Asymptotic Analysis and Fast Computation for Predictive Design of Inertial Microfluidic Devices

在惯性微流体装置中，强大的压力泵推动液体样本，如血液，通过微米大小的通道网络。通道内的流动可用于分离样品中的颗粒，如血液中的细胞，根据它们的大小或形状，将它们运送到有规则间隔的链的测试区域，或者有选择地将它们从一种液体转移到另一种液体。尽管这些设备已经在样品测试和处理中找到了许多应用，但缺乏定量准确的模型来说明颗粒如何在设备内产生的流动中移动。如果没有足够快的模型来测试可能的设备几何形状，预测建模就很少用于设备的原型设计或优化设计。事实上，人们甚至对粒子所承受的力的性质和数量也存在分歧。在这个项目中，PI将开发近似方法，使设备周围流场的快速解决方案。这项工作的目标是揭示诸如细胞之类的粒子在惯性微流体装置中所经历的力的类型，并创建和共享可用于笔记本电脑上的设备构建组的强大模拟工具。PI将整合多种教育和推广元素，包括指导本科生研究人员和未来的高中数学教师进行前沿水平的研究。此外，PI还将制定高中数学课程计划和教材，供加州各地的教师使用，并通过数学圈和制作视频，向K-12学生提供直接联系，展示如何使用应用数学来设计和改进技术。惯性微流体装置的设计是利用有限的雷诺数力，导致粒子迁移流体流线，自组织成晶格，并被过滤成涡流。力是由Navier-Stokes方程中的非线性引起的，并且不能被用于常规微流体装置预测设计的快速线性求解器捕获。PI将开发和利用用于描述流体流动和粒子运动的Navier-Stokes方程结构的渐近工具。PI也将剖析方程的渐近结构，在小和有序的单位粒子雷诺数的极限。此外，PI将揭示方程中的主要平衡，以及不同主要平衡区域之间的匹配条件，重点关注形状从粒子流出的奇异项。对主导平衡的分析将使我们能够更全面地了解作用在粒子上的力的物理起源。融合渐近和数值方法将用于开发低复杂性的表示，类似于浸入边界方法，其中粒子由少量几何捕获奇点建模。这些模型将与加州大学洛杉矶分校的迪诺·迪卡洛小组合作进行实验测试。最后，PI将使用混合数值方法来预测颗粒大小，形状和背景流如何控制颗粒轨迹。这些模型将用于创建低复杂性和低计算成本的数值模拟，并打包成一个名为inFocus的软件工具，可由设备设计人员直接使用，以测试设备几何形状和预测功能。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

In inertial microfluidic devices, powerful pressure pumps push liquid samples, such as blood, through micron-sized networks of channels. The flows within the channels can be used to separate particles within the samples, such as the cells in the blood, by their sizes or shapes, deliver them to testing areas regularly spaced chains, or to move them selectively from one fluid to another. Although the devices have found many applications in sample testing and handling, there is a lack of quantitatively accurate models for how particles move in the flows created within a device. Without models that can be solved fast enough to test possible device geometries, predictive modeling has been little used for prototyping or optimizing the design of devices. Indeed, there is even disagreement about the nature and number of forces that particles experience. In this project, the PI will develop approximation methods that enable fast solutions of the flow fields around devices. The goal of this work is to reveal the types of forces that particles such as cells, experience within inertial microfluidic devices, and to create and share robust simulation tools that can be used by device-building groups on laptop computers. The PI will integrate multiple educational and outreach elements, including mentoring of undergraduate researchers and future high school math teachers to do frontier level research. In addition, the PI will create high school math lesson plans and teaching materials to be used by teachers across California, and provide direct outreach to K-12 students through a math circle, and through the creation of videos showcasing how applied math can be used to design and improve technologies.Inertial microfluidic devices are designed to exploit finite Reynolds number forces that cause particles to migrate across fluid streamlines, self-organize into lattices, and get filtered into eddies. The forces arise from nonlinearity within the Navier-Stokes equations, and are not captured by the fast, linear solvers that are used for predictive design of regular microfluidic devices. The PI will develop and exploit asymptotic tools for structure of the Navier-Stokes equations that describe fluid flow and particle movements. The PI will also dissect the asymptotic structure of the equations, in the limits of small and order unity particle Reynolds numbers. In addition, the PI will expose the dominant balances within the equations, and the matching conditions between different dominant balance regions, focusing on the singular terms that shape flows away from the particles. Analysis of dominant balances will enable a more complete picture of the physical origin of the forces upon particles. Fusing asymptotic and numerical methods will be used to develop low-complexity representations, akin to the immersed boundary method, in which the particles are modeled by a small number of geometry-capturing singularities. The models will be tested experimentally, in collaboration with the group of Dino DiCarlo at UCLA. Finally, the PI will use the hybrid numerical methods to predict how particle size, shape, and background flow control particle trajectories. The models will be used to create low complexity and low computational-cost numerical simulations, packaged as a software tool called inFocus that can be used directly by device designers to test device geometries and predict function.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.