Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session BF: Gravity Driven Instabilities in Films and Interfaces |
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Chair: Pierre Colinet, Universite Libre de Bruxelles Room: 003B |
Sunday, November 23, 2008 10:30AM - 10:43AM |
BF.00001: Reverse draining of a magnetic soap-film: Experiment John Pelesko, Derek Moulton The draining of vertically suspended soap films under the action of gravity has been studied since at least the time of Newton. Today, understanding this draining is of interest in a variety of areas including the study of foams, the study of rupture, and the study of non-Newtonian fluids. Here, we present experimental results on the drainage of a magnetic soap film. An ordinary soap bubble solution was mixed with an aqueous suspension of magnetic nanoparticles in order to form a magnetic soap solution capable of producing a stable thin film. The film was suspended vertically and the thinning behavior studied in the presence and absence of a magnetic field. Both flat films and cylindrical films were studied. In the absence of a magnetic field, the film thins most at the top and produces a region known as ``black film.'' In the presence of a magnetic field, we show that this black film may be produced at the bottom of the film indicating reverse draining. [Preview Abstract] |
Sunday, November 23, 2008 10:43AM - 10:56AM |
BF.00002: Reverse draining of a magnetic soap-film: Theory Derek Moulton, John Pelesko A vertical soap-film drains under gravity, with a growing region of very thin film, termed black film, forming at the top. This basic problem has been studied since the 1950's starting with the work of Isenberg, yet the mechanisms behind the process remain controversial. In this work, we investigate the drainage of a magnetic soap-film - that is, a film with a stable colloidal suspension of magnetic nanoparticles - placed in a magnetic field. An evolution equation is developed for the film thickness from the Navier-Stokes equations using lubrication theory. In doing this we utilize a magnetic stress tensor for an arbitrary magnetic field under the assumption of a dilute colloid. We then present analytical and numerical results for particular known magnetic fields. In the case of a strong bar magnet or current loop placed above the film, we demonstrate how the drainage may be reversed so that the region of black film forms at the bottom and grows upward. [Preview Abstract] |
Sunday, November 23, 2008 10:56AM - 11:09AM |
BF.00003: Hydraulic jump in falling soap films Tuan Tran, Pinaki Chakraborty, Gustavo Gioia, Stanley Steers, Walter Goldburg We perform experiments to study the flow of soap films driven by gravity. We find that the velocity of the flow attains a maximum value after the film has fallen for about 1m under the effect of gravity, but then the velocity drops rapidly to a low value at the outlet. We show theoretically and computationally that the drop in velocity corresponds to a hydraulic jump associated with the Marangoni elasticity of the soap film. We support our conclusions by a detailed comparison between our experimental measurements and computations. [Preview Abstract] |
Sunday, November 23, 2008 11:09AM - 11:22AM |
BF.00004: Turbulent Dynamics of a Hydraulic Jump in two dimensions: Soap film flow Jason Larkin, Walter Goldburg, Tuan Tran, Pinaki Chakraborty, Gustavo Goia A hydraulic jump is an abrupt and (usually) turbulent transition frequently observed in open channel flows. By using an appropriately defined Froude number $Fr$, the abrupt flow transition is marked by a change from supercritical to subcritical flow. In open channels this results in fast moving flow slowing rapidly and piling up like the formation of a shockwave. The Froude number is $Fr=V/V_c$, where V is the flow speed and V$_c$ is the relevant wave speed. If the initial speed of the flow is below the relevant critical wave speed ($Fr<1$), then no jump is formed. For $Fr > 1$, we study the effects of a hydraulic jump in a two dimensional (2-D) flowing soap film. The relevant wave speed, $V_c$, is the speed of elastic Marangoni waves from surface tension. The jump manifests itself as a sudden thickening of the film in the flow direction and the generation of turbulence in the vicinity of the jump. Properties of the turbulence, including energy spectra, near the thickening transition are reported. [Preview Abstract] |
Sunday, November 23, 2008 11:22AM - 11:35AM |
BF.00005: ABSTRACT WITHDRAWN |
Sunday, November 23, 2008 11:35AM - 11:48AM |
BF.00006: Spatial response of a film flowing down a fiber Camille Duprat, Christian Ruyer-Quil, Frederique Giorgiutti-Dauphine We consider the stability and the nonlinear dynamics of a liquid viscous film flowing down a vertical fiber. This instability involves different mechanisms: the Rayleigh-Plateau instability promoted by the fiber curvature, the advection by the flow and the hydrodynamic instability of a falling film due to inertia. The study of the initial response of the flow to natural noise shows a well-defined transition between an absolute and a convective instability [1]. In the convective case, the film behaves as a selective noise amplifier and its spatial response to periodic forcing is studied through experimental data and comparisons to the solutions of a model in the nonlinear regime. This model includes all physical effects, especially viscous dispersion and inertia [2]. We found that the characteristics of the waves strongly depend on the frequency. For high forcing frequency, the formation of saturated wavetrains is observed, whereas at low forcing frequencies a sequence of pairing leads ultimately to solitary-like waves with high velocities and amplitude. The role of inertia on the shape and steepening of the wave front is evidenced. The model recovers the main features of the waves such as velocity, amplitude, and wavelength. [1] C. Duprat, C. Ruyer-Quil, S. Kalliadasis and F. Giorgiutti-Dauphin\'{e}, Phys. Rev. Letters, 98, 244502 (2007) [2] C. Ruyer-Quil, P. Treveleyan, F. Giorgiutti-Dauphin\'e, C. Duprat and S. Kalliadasis, J. Fluid. Mech., 603, pp 431-462 (2008) [Preview Abstract] |
Sunday, November 23, 2008 11:48AM - 12:01PM |
BF.00007: ABSTRACT WITHDRAWN |
Sunday, November 23, 2008 12:01PM - 12:14PM |
BF.00008: Gravity-driven Propagation of Thin Non-isoviscous Rivulets on Vertical and Inclined Planes Gaozhu Peng, Andrey Filippov Many practical problems require the spreading of a liquid on a solid. The liquid may be paint, a lubricant, and ink, polymer, or a dye. In the glass industry, flows of molten glass on a vertical or inclined, in respect to the vertical, solid refractory surface are parts of several important applications. In present paper, propagation of a thin and relatively narrow rivulet on vertical and inclined solid planar surface is considered within a mathematical frame of general lubrication theory. In contrast to most of previous studies, the addressed flows are gravity driven, and the coefficient in front of the surface tension term in the dimensionless equations (the inverse Bond number) is small. It has been found that the flow pattern strongly depends on the inclination angle. For example, the rivulets on the positively inclined plates spread, increasing their width. On the contrary, the contact line of rivulets propagating on vertical and negatively inclined plates becomes unstable, sending ahead one or several smaller forerunner rivulet (finger) having a higher amplitude and moving faster than the main rivulet. This instability is similar to fingering instability of infinite films on solid surfaces, but the pattern of the flow was symmetric in respect to the middle line of the rivulet rather than a periodic. In the case of the gradient of viscosity applied in the cross-direction to the main flow, the symmetry broke and motion of both main rivulet and forerunners diverted in the direction of areas with lower viscosity. [Preview Abstract] |
Sunday, November 23, 2008 12:14PM - 12:27PM |
BF.00009: Wave regimes in two-layer microchannel flow Chris Lawrence, Grigori Sisoev, Daniele Sileri, Omar Matar We consider vertical channel flow of two immiscible fluids separated by an interface. Varying the flow conditions, the problem is reduced into the falling film flow case, and we consider values of the Reynolds number when only the film instability mechanism exists. To describe the wave regimes present, nonlinear evolution equations for the interface and flow rate of one of layers are derived by applying the Karman-Pohlhausen method in conjunction with boundary-layer theory. Use of bifurcation analysis allows us to identify the various families of steady travelling waves in the microchannel flow as a function of system parameters. [Preview Abstract] |
Sunday, November 23, 2008 12:27PM - 12:40PM |
BF.00010: Interaction of solitary pulses in active-dispersive media Sergey Saprykin, Dmitri Tseluiko, Serafim Kalliadasis We develop a coherent structures theory for solitary pulses in active media with energy supply, dissipation, dispersion and nonlinearity, such as a film falling down a planar substrate. The overall profile is written as a superposition of the pulses and an overlap function. By projecting the dynamics of this function onto the zero modes of the eigenvalue problem that governs the interaction we obtain dynamical system for the location of the pulses. We show that for the generalized Kuramoto-Sivashinsky equation, in particular, it is necessary to solve a generalized eigenvalue problem due to the nature of the nonlinearity. As a consequence, the underlying dynamical system is a two-dimensional one. We examine the influence of dispersion onto the seperation distance of equilibrium pulses and we contrast the theoretical predictions with statistical data from time-dependent computations. [Preview Abstract] |
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