Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session L14: Free Surface Flows: Jets, Films, Propagation, and Spreading |
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Chair: Emmanuel Villermaux, Aix Marseille University Room: C125-126 |
Monday, November 21, 2016 4:30PM - 4:43PM |
L14.00001: The Whole Elephant: A Synoptic View of Liquid Rope Coiling Neil Ribe Liquid rope coiling is the instability that occurs when e.g. a thin stream of honey is poured onto toast. While we now have a fine-grained understanding of each of the four principal coiling modes (viscous, gravitational, inertio-gravitational and inertial), we still lack a global view of how the modes cohere to form a larger whole. Using a numerical continuation procedure, I determine how the dimensionless coiling frequency depends on the dimensionless fall height and flow rate, for several values of the dimensionless nozzle diameter. Starting with the onset of coiling, I propose a purely geometrical definition of the critical surface between coiling and no coiling as the locus of points where the radius $a_1$ of the rope at the contact point is just equal to the coil radius $R$. Coiling with $a_1 > R$ is impossible because the rope would intersect itself. I characterize the asymptotic limits of the critical surface as well as the structure of the supercritical volume inside that surface. The procedure reveals a new mode of coiling onset that has not yet been identified. [Preview Abstract] |
Monday, November 21, 2016 4:43PM - 4:56PM |
L14.00002: Effect of Elasticity on Stability of Viscoelastic Liquid Curtain Alireza Mohammad Karim, Wieslaw Suszynski, Lorraine Francis, Marcio Carvalho Curtain coating is one the preferred methods for high-speed precision application of single-layer and multi-layer coatings in industry. Despite the extensive variety of applications of curtain coating, its operation is challenging and uniform coating is only obtained in a certain range of operating parameters, called the coating window. The two main physical mechanisms that limit curtain coating are the breakup of the liquid curtain, below a critical flow rate, and the catastrophic event of air entrainment, which occurs above a certain web speed. The rheological characteristics of the coating liquid play an important role on these mechanisms, but the fundamental understanding of the role of rheology is still not complete. In this work, we analyze the relative importance of shear and extensional viscosity on both curtain breakup and dynamic contact line instability (i.e. air entrainment). Aqueous solutions of polyethylene oxide (PEO) and polyethylene glycol (PEG) of different molecular weights were used as model liquids to obtain fluids with different levels of extensional thickening behavior. [Preview Abstract] |
Monday, November 21, 2016 4:56PM - 5:09PM |
L14.00003: Effect of added polymer in free jets of a dilute polymer solution Marie-Charlotte RENOULT, Jean-Baptiste CHARPENTIER, Olivier CRUMEYROLLE, Innocent MUTABAZI The instability of a free viscoelastic jet is experimentally investigated by extruding an aqueous solution containing five parts per million of Poly(ethylene oxide) into air from a sixty micrometers orifice at relative low speeds. A method of image analysis was developed to quantify the effect of the added polymer on the morphology and the stability of the jet breakup. Three main representations were considered: the area versus perimeter relation for all liquid objects detected on the images, i.e. jets and jet fragments, the equivalent diameter distribution of jet fragments and the standard deviation curve of jets profiles. The former two provide information on the morphology of jet fragments: distinction of two classes, products and residues, and existence of coalescence. The latter gives information on the jet breakup stability: measurement of the growth rate and initial amplitude of the jet instability and detection of beads-on-a-string structures in the jet interface deformation. Experimental results will be presented and compared to theory. [Preview Abstract] |
Monday, November 21, 2016 5:09PM - 5:22PM |
L14.00004: Wave-front propagation of rinsing flows on rotating semiconductor wafers. John M. Frostad, Andy Ylitalo, Daniel J. Walls, David S. L. Mui, Gerald G. Fuller The semiconductor manufacturing industry is migrating to a cleaning technology that involves dispersing cleaning solutions onto a rotating wafer, similar to spin-coating. Advantages include a more continuous overall fabrication process, lower particle level, no cross contamination from the back side of a wafer, and less usage of harsh chemicals for a lower environmental impact. Rapid rotation of the wafer during rinsing can be more effective, but centrifugal forces can pull spiral-like ribbons of liquid radially outward from the advancing wave-front where particles can build up, causing higher instances of device failure at these locations. A better understanding of the rinsing flow is essential for reducing yield losses while taking advantage of the benefits of rotation. In the present work, high-speed video and image processing are used to study the dynamics of the advancing wave-front from an impinging jet on a rotating substrate. The flow-rate and rotation-speed are varied for substrates coated with a thin layer of a second liquid that has a different surface tension than the jet liquid. The difference in surface tension of the two fluids gives rise to Marangoni stresses at the interface that have a significant impact on the rinsing process, despite the extremely short time-scales involved. [Preview Abstract] |
Monday, November 21, 2016 5:22PM - 5:35PM |
L14.00005: Simulating wave-turbulence on thin elastic plates with arbitrary boundary conditions Wim M. Van Rees, L. Mahadevan The statistical characteristics of interacting waves are described by the theory of wave turbulence, with the study of deep water gravity wave turbulence serving as a paradigmatic physical example. Here we consider the elastic analog of this problem in the context of flexural waves arising from vibrations of a thin elastic plate. Such flexural waves generate the unique sounds of so-called thunder machines used in orchestras - thin metal plates that make a thunder-like sound when forcefully shaken. Wave turbulence in elastic plates is typically investigated numerically using spectral simulations with periodic boundary conditions, which are not very realistic. We will present the results of numerical simulations of the dynamics of thin elastic plates in physical space, with arbitrary shapes, boundary conditions, anisotropy and inhomogeneity, and show first results on wave turbulence beyond the conventionally studied rectangular plates. Finally, motivated by a possible method to measure ice-sheet thicknesses in the open ocean, we will further discuss the behavior of a vibrating plate when floating on an inviscid fluid. [Preview Abstract] |
Monday, November 21, 2016 5:35PM - 5:48PM |
L14.00006: Propagation of a viscous thin film over an elastic membran Zhong Zheng, Ian Griffiths, Howard Stone We study the buoyancy-driven spreading of a thin viscous film over a thin elastic membrane. Neglecting the effects of membrane bending and the membrane weight, we study the case of constant fluid injection and obtain a system of coupled partial differential equations to describe the shape of the air-liquid interface, and the deformation and the radial tension of the stretched membrane. We obtain self-similar solutions to describe the dynamics. In particular, in the early time period, the dynamics is dominated by buoyancy-driven spreading of the liquid film, and membrane stretching is a response to the buoyancy-controlled distribution of liquid weight; the location of the liquid front obeys the power-law form $r_f(t) \propto t^{1/2}$. However, in the late time period, the system is quasi-steady, the air-liquid interface is flat, and membrane stretching, due to the liquid weight, causes the spreading of the liquid front; the location of the front obeys a different power-law form $r_f(t) \propto t^{1/4}$ before the edge effects of the membrane become significant. In addition, we report laboratory experiments for constant fluid injection using different viscous liquids and thin elastic membranes. Very good agreement is obtained between the theory and experiments. [Preview Abstract] |
Monday, November 21, 2016 5:48PM - 6:01PM |
L14.00007: ABSTRACT WITHDRAWN |
Monday, November 21, 2016 6:01PM - 6:14PM |
L14.00008: Dry patches in a flowing film : Predicting rewetting and the effects of inertia Luc Lebon, Julien Sebilleau, Laurent Limat We study the effects of inertia on the shape and stability of dry patches using liquids of decreasing viscosities. These dry patches are formed when a liquid film flows down along a substrate under partial wetting conditions. They become stationary and exhibit an “arch” shape well described by a simple viscous model developed long ago by Podgorski. Surprisingly, this “arch” shape appears to be robust when one decreases the fluid viscosity which increases inertial effects, but the evolution of the apex curvature upon flow rate is strongly affected. We here proposed an improved description of the dry patch evolution taking into account several physical effects as the hydrostatic pressure in the liquid film, the curvature of the contact line, and these inertial effects. These ones affect both the mechanical equilibrium of the rim surrounding the dry patch and the flow inside the rim. This model allows us to show that the dry patch shape remains extremely close to the viscous -Podgorski- prediction but with a rescaling of the apex curvature. It also allows us to get a better prediction of the apex curvature dependence upon flow rate and a prediction of the rewetting threshold above which dry patches are swept away by the film flow. [Preview Abstract] |
Monday, November 21, 2016 6:14PM - 6:27PM |
L14.00009: Node dynamics and cusps size distribution at the border of liquid sheets Emmanuel Villermaux, Christophe Almarcha We study the intrinsic dynamics of cusps, or indentations, moving along a liquid sheet border, an characterize their ensemble statistics. Gordillo and collaborators ({\it J. Fluid Mech., \bf 754} (2014)) have shown that the symmetrical stationary cusp is the only structure accommodating for both mass and momentum conservation at a steadily receding liquid sheet rim. Cusps are also known to typically move along a sheet border, to present an asymmetry, and to be distributed in size around a mean. We show here why an heterogeneous assembly of cusps travelling along the sheet rim occurs spontaneously, why big and small cusps coexist at the same time and, more precisely, we establish the specific link between the microscopic dynamics directing their motion, and the ensemble averaged distribution of their sizes. [Preview Abstract] |
Monday, November 21, 2016 6:27PM - 6:40PM |
L14.00010: Non-classical dispersive shock waves in shallow water Patrick Sprenger, Mark Hoefer A classical model for shallow water waves with strong surface tension is the Kawahara equation, which is the Korteweg-de Vries (KdV) including a fifth order derivative term. A particular problem of interest to these types of equations is step initial data, known as the Riemann problem, which results in a shock in finite time. Unlike classical shock waves, where a discontinuity is resolved by dissipation, the dispersive regularization results in the discontinuity resolved as a dispersive shock wave (DSW). When parameter choices result in non-convex dispersion, three distinct dynamic regimes are observed that can be characterized solely by the amplitude of the initial step. For small jumps, a perturbed KdV DSW with positive polarity and orientation is generated, accompanied by small amplitude radiation from an embedded solitary wave leading edge, termed a radiating DSW. For moderate jumps, a crossover regime is observed with waves propagating forward and backward from the sharp transition region. For sufficiently large jumps, a new type of DSW is observed we term a translating DSW were a partial, non-monotonic, negative solitary wave at the trailing edge is connected to an interior nonlinear periodic wave and exhibits features common to both dissipative and dispersive shock waves. [Preview Abstract] |
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