Microscale Fluid--Structure Interactions: Towards a Predictive Theory of Their Dynamic Response

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Microfluidics, which refers to fluid flows at micrometer scales (for some perspective, a human hair has a diameter between 20 and 100 micrometers), has fundamentally impacted fields ranging from cell biology to medical "lab on a chip" diagnostics to chemical manufacturing. Despite all the success achieved in practice, fundamental questions regarding fluid behavior at such small length scales remain unanswered. This research project involves formulating theoretical models that will be able to accurately emulate and predict the static and dynamic responses of microfluidic systems. Solving these foundational problems can lead to the design of even more effective microfluidic systems. This research project is being performed by a diverse team led by a PI with a strong commitment to mentorship and significant experience with industrial research and government partnerships. In line with Purdue's principles and long-standing achievements of inclusion and promotion of a diverse workforce and environment, early-career scholars trained as part of this project are being taught to achieve excellence in their scientific endeavors and to become champions of broadening participation of underrepresented groups in STEM-based careers. This research project involves formulating models that combine theories of low Reynolds number hydrodynamics with elasticity, using partial differential equations, to extend heuristic expressions currently in use. This fusion of advanced techniques will yield rigorous, predictive equations that better represent the static and dynamic responses of soft microfluidic systems. Specifically, the PI is developing, through a first-principles mathematical analysis, parameter-free relations between the flow rate through a soft microchannel and the corresponding pressure drop across it. While the static (steady-state) case is typically of most interest, the dynamic response is also relevant in, for example, stop-flow and soft lithography. Therefore, the inflation and relaxation of soft microchannels is also being analyzed as part of this project, providing analytical results for the transient motion and benchmarking this against high-fidelity numerical simulations. The complex material rheology of soft solids is also being considered. Finally, all analytical and computational results are being validated against experimental data from the literature. The ultimate objective of this project is to develop a catalog of flow rate-pressure drop relations, without fitting parameters and capable of useful predictions for real-world applications, for a variety of deformable microchannel shapes and types that arise in micro- and bio-fluid applications.