The motion of an object through a fluid surface has drawn the attention of scientists and engineers interested in physical processes involving the interplay of inertia, gravity, viscous forces, surface tension, and hydrophobicity. Water-entry phenomena are ubiquitous in engineering applications and in nature. Such engineering applications include ship motion, ocean structure-wave interaction, and ballistics. Biological examples include the locomotion of the basilisk lizard on the water surface and the drinking processes of animals. Despite the great interest in water-entry physics, an approach unifying all physical forces governing the water-entry process is not well developed. This can be attributed to the fact that during the entry process the relative importance of the physical parameters involved is continuously changing. These parameters are inertia, gravity, surface tension, hydrophobicity, and the pressure jump across the interface. The PIs propose to perform state-of-the-art experiments and develop a comprehensive mathematical model that captures all physical factors involved. In the modeling of interfacial dynamics, the PIs will develop a splash-curtain model to capture the dome-closing shape above the free surface, investigate the instability of cavity ripples after the pinch-off, and account for the effect of surface tension, as well as pressure jump across the interface. In physical experiments, the PIs will quantitatively study the dynamics of water entry with various well-controlled parameters and introduce a method to measure the internal air pressure using digital particle image velocimetry (DPIV) velocity fields. The PIs will perform ultrafast synchrotron x-ray imaging experiments in order to capture the dynamics of the advancing contact line during water entry. By overcoming the limitations of current experimental and mathematical methods, the PIs aspire to transform our understanding of water-entry processes and provide the enabling knowledge for advances across the numerous engineering applications involving water entry. Previous studies have focused only on inertia and gravity, which are dominant in the initial stage of impact, but they often neglect many other physical factors, such as viscous or surface tension effects. As a result, models describing the fundamental mechanics within the intermediate range of these physical parameters are lacking. Biological systems, such as those described above, often operate within this intermediate range of conditions. Hence, this work is focused on understanding the physical processes governing water entry within the intermediate conditions of the physical parameters. In terms of the broader impacts, this research should provide insights at the interface of engineering, math, and physics. This work should provide an improved understanding of water-entry dynamics and enable the development of novel bio-inspired engineering systems that, for example, minimize loads and possible catastrophic damage on structures upon water impact. This project will provide interdisciplinary education for graduate and undergraduate students by training them in advanced experimental methods combined with rigorous mathematical modeling. Moreover, the results and accomplishments of this work will translate into the classroom through graduate and undergraduate courses that the PIs teach, thus contributing to the development of engineers and researchers that appreciate, promote, and develop cross-disciplinary technologies. The PIs will leverage current, successful Virginia Tech diversity and outreach programs, including recruiting initiatives and retention of underrepresented groups with which the PIs collaborate.

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