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

微流体，指的是微米级的流体流动（从某种角度来看，人类头发的直径在20到100微米之间），从根本上影响了从细胞生物学到医学“芯片实验室”诊断到化学制造的各个领域。尽管在实践中取得了所有的成功，在这样小的长度尺度上关于流体行为的基本问题仍然没有答案。 该研究项目涉及制定理论模型，这些模型将能够准确地模拟和预测微流体系统的静态和动态响应。 解决这些基本问题可以设计出更有效的微流体系统。这个研究项目是由一个PI领导的多元化团队执行的，该团队致力于导师制，并在工业研究和政府合作方面拥有丰富的经验。根据普渡大学的原则和包容性和促进多元化劳动力和环境的长期成就，作为该项目的一部分接受培训的早期职业学者正在接受教育，以在他们的科学努力中取得卓越成就，并成为扩大代表性不足的群体参与STEM职业的冠军。该研究项目涉及使用偏微分方程制定将低雷诺数流体动力学理论与弹性结合起来的联合收割机模型，以扩展当前使用的启发式表达式。这种先进技术的融合将产生严格的预测方程，更好地代表软微流体系统的静态和动态响应。具体来说，PI正在开发，通过第一原理的数学分析，通过软微通道的流量和相应的压降之间的无参数的关系，而静态（稳态）的情况下，通常是最感兴趣的，动态响应也是相关的，例如，停止流和软光刻。 因此，软微通道的膨胀和松弛也作为该项目的一部分进行了分析，为瞬态运动提供了分析结果，并将其与高保真数值模拟进行了基准测试。 软固体的复杂材料流变学也被考虑。最后，所有的分析和计算结果进行了验证，从文献中的实验数据。该项目的最终目标是开发一个目录的流量压降关系，没有拟合参数，并能够为现实世界的应用，为各种可变形的微通道形状和类型的微和生物流体应用中出现的有用的预测。

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.