Inertial microfluidic devices manipulate nano-liter volumes of fluids, allowing for precise control of individual cells and small particles. These devices consist of channels and chambers whose geometry exploits interaction between fluid flow and particles to manipulate particles of different sizes. This exploitation is a physical phenomenon called inertial migration which causes particles to migrate across streamlines when suspended in high velocity flow. Inertial microfluidics has found many academic and medical applications, including trapping of rare cancer cells from blood samples, flow cytometry, and genomic analysis.
However, rational design of microfluidic devices has been held back from its full potential by a lack of quantitative modeling of inertial migration forces. In this thesis I will describe a novel hybrid asymptotic-numerical method, in which particles are accurately modeled as singularities in a linearized flow field to rapidly calculate inertial migration forces. Improvements to asymptotics and numerical techniques allow for large particles to be resolved without any refinement needed to the numerical mesh, leading to an average computation time of 20 seconds per time point on a work station. A particular focus of our study will be the design of micro-centrifuges, notches that capture large particles from inertial streams, allowing for preferential capture and identification of rare circulating cancer cells. Particle capture and retention in microcentrifuges relies on complex entry patterns of streamlines in the background flow. Adding particles creates a moving geometry problem that is hard to simulate using existing numerical methods. Since microcentrifuges motivate our methods development, we analyze them extensively, but our methods are generally applicable for the study of inertial microfludiic devices with Reynolds numbers between 1 and 200. Throughout, results are validated against high speed video and particle tracking is used to elucidate previously unknown 3D dynamics.