Abstract: The liquid droplet growth from a punctured, pressurized vessel immersed in a quiescent medium is studied under steady flow conditions. Local strain rates at the puncture site are also investigated. The droplet growth and local strain rates at the puncture are characterized as functions of various hydrodynamic and geometric conditions. Dimensional analysis shows that the fractional droplet growth rate, Q*, is a function of the Reynolds number, Weber number, hole-to-main tube diameter ratio, D*, and the puncture geometry. A 3-D finite volume computational model is constructed for laminar flow of a Newtonian fluid under steady conditions and validated with supporting experiments. The results show that the fractional growth rate Q* increases with the Weber number and is largest for the lowest Reynolds number of one. In addition, the droplet shape is spherical at low Weber numbers (2.6) and ellipsodial at high Weber numbers (7.8). Additional simulations detail how the growth ratio is lower for small diameter ratios and rectangular punctures. Physiological implications for the hemostatic response (clotting) of a punctured blood vessel can be found by examining the local strain rates in the vicinity of the puncture. The strain rate displays the largest values for the highest Reynolds number (100). In addition, when D* = 0.04 the strain rate is greater at the low (2.6) and high (7.8) Weber numbers, while the strain rate is larger for D* = 0.075 when the Weber number is 5.2. The strain rate is also affected by the puncture shape and displays higher values for the rectangular puncture when Weber < 5.2. Finally, the impact of microgravity on droplet formation was studied. Numerical simulations and quantification of the forces on fluid particles show that there is no effect from gravity on the droplet growth rate or strain rate in medium and large sized veins.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).