application, important for bio-medical, pharmaceutical, and environmental industries. Well-controlled manipulations of bio-particle transport are the basis of the working principle of LoC. For instance, electrical cell separation by deformability in a microfluidic reservoir can be demonstrated using the proposed numerical framework, which will benefit inexpensive point-of-care diagnostics of pathogens that affect the biomechanical properties of human cells such as parasite-infected red blood cells in malaria. The project will complement and advance the current knowledge of particle electrokinetics in microfluidic devices, and build the fluid mechanics foundation for the design and electric control of future bioparticle manipulation microdevices. In addition, this proposed research will be intimately integrated with undergraduate and graduate education programs.