Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session E12: Life and Death of Drops |
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Chair: John Bush, Massachusetts Institute of Technology Room: Georgia World Congress Center B217 |
Sunday, November 18, 2018 5:10PM - 5:23PM |
E12.00001: The shaky life of a water drop in an anise oil-rich environment Oscar Enríquez, Daniel Robles, Pablo Peñas, Javier Rodríguez We explore the fate of a water droplet (d∼ 4 mm) placed in a host liquid composed of anise oil (anethole) and a small fraction of ethanol. Water is more dense than this mix, so the droplet sinks to the bottom. There, instead of dissolving by diffusion into the bulk, it starts to grow by incorporating ethanol. After a time t∼10 s from the deposition moment, the drop starts to oscillate in a manner that reminds of Leidenfrost drops, but without depinning from the bottom. Later, it becomes apparent that a mircoemulsion of anethole is also developing inside the droplet. As it keeps growing -whilst reducing its density- it deforms due to buoyancy until at t∼100 s part of the droplet detaches and floats away. The water cap left behind repeats the cycle, now at a slower rate. We discuss the shape evolution, growth rate and oscillation frequency of the droplet as well as the flow fields that develop both inside the drop and on the liquid bulk. |
Sunday, November 18, 2018 5:23PM - 5:36PM |
E12.00002: A bouncing oil droplet in a stratified liquid and its sudden death Yanshen Li, Christian Diddens, Andrea Prosperetti, Kai leong Chong, Xuehua Zhang, Detlef Lohse A millimeter-sized oil droplet is released in a stratified liquid consisting of ethanol carefully deposited on water. The droplet slowly sinks due to gravity, but before reaching the density matched position, it suddenly jumps up by ~ 5 mm, and then settle again for a minute or so, after which the sudden jump occurs again. This process can repeat 30 to 40 times, with the jumping height even increasing, but then the drop all the sudden falls dead. We identify the Marangoni flow at the interface between the oil drop and the stratified liquid as the driven force of the jumping: It exponentially builds up, because it pulls down ethanol-rich liquid, thus increasing the Marangoni force more and more, up to a time that the drop is pulled upwards. We also explain why the jumping expires all the sudden. |
Sunday, November 18, 2018 5:36PM - 5:49PM |
E12.00003: A hydrodynamic analog of the quantum potential John Bush, Matthew Durey, Paul Milewski A droplet may walk on a vibrating fluid bath through a resonant interaction with its own wave field. This walking droplet system has become the subject of research in the nascent field of hydrodynamic quantum analogs. We here consider the motion of droplets walking in closed systems, and demonstrate the relation between the histogram of the particle and its mean pilot-wave field. Furthermore, we demonstrate that as the Faraday threshold is approached, the instantaneous wave field converges to its mean. The resulting mean pilot-wave potential thus plays the role of the quantum potential in Bohmian mechanics. Our study highlights the differences between Bohmian mechanics and de Broglie's relatively rich double-solution theory of quantum dynamics. |
Sunday, November 18, 2018 5:49PM - 6:02PM |
E12.00004: Theoretical modeling of walker interactions with slowly varying topography Sam Turton, Rodolfo R Rosales, John Bush A droplet may bounce indefinitely on the surface of an oscillating fluid bath. Beyond a critical forcing acceleration, the bouncing state is destabilized by the underlying wavefield, causing the droplet to be propelled horizontally. Many interesting phenomena arise when these walking droplets interact with abrupt changes in bottom topography. The model of Faria (2017) permits a theoretical treatment of such problems. We here present the results of an integrated theoretical and experimental study into the motion of a walker on a bath whose depth varies slowly in space. In this limit, it is possible to derive an asymptotic correction to the integral stroboscopic wave model derived by Oza et al. (2013). We compare the theoretical predictions of this model with experiments of droplets walking on a bath with a bottom varying linearly; firstly in a single direction, so that the bottom forms a linear slope; and secondly in the radial direction, so that the bottom forms an inverted cone. The latter configuration gives rise to circular orbits, which destabilize into precessing orbits and more complex motion as the forcing acceleration is increased progressively. |
Sunday, November 18, 2018 6:02PM - 6:15PM |
E12.00005: Unraveling chaotic attractors of walking droplets by symmetry reduction Nazmi Burak Budanur Droplets bouncing on the vibrating bath of the same fluid were shown to exhibit chaotic dynamics in the presence of a confining radial force and sufficiently high vibration amplitude (Tambasco et al., Chaos 25, 103107 (2016)). Complex dynamics in these systems arise as a result of their "memory": At an instance, the surface of the bath is shaped by the waves generated at previous bounces of the droplet; thus, the bath surface "remembers" the droplet's trajectory. In addition, the continuous rotation symmetry of these systems further complicates their dynamics since each generic solution has infinitely many symmetry-copies. We will present a continuous symmetry-reduction scheme for walking droplets that can be applied in both numerical and laboratory settings. We will demonstrate with examples that the symmetry-reduction reveals surprisingly simple chaotic attractors and yields an intuitive picture of global dynamics of the system. |
Sunday, November 18, 2018 6:15PM - 6:28PM |
E12.00006: The juggling soliton Belen Barraza, Camila Sandivari, Nicolas Mujica Non-propagating hydrodynamic solitons (NPHS) have been studied as prototypes of non-equilibrium localized structures. We have recently discovered a new combined structure: the juggling soliton. It is observed in a classical Faraday wave system were a NPHS exists, on top of which small drops of the same liquid can be stabilized, bouncing periodically for very long times, up to about an hour. We use distilled water with a few ml of photoflo and some drops of black ink. The NPHS can juggle one or more drops, typically of 3 mm diameter. These do not coalesce due to a thin layer of air that is continuously renewed at each rebound, as previously observed in bouncing drops below the Faraday instability. The soliton can juggle one or two drops on each side, with different equilibrium positions for each case: for a single drop this position is at the soliton’s center; for two drops, each one drifts a few mm away from the soliton’s center, finding new equilibrium positions. The NPHS is also able to handle three or four drops at once (two and one at each side and two on each side, respectively). For a single drop we present its stability diagram in terms of frequency and vibration amplitude, which is reduced with respect to the phase diagram of the NPHS alone. |
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