Interactions of shapeable boundaries with flowing fluids:Experiments and mathematical modeling

自然界、工业和日常生活中的许多过程都涉及流体和柔性物体或边界的耦合运动。如果要在工程、工业和技术应用中利用或控制这些效应，理解这些复杂的相互作用是具有挑战性的，但也很重要。拟议的项目确定了自然科学和应用科学中有待研究的流体-结构相互作用的关键问题，这些问题将受益于实验室实验和数学建模。重点领域包括由于流体侵蚀和溶解而改变形状的固体边界，以及由流动重塑的液体界面和薄膜。提出的工作重点是通过实验揭示和模型再现的基本相互作用。这些研究将为形成自然地貌的过程以及如何在化学、制药和制造应用中使用这些影响提供见解。该项目还将对本科生和研究生进行数学科学和工程方面的培训和教育，并将通过纽约市弱势群体高中学生的参与，进一步推动全国数学和科学教育计划。基本的流动-边界相互作用机制将通过实验来研究内部流动可侵蚀边界的演变，由于自生对流流动导致的表面溶解，以及流动驱动的薄膜和界面的变形和膨胀。选择这些设置是为了与基于相关流体动力学（例如边界层和自由流线理论）与边界演化方程（例如剪切应力侵蚀定律、菲克扩散定律和杨-拉普拉斯定律）耦合的数学模型紧密联系起来。实验和模型将相互告知，以理解边界流反馈过程在决定形状动力学中的作用，重点放在描述在这些过程中起关键作用的奇异几何形状（例如角、尖峰、表面图案）和奇异事件（例如分岔、几何冲击、破裂）。这些结果如何扩展到更复杂的几何形状（如可蚀/可溶流动网络）和更复杂的情况（如形状演变耦合到流体中的自由运动）也将被探索。更广泛的目标是通过扩大以这种方式看待问题的范围和提供新技术来扩展流体-结构相互作用的范围。更广泛的科学影响涉及在地貌、化学和工业过程的背景下更好地理解流动驱动的侵蚀、腐蚀、融化和溶解。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Many processes in nature, industry and everyday life involve the coupled motions of fluids and compliant objects or boundaries. Understanding these complex interactions is challenging but important if these effects are to be exploited or controlled in engineering, industrial and technological applications. The proposed projects identify key problems from the natural and applied sciences yet to be studied as fluid-structure interactions and which stand to benefit from laboratory experiments and mathematical modeling. Focus areas include solid boundaries that change shape due to fluidic erosion and dissolution, as well as liquid interfaces and films reshaped by flows. The proposed work focuses on the fundamental interactions to be revealed by experiments and reproduced in models. These studies will provide insight into the processes that shape natural landforms and how such effects can be used in chemical, pharmaceutical and manufacturing applications. The program will also train and educate undergraduate and graduate students towards careers in the mathematical sciences and engineering, and it will further national math and science education initiatives through the engagement of New York City high school students from under-represented groups.Fundamental flow-boundary interaction mechanisms will be studied through experiments on the evolution of erodible boundaries by internal flows, the dissolution of surfaces due to self-generated convective flows, and the flow-driven deformation and inflation of films and interfaces. These settings are chosen to closely link with mathematical models to be developed based on the relevant fluid dynamics (e.g. boundary-layer and free-streamline theories) coupled to boundary evolution equations (e.g. shear-stress erosion laws, Fick's law of diffusion, and the Young-Laplace law). Experiments and models will inform one another to understand the role of boundary-flow feedback processes in dictating the shape dynamics, with emphasis placed on characterizing the singular geometries (e.g. corners, spikes, surface patterning) and singular events (e.g. bifurcations, geometric shocks, rupture) that play critical roles in these processes. How these results extend to more complex geometries (e.g. erodible/dissolvable flow networks) and in more complex situations (e.g. shape evolution coupled to free motion in a fluid) will also be explored. A broader goal is to extend the reach of fluid-structure interactions by expanding the scope of problems viewed in this way and by providing new techniques. Broader scientific impacts pertain to better understanding flow-driven erosion, corrosion, melting and dissolution in the context of geomorphological, chemical and industrial processes.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.