Collaborative Research: Scaling of ciliary flows at intermediate Reynolds number

纤毛是一种柔软的毛发状附属物，通常用于在生物系统中创造流体运动，促进游泳、进食、繁殖和其他功能行为。典型的纤毛有几十微米长，但纤毛虫(梳状水母)使用的纤毛规模要大得多--大约一毫米长。在小尺度上，纤毛流动受到流体粘度的高度限制。然而，在更大的尺度上，惯性变得更加重要，导致纤毛产生的速度和力在数量和质量上的差异。这些差异将通过实验室实验和计算模拟相结合的方式来探索，使用纤毛虫作为大规模纤毛的模型系统。更好地了解纤毛在不同尺度上的流体动力学将为提出和回答与生物学、生态学和柔性结构如何产生跨尺度流动的基本物理学相关的问题提供新的工具。这些知识可能会导致工程学的新发展，包括生物灵感设备、传感器和机器人。该项目还将包括几个教育组成部分的开发，包括针对高中物理学生的粘性-惯性转变的新模块，以及针对对工程感兴趣的年轻女性的外展活动。该项目的总体目标是了解支配纤毛流动从低雷诺数到中雷诺数的物理原理。这项研究将明确检查基质几何形状和变形能力对纤毛流动的影响。采用实验-数值相结合的方法研究了中低雷诺数下多个柔性推进器的水动力相互作用，并发展了有用的标度律。该实验方法将使用平面和体积粒子图像测速技术来可视化各种动物和推进器大小范围内的活体生物所产生的流动。纤毛基质(中胚层)的材料特性也将在调查期间进行表征。这些结果将指导可伸缩计算流体力学模型的发展，该模型将用于研究跨尺度纤毛流动产生的更大参数空间。该项目将侧重于三个关键变量的影响：(1)推进器运动学，包括弯曲程度和时空不对称；(2)衬底几何形状，从平坦到弯曲；(3)衬底变形性，从刚性到高度变形。这一综合方法将使我们能够深入调查柔性结构如何在粘性-惯性转变过程中产生流动，并开发出广泛适用的比例原则来指导未来的技术发展。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Cilia are flexible hair-like appendages commonly used to create fluid motion in biological systems, facilitating swimming, feeding, reproduction, and other functional behaviors. Typical cilia are tens of microns long, but ctenophores (comb jellies) use cilia at much larger scales—around a millimeter in length. At small scales, ciliary flow is highly constrained by fluid viscosity. However, at larger scales, inertia becomes more important, leading to quantitative and qualitative differences in the velocities and forces produced by the cilia. These differences will be explored with a combination of laboratory experiments and computational simulations, using ctenophores as a model system for large-scale cilia. A better understanding of the fluid dynamics of cilia across scales will provide new tools to ask and answer questions related to biology, ecology, and the fundamental physics of how flexible structures create flow across scales. This knowledge may lead to new developments in engineering, including bioinspired devices, sensors, and robots. The project will also include the development of several educational components, including a new module on the viscous-inertial transition for high school physics students and outreach activities for young women interested in engineering.The overall goal of the project is to understand the physical principles that govern ciliary flows from low to intermediate Reynolds numbers. This study will explicitly examine the effects of substrate geometry and deformability on ciliary flows. A combined experimental-numerical approach will be used to investigate hydrodynamic interactions of multiple flexible propulsors at low-to-intermediate Reynolds numbers and develop useful scaling laws. The experimental approach will employ both planar and volumetric particle image velocimetry to visualize the flows generated by living ctenophores across a range of animal and propulsor sizes. The material properties of the ciliary substrate (mesoglea) will also be characterized during the investigation. These results will guide the development of a scalable computational fluid dynamics model, which will be used to investigate the larger parameter space of ciliary flow generation across scales. The project will focus on the effects of three key variables: (i) propulsor kinematics, including the degree of bending and spatiotemporal asymmetry; (ii) substrate geometry, from flat to curved; and (iii) substrate deformability, from rigid to highly deformable. This integrated approach will enable an in-depth investigation of how flexible structures generate flow across the viscous-inertial transition, and the development of broadly applicable scaling principles to guide future technology development.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.