Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session G4: Drops IV |
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Chair: Sigurdur Thoroddsen, King Abdullah University of Science and Technology, Saudi Arabia Room: 23C |
Monday, November 19, 2012 8:00AM - 8:13AM |
G4.00001: The breakup of thin air films caught under impacting drops Sigurdur Thoroddsen, Marie-Jean Thoraval, Kohsei Takehara, T. Goji Etoh When a drop impacts a pool at very low velocities $V$, an air layer cushions the impact and prevents immediate contact. This air layer is stretched into a hemispheric shape and thins to a submicron thickness. We use silicone oils, where these films are more stable than for water [Saylor \& Bounds (2012), {\it AIChE J.}, online: {\it doi 10.1002/aic.13764} ]. We observe three main breakup mechanisms which are imprinted onto the micro-bubble morphology. First, for lowest $V$ the film ruptures at isolated holes which grow rapidly, leaving {\it bubble necklaces} where their edges meet. Based on micro-bubble volumes, we show the film breaks by van der Waals, when its thickness $\sim$ 100 nm. Secondly, for slightly larger $V$ a ring of holes appearing a fixed depth, where the film is thinnest, producing {\it bubble chandeliers}. Finally, for larger $V$ an air jet within the drop, ruptures it at the bottom tip, in an axisymmetric breakup. We measure the rupture speed and find that for very viscous liquids, the breakup moves faster than the capillary-viscous velocity, through the repeated ruptures. [Thoroddsen, Thoraval, Takehara \& Etoh (2012), {\it J. Fluid Mech.} online: {\it doi:10.1017/jfm.2012.319}]. [Preview Abstract] |
Monday, November 19, 2012 8:13AM - 8:26AM |
G4.00002: Toroidal bubble entrapment under an impacting drop Marie-Jean Thoraval, Sigurdur T. Thoroddsen, Kohsei Takehara, Takeharu Goji Etoh We use ultra-high-speed imaging and numerical simulations (GERRIS, http://gfs.sf.net) to observe and analyze the formation of up to 14 air tori when a water drop impacts on a thin liquid film of water or other miscible liquids. They form during the early contact between the drop and the pool by the vertical oscillations of the ejecta sheet. They then break in micro-bubble rings by the Rayleigh instability. Their formation is associated with the shedding of an axisymmetric vortex street into the liquid from the free surface. These vorticity structures and their dynamics are made apparent by the dynamics of the micro-bubbles, added seed particles and the difference of refractive index for different liquids in the drop and the pool. More robust entrapments are observed for a thin film of ethanol or methanol. We show that while the non-spherical drop shape is not responsible for the toroidal bubble entrapments, the number of rings is increasing for more oblate drops. Individual bubble entrapments are also observed from azimuthal destabilizations of the neck between the drop and the pool. [M.-J. Thoraval, K. Takehara, T. G. Etoh, S. Popinet, P. Ray, C. Josserand, S. Zaleski and S. T. Thoroddsen (2012). von K\'arm\'an Vortex Street within an Impacting Drop. Phys. Rev. Lett., 108, 264506.] [Preview Abstract] |
Monday, November 19, 2012 8:26AM - 8:39AM |
G4.00003: Bouncing and walking droplets Jan Molacek, John Bush Motivated by the hydrodynamic quantum analogue system of Yves Couder, we examine the dynamics of silicone oil drops bouncing on a vertically vibrating liquid bath. We report regime diagrams indicating the dependence of the vertical drop motion on the system parameters. A logarithmic spring model for the interface is developed, and provides new rationale for the regime diagrams. We further examine the spatio-temporal evolution of the standing waves created on the bath surface by repeated drop impacts. Measurement of the tangential coefficient of restitution of drops bouncing on a quiescent bath enables us to accurately determine all the major forces acting on the drop during flight and impact. By combining the horizontal and vertical dynamics, we thus develop a model for the walking drops that enables us to rationalize both the extent of the walking regime and the walking speeds. The model predictions compare favorably with experimental data in the parameter range explored. [Preview Abstract] |
Monday, November 19, 2012 8:39AM - 8:52AM |
G4.00004: A trajectory equation for walking droplets Anand Oza, Rodolfo Rosales, John Bush Yves Couder and coworkers have demonstrated phenomena reminiscent of quantum mechanics in a macroscopic hydrodynamic system. Specifically, they have discovered that millimetric droplets walking on a vibrating fluid bath exhibit wave-particle phenomena previously thought to be peculiar to the microscopic quantum realm, including single-particle diffraction and tunneling. Orbital quantization may be observed by placing a walking drop on a rotating fluid bath, which suggests a correspondence between the drop's quantized orbits and the Landau levels of an electron in a uniform magnetic field. We here develop an integro-differential trajectory equation for these walking droplets with a view to gaining insight into their subtle dynamics. We present an exact formula for the walking speed and compare it to experimental data. We also analyze the stability of the walking solution to infinitesimal perturbations. The trajectory equation is used to model the walking drop in a rotating fluid bath, which allows us to rationalize the observed orbital quantization. We predict the existence of self-orbiting or \lq\lq spin\rq\rq\,states and a mechanism reminiscent of the Zeeman effect in quantum mechanics. [Preview Abstract] |
Monday, November 19, 2012 8:52AM - 9:05AM |
G4.00005: Bouncing droplets in quantized orbits Matthieu Labousse, St\'ephane Perrard, Marc Miskin, Emmanuel Fort, Yves Couder, John Bush A drop of silicon oil on a vibrating bath can surprisingly bounce without coalescing. Slightly below the Faraday threshold, each impact creates a slowly decreasing stationary wave. Driven by the whole past field, a small increment of momentum is given to the droplet at each rebound that leads to a walking regime. This macroscopic wave particle system exhibits fascinating quantum-like behaviour that is strongly experimentally supported by diffraction interference, double slits, Landau levels, tunnel effect, Zeeman effect, cavities. A new step has been taken in the understanding of this system by applying an external potential to a double-structured ferrofluidic drop. Depending of the magnitude of its past field, i.e. the memory of the system, a shift from classical to statistically-quantized behaviours arises. First, we will report the experimental observations of this dual system in the light of the previous experiments. Then, a brief overview of a theoretical approach will be presented to simply rationalize these quantized behaviours. [Preview Abstract] |
Monday, November 19, 2012 9:05AM - 9:18AM |
G4.00006: Hydrodynamic quantum analogues: droplets walking on the impossible pilot wave John Bush Yves Couder and coworkers have demonstrated that droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic quantum realm. We explore the connection between this hydrodynamic system and the pilot-wave theory of quantum mechanics proposed by de Broglie and extended by workers in the field of stochastic electrodynamics. Critical common features of these ostensibly disparate systems are identified, and quantitative differences noted. [Preview Abstract] |
Monday, November 19, 2012 9:18AM - 9:31AM |
G4.00007: Splashing of droplets on liquid surfaces Michael Chemama, Shreyas Mandre, Michael Brenner High-velocity impacts of liquid droplets on a solid surface produce a splash. This splash is usually accepted to be the consequence of the ejection of a thin sheet of fluid near the impact point. Recent works have shed light on the formation of this liquid sheet by studying the interaction between the droplet and the thin layer of air above the solid surface just before the impact, both experimentally and theoretically. Here we apply the theoretical approach previously applied to splashing on a solid surface [Mandre and Brenner; JFM, 690, 148 (2012)] to the study of splashing on a liquid surface, where the compressed air layer can now deform two liquid interfaces. We show how the nonlinearities in Navier-Stokes equations lead to the ejection of a thin liquid sheet and how this relates to the experimental observations. [Preview Abstract] |
Monday, November 19, 2012 9:31AM - 9:44AM |
G4.00008: Numerical investigation of microbubble formation in liquid-liquid impact events Seyedshahabaddin Mirjalili, Ali Mani A numerical study of the problem of a droplet impacting another layer of the same liquid is performed with the primary motivation of understanding the steps that lead to the formation of multiple micro-bubbles in the Mesler entrainment mechanism. Simulations start before impact, where a thin gas layer is present and are continued to stages after impact, taking care of topological changes, and finally depicting the formation of the chandelier-like pattern of small bubbles observed in Mesler entrainment. A two dimensional boundary element approach similar to the work of M. Mani, Mandre and Brenner (JFM, vol. 647, p. 163, 2010) is undertaken with the appropriate assumption of inviscid, incompressible potential flow in the liquid bodies, thin structure lubrication flow in the gas layer, with modifications to allow for large interface deflection and topological changes assuming uniform pressure in the bubbles. [Preview Abstract] |
Monday, November 19, 2012 9:44AM - 9:57AM |
G4.00009: Droplet impact on a liquid pool: air bubble entrainment Tuan Tran, Helene de Maleprade, Chao Sun, Detlef Lohse A range of spectacular phenomena result from impacts of droplets on the surface of a liquid pool, such as splashing, bubble entrapment, or droplet bouncing off from the surface. Here we provide experimental results on the dynamics that precede these striking events, in particular on the entrapment process of an air bubble between the impacting droplet and the pool's surface. We focus on the impact dynamics at early time with an emphasis on the air layer from its formation to its rupture. We identify the dependence of the rupture position on the liquid viscosity and the impact velocity. We show that the volume of the entrapped air under impacting droplets can be related to both that of impacting droplets on solid surfaces and that of impacting rigid spheres on liquid surfaces. [Preview Abstract] |
Monday, November 19, 2012 9:57AM - 10:10AM |
G4.00010: Drop impact on a non-miscible liquid Henri Lhuissier, Chao Sun, Andrea Prosperetti, Detlef Lohse The impact of a drop on a deep liquid bath is well-known to transiently open a crater in the bath and possibly eject a liquid sheet and a jet. For non-miscible drop and bath liquids at impact the drop can fragment and disperse into a collection of non-coalescing daughter drops. At impact the drop flattens, spreads at the crater surface and reaches a maximal deformation, which gets larger with increasing impact velocity, before surface tension drives its recession. This recession can promote the fragmentation by two different mechanisms: At moderate impact velocity, the drop recession converges to the axis of symmetry to form a jet which then fragments by a Plateau-Rayleigh mechanism. At higher velocity the edge of the receding drop destabilizes and shapes into ligaments which subsequently fragment. For this later mechanism, the dependence of the critical velocity for fragmentation on the bath viscosity and the number and size distribution of the daughter drops as a function of impact velocity will be discussed. [Preview Abstract] |
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