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

这项提议旨在开发一种新的计算框架来模拟包含复杂的流体-结构-电相互作用的微流体装置中的电动生物颗粒传输。由于多物理和多尺度现象的复杂性，必须解决以下几个重要的数值问题：(1)强流固相互作用引起的数值刚度和收敛挑战；(2)流动与可变形运动边界相互作用引起的尾迹、分离和旋涡等非定常现象的解决；(3)强电结构相互作用带来的收敛和精度挑战。这位研究人员和她的团队建议将格子Boltzmann方程(LBE)用于流体运动，因为它具有精度(低耗散/低色散和更好的各向同性)和计算优势，包括出色的并行可伸缩性，不需要为压力场求解耗时的椭圆型泊松方程，以及易于在笛卡尔网格上表示复杂边界。采用浸没边界法(IBM)跟踪可变形运动边界，无需重新划分网格即可生成贴体网格。采用松弛法和多重网格法对拉普拉斯方程表示的电场进行求解。这项提议的一个中心主题是通过对LBE、IBM和多重网格技术进行更严格的数学描述并结合它们的数值分析，以及通过应用现有的数值算法和开发新的高效数值技术来提高这些方法的能力。这项研究的主要动机之一来自于芯片实验室(LoC)的应用，这对生物医疗、制药和环境行业非常重要。对生物颗粒传输的良好控制是LOC工作原理的基础。例如，可以使用所提出的数值框架来证明微流控储存库中通过变形性进行的电细胞分离，这将有助于对影响人类细胞生物力学特性的病原体进行廉价的护理点诊断，例如疟疾中被寄生虫感染的红细胞。该项目将补充和发展微流控器件中颗粒电动力学的现有知识，并为未来生物粒子操纵微器件的设计和电气控制奠定流体力学基础。此外，这项拟议的研究将与本科生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.