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

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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.