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

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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.