Collaborative Research: The leaky rake to solid plate transition on flow through biological filtering structures

许多在水流中游泳、飞行、嗅觉或觅食的小型生物依赖于对生物和生物医学应用具有重要意义的分枝、毛茸茸的结构。这些毛茸茸的层的运动和方向可以改变流经它们的空气或水的行为，使它们可以充当实心板或泄漏的铲子。了解动物如何创造性地利用这种流动转变可以为过滤器和采样设备的设计提供信息。尽管已经在许多系统中对这种流动进行了研究，但仍然没有关于泄漏斜板到固体平板过渡的预测数学模型。这个项目的目标是通过数学建模和实验来揭示这种转变背后的物理机制。开发的理论模型可以应用于生物医学问题，如淋巴和血液在多孔组织和血管保护层中的流动。在教育和外展方面，学生将通过跨学科课程、实地研究和多学科小组会议，在工程、数学和生物的界面上进行培训。不同的学生将通过路易斯·斯托克斯少数人参与联盟(LSAMP)招募。这项研究将阐明在惯性和粘性力几乎平衡的中尺度上运行的生物和生物灵感过滤阵列的基本流体动力学。它还将揭示当平流和扩散接近平衡时粒子捕获和交换的基本物理学。将研究两种类型的海洋无脊椎动物：1)倒置的水母，它们通过3D毛茸茸的口腔手臂驱动水流；2)海扇，它被分成大约2D片。由于需要同时解决微米级结构周围的小规模流动和厘米级阵列周围的整体流动，因此对泄漏到固体的转变进行建模是具有挑战性的。在实验的基础上，将建立新的数学模型来描述柔性滤层的有效孔隙率。粒子捕获率和中尺度过滤阵列周围的浓度分布将在生物体和物理模型中进行实验量化。化学交换的更多细节将使用浸没边界方法进行数值求解。在生物学方面，这些生物代表了许多例子中的一个，其中粒子捕获和养分吸收发生在中尺度的刷毛阵列中。揭示这一策略是如何有利的，直接有助于NSF的生活规则。在生物灵感设计方面，这些系统展示了固有的多尺度过滤和交换解决方案，将为过滤结构的生物灵感设计提供新的见解。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。

Numerous small organisms that swim, fly, smell, or feed in flow rely on branched, bristled and hairy structures that are significant to biological and biomedical applications. The movement and orientation of such bristled layers can change the behavior of the air or water flow through them such that they may act as either solid plates or leaky rakes. Understanding how animals creatively take advantage of this type of flow transition could inform the design of filters and sampling devices. Although such flows have been studied in many systems, predictive mathematical models of the leaky rake to solid plate transition remain unavailable. The goal of this project is to reveal the physical mechanisms behind this transition through mathematical modeling and experimentation. The theoretical models developed could find applications in biomedical problems such as the flow of lymph and blood through porous tissues and vascular protective layers. In terms of education and outreach, students will be trained at the interface of engineering, mathematics, and biology through interdisciplinary courses, field research, and multidisciplinary group meetings. Diverse students will be recruited through the Louis Stokes Alliance for Minority Participation (LSAMP).This research will elucidate the fundamental fluid dynamics of biological and bioinspired filtering arrays operating at the mesoscale, where inertial and viscous forces are nearly balanced. It will also reveal the fundamental physics of particle capture and exchange when advection and diffusion are nearly balanced. Two types of marine invertebrates will be examined: 1) upside-down jellyfish that drive flow through 3D bristled oral arms, and 2) sea fans that are branched into approximately 2D sheets. Modeling the leaky-to-solid transition is challenging due to the need to simultaneously resolve small-scale flow around micron-scale structures and bulk flow around centimeter-scale arrays. New mathematical models, informed by experiments, will be developed to describe the effective porosity of flexible filtering layers. Particle capture rates and concentration profiles around mesoscale filtering arrays will be quantified experimentally in organisms and physical models. Further details of chemical exchange will be resolved numerically using the immersed boundary method. In terms of biology, these organisms represent one of many examples where particle capture and nutrient uptake occur in mesoscale bristled arrays. Revealing how this strategy is advantageous contributes directly to the NSF Rules of Life. In terms of bioinspired design, these systems exhibit inherently multiscale solutions for filtering and exchange that will provide new insights into the bioinspired design of filtering structures.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.