Fluid-Structure Interaction of a squishy cell in an inertial microfluidic channel Science Academic Year 2023 Accepted Applied Math, Fluid Mechanics, Physics, Engineering, Mathematical Modeling, Data Analysis Microfluidic devices are increasingly used for lab-on-a-chip technology for medical diagnostics, (other applications). Here, microfluidics means micron scale (10^-6 m) fluid mechanics. I am particularly interested in inertial microfluidics: where the small length scale is offset by very fast speeds. In this regime, very interesting behavior called inertial migration arises from the nonlinear equations of motion: the Navier-Stokes Equations. Add to this device a squishy cell (for example, a blood cell or tumor cell) and the level of complexity increases. The fluid flow deforms the shape of the cell, and the deformation of the cell alters the fluid flow, a phenomenon called Fluid-Structure Interaction (FSI). This project we will use the Immersed Boundary Method in 2d (using a matlab code called IB2d) to model the FSI of a squishy cell in an in inertial microfluidic channel. Objectives: 1. How does the elasticity of the cell affect inertial migration? 2. How does the FSI affect the dispersion of a dye out of the cell? 3. What is the length scale of interaction between two squishy cells? Kaitlyn T. Hood Kaitlyn T. Hood Write codes to implement the IB2d method for a squishy cell in an inertial microfluidic channel. Then use data analysis and mathematical modeling to interpret the results and make predictions about what will happen in 3D and in experiments. We will be using IB2d: an immersed boundary method in 2D written for matlab or python. Here is a link about the method, which can be downloaded from github: https://nickabattista.wixsite.com/home/ib2d Differential Equations, programming in Matlab or Python, Critical thinking, Good communication skills 3 9 (estimated)

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