Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session BG: Free Surface Flows II |
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Chair: Kenneth Breuer, Brown University Room: 101G |
Sunday, November 22, 2009 10:30AM - 10:43AM |
BG.00001: Liquid bridge stability and breakup with a receding contact line Kenneth Breuer, Bian Qian We have used experimental and theoretical methods to study the evolution and pinch-off of a liquid bridge fixed at the upper attachment point, but with a free contact line at the lower attachment point. High speed video shows that the contact line motion consists of two stages: a slow retraction at the beginning and a rapid retraction immediately prior to the bridge pinch-off. During the first stage, the evolution is quasi-static, and only a function of the bridge's height and volume. Agreement between experiments and solutions to the Young-Laplace equation is excellent during this phase. At some point, however, the static solution becomes unstable, and the contact line retreats rapidly, pinching off to form a droplet on the substrate. Theoretical and numerical approaches are used to analyse and predict this motion. Excellent agreement with experiments is achieved using a Tanner-like formulation for the dynamic contact angle. [Preview Abstract] |
Sunday, November 22, 2009 10:43AM - 10:56AM |
BG.00002: Building water bridges in air: Can Taylor and Melcher's leaky dielectric model explain such a striking phenomenon? \'Alvaro G. Mar\'In, Detlef Lohse A liquid bridge forms when applying a high voltage between two glass beakers full of water. Surprisingly, the water bridge defies gravity even when the beakers are separated at distances of around $2 cm$. Experimental measurements have been done to characterize its shape and correlations have been found with the electrical current passing through the bridge. A complicated flow pattern within the bridge has been also visualized using high speed recordings and particle velocimetry measurements will show its origin. Although the presented results are preliminary, some mechanisms are proposed and discussed for the stability of the bridge and the source of the flow, revealing an important role of polarization forces on the stability of the water bridge. The system would therefore behave as an extreme example of a \emph{leaky dielectric} which would permit to make use of the famous model developed by Taylor and Melcher.\footnote{J. R. Melcher and G. I. Taylor, \emph{Electrohydrodynamics: A review of the role of interfacial shear stresses}, Annual Review of Fluid Mechanics, vol. 1,~111-146 ~(1969).} [Preview Abstract] |
Sunday, November 22, 2009 10:56AM - 11:09AM |
BG.00003: Hydrostatics, steady flow, and dynamics in helically-supported capillary channels David Thiessen, Jerry Oelerich, Kelsey Cline, Likun Zhang Helically-supported capillary channels consisting of water-filled, slightly stretched, horizontal springs constitute an ideal system for the study of the hydrostatics and hydrodynamics of capillary channels. This unique geometry allows for sub-micron measurement of the radial position of the meniscus as a function of axial distance down the channel using digital image analysis. Hydrostatic measurements on a 300 micron diameter channel, with a length-to-diameter ratio of 120, give a profile of channel compliance as a function of axial position. Capillary-driven flow in this channel has been demonstrated at flow rates up to 0.8 mL/min (average axial velocity 0.25 m/s). The flow rate limits in these channels are understood in terms of capillary pressure limits. Larger diameter channels (~3 mm) connected to a pressure reservoir are being studied for application to microgravity phase separation. In this case, the channel diagnostics are used to examine droplet impact and absorption into the channel as well as for the detection of capillary waves that emanate from the impact point. [Preview Abstract] |
Sunday, November 22, 2009 11:09AM - 11:22AM |
BG.00004: Vibration impact on longwave thermocapillary instability in a binary mixture with the Soret effect Irina Fayzrakhmanova, Sergey Shklyaev, Alexander A. Nepomnyashchy We study the influence of vibrations on the longwave Marangoni convection in a layer of a binary mixture with the Soret effect. At the lower solid boundary of the layer a fixed heat flux is specified; the upper free boundary is assumed to be nondeformable. In the absence of vibrations, this problem was analyzed in [1]. The vibration frequency is comparable with the eigenfrequency of the oscillatory mode; its amplitude is sufficiently large to provide finite values of the inertia force. A linear stability analysis is performed by means of the Floquet theory. Several limiting cases are treated analytically. In the parameters region, where an oscillatory instability exists in the absence of the vibration [1], a subharmonic mode is critical. With the increase in the vibration amplitude, substantial decrease in the critical Marangoni number is observed. In the parameters region, where a monotonic mode is found in [1], a synchronous mode emerges. In the latter case, either stabilization or destabilization of the system can take place depending on the problem parameters. [1] A. Oron, A.A. Nepomnyashchy, PRE {\bf 69}, 016313 (2004). We acknowledge the support by Israel Science Foundation (grant 812/06) and Israeli Ministry of Science (grant 3-5799). [Preview Abstract] |
Sunday, November 22, 2009 11:22AM - 11:35AM |
BG.00005: Computation of time-periodic solutions of the vortex sheet with surface tension Jon Wilkening, David Ambrose I will describe a spectrally accurate numerical method for finding non-trivial time-periodic solutions of nonlinear PDE. We minimize a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We use adjoint methods (originally developed for shape optimization in fluid mechanics) to compute the gradient of this functional with respect to the initial condition. We then minimize the functional using a quasi-Newton gradient descent method (limited memory BFGS). We use our method to compute families of time-periodic solutions of the vortex sheet with surface tension separating two incompressible, irrotational, immiscible, inviscid fluids. As a starting guess, we use analytically determined time-periodic solutions of the linearized problem about a flat interface with constant vortex sheet strength. We then use our numerical method to continue these solutions beyond the realm of linear theory to explore the topology and bifurcation structure of a two-parameter manifold of symmetric breathing solutions. [Preview Abstract] |
Sunday, November 22, 2009 11:35AM - 11:48AM |
BG.00006: Nonlinear dynamics of coiling, and mounding in viscoelastic jets Trushant Majmudar, Thomas Ober, Gareth McKinley Free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes like bottle filling, remain poorly understood in terms of fundamental fluid dynamics. Here we present a systematic study of the effect of viscoelasticity on the dynamics of continuous jets of worm-like micellar surfactant solutions of varying viscosities and elasticities, and model yield-stress fluids. We systematically vary the height of the drop and the flow rate in order to study the effects of varying geometric and kinematic parameters. We observe that for fluids with higher elastic relaxation times, folding is the preferred mode. In contrast, for low elasticity fluids we observe complex nonlinear dynamics consisting of coiling, folding, and irregular meandering as the height of the fall increases. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the ``leaping shampoo" or the Kaye effect. Upon increasing the flow rate to very high values, the ``leaping shampoo" state disappears and is replaced by a pronounced mounding or ``heaping". A subsequent increase in the flow rate results in finger-like protrusions to emerge out of the mound and climb up towards the nozzle. This novel transition is currently under investigation and remains a theoretical challenge. [Preview Abstract] |
Sunday, November 22, 2009 11:48AM - 12:01PM |
BG.00007: Equilibrium shapes of drops emerging slowly on top of vertical tubes Abel Lopez-Villa, Abraham Medina, Francisco Higuera In this work we are interested in describing the shape of a single drop which emerges on top of a vertical tube just when it reaches the edge of the tube. We assume that the liquid is injected at a very low, constant, volume flow rate Q. We consider, as a first approximation, that the drop shape can be calculated by using a balance of force equation that relates the hydrostatic and capillary presures. The results are valid for cases of good and poor wetting, respectively, and for high and low Bond numbers. We present experiments that validate the numerical results obtained for the drop shapes. [Preview Abstract] |
Sunday, November 22, 2009 12:01PM - 12:14PM |
BG.00008: Cowboy Fluid Mechanics: Lariat Modes of a Viscous Rope Neil Ribe, Sarah Badr, Stephen Morris A thin filament of viscous fluid falling onto a surface winds itself into a helical coil whose angular frequency of rotation $\Omega$ depends on the fall height $H$, the flow rate, and the fluid properties. We have studied a novel variant of this phenomenon in which the nozzle ejecting the fluid rotates about a vertical axis at a constant rate $\omega$. In laboratory experiments using viscous corn syrup, we observe that the filament coils in the normal way when $\omega\ll\Omega$. However, when $\omega\approx\Omega$ and $H$ is sufficiently large, a new ``lariat'' mode appears in which the filament is thrown outward in the form of a spiral of large diameter (up to tens of cm) rotating at a rate $\approx 0.9\omega$. The transition between the coiling and lariat modes is hysteretic with respect to variations in $\omega$. In addition to the laboratory experiments, we will also present preliminary results of numerical calculations of the lariat mode based on a ``slender body'' model for a viscous filament with inertia. [Preview Abstract] |
Sunday, November 22, 2009 12:14PM - 12:27PM |
BG.00009: An other viscous catenary Jacopo Seiwert, Marie Le Merrer, David Qu\'er\'e, Christophe Clanet The classical viscous catenary is obtained by the gravitational deformation of an initially horizontal thread of viscous fluid (honey for example). A second shape exists, roughly composed of three perpendicular pieces (like a flying trapeze). We study the physics of this flying trapeze-shape and show in particular that its origin is independent of the liquid viscosity, and is only fixed by the geometric characteristics (length and radius) of the (initial) filament. [Preview Abstract] |
Sunday, November 22, 2009 12:27PM - 12:40PM |
BG.00010: ABSTRACT WITHDRAWN |
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