Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session LF: Interfacial and Thin Film Instabilities IV |
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Chair: Burt Tilley, Olin College of Engineering Room: Hilton Chicago Continental C |
Tuesday, November 22, 2005 8:00AM - 8:13AM |
LF.00001: Three-dimensional wave patterns in falling films Benoit Scheid, Christian Ruyer-Quil, Paul Manneville A large number of studies have been devoted to the modeling of film flows down inclined planes since the pioneering work of Kapitza \& Kapitza (1949). Ruyer-Quil \& Manneville (2000,2002) have extended the Shkadov formulation (1967) applying weighting residual techniques and expanding the flow field over a complete basis of polynomial functions. Inspired from a Pad\'e-like approximant technique initially proposed by Ooshida (1999), a refined model is now formulated which also includes second-order inertia effects arising from the deviation of the streamwise velocity profile from its parabolic shape. The stability of two- dimensional traveling waves against three-dimensional perturbations is investigated using this model. The secondary instability is found to be not really selective which explains the widespread presence of the synchronous instability observed in the experiments by Liu {\it et al.} (1995), though theory predicts in most cases a subharmonic scenario. Three-dimensional wave patterns are next computed assuming periodic boundary conditions. Transition from 2D to 3D flows is shown to be strongly dependent on initial conditions. The herringbone patterns, the synchronously deformed fronts, the oblique and the V-shape solitary waves observed in various experimental data (Liu {\it et al.} 1995; Park \& Nosoko 2003; Alekseenko {\it et al.} 1994) are reliably recovered. [Preview Abstract] |
Tuesday, November 22, 2005 8:13AM - 8:26AM |
LF.00002: Stability of a Falling Liquid Film Zhi Liang Wang, S.P. Lin Absolute instability was not found in a falling viscous liquid layer over a plane by Joo and Davis (1992). They assumed that the wave length of disturbance is much longer than the layer thickness. Their results are valid for the case of a vertical plane in a limited parameter range associated with gravity and surface tension. Their assumption and limitations are removed in this investigation. No absolute instability is found in a liquid layer. The instability is convective. The physical mechanism of convective instability is elucidated by comparing each terms in the energy budget. [Preview Abstract] |
Tuesday, November 22, 2005 8:26AM - 8:39AM |
LF.00003: On dimpled thin liquid falling films H. Grandjean, B.S. Tilley, A.E. Hosoi, L. Kondic The interfacial dynamics of a thin liquid falling film flowing on a plane inclined with respect to gravity is investigated. The glycerol-water mixture is recirculated through the experiment, and after a significant time, isotropic, transient depressions along the fluid surface appear and disappear. The locations of these events, which we call ``dimples'' are shown to be independent of spatial location, and are more pronounced as the average film thickness is reduced. Potential mechanisms for this transient behavior could involve large Peclet-number dynamics of soluble surfactant, Marangoni and inertial fluid effects and shear-induced migration of particles within the bulk. Comparison of the theory to the experiment is presented. [Preview Abstract] |
Tuesday, November 22, 2005 8:39AM - 8:52AM |
LF.00004: Localized running drops on a binary mixture thin film Michael Bestehorn, Ion Borcia We examine hydrodynamic instabilities occuring in a liquid binary mixture with a free and deformable surface. The derived reduced model is based on the long wave length (lubrication) approximation. It consists of a a set of two coupled equations, one for the surface profile $h(x,y,t)$, the other one for the concentration $n(x,y,t)$ on the surface: \begin{eqnarray*} \partial_t h & = & -\nabla \left(\nabla h + \nabla\Delta h - \nabla(h^3)+\Psi\nabla n \right)\\ \partial_t n & = & L(\Delta n - \Delta h) \end{eqnarray*} Here, $\Psi$ is the separation ratio and $L$ the Lewis number. Linear stability analysis as well as numerical solutions of the non-linear model equations in three spatial dimensions will be presented. The mechanism responsible for an oscillatory (Hopf) instability at onset of convection due to the Soret effect is examined. We show the formation of running drops or holes along the free surface, driven by a self-organized concentration gradient in lateral direction. [Preview Abstract] |
Tuesday, November 22, 2005 8:52AM - 9:05AM |
LF.00005: WITHDRAWN: Rapidly rotating rimming flow with shocks Miguel Villegas-Diaz We study the shape of the interface in a partially filled horizontal cylinder which is rotating rapidly around its horizontal axis. The rimming flow presented in this work includes both higher-order effects due to weak gravity, inertia and surface tension and the leading-order effect of a constant shear acting at the free boundary. We numerically determine film thickness profiles featuring smoothing shocks in the regime in which the cylinder is rapidly rotating. [Preview Abstract] |
Tuesday, November 22, 2005 9:05AM - 9:18AM |
LF.00006: Simulations of Density-Stratified Kelvin-Helmholtz Instability in the Inclined Channel Lyudmyla Barannyk, Robert Krasny A system of two incompressible inviscid immiscible fluids of different densities shearing one past another in the inclined channel is considered. The first approach uses a boundary integral representation in which the fluid interface is approximated by a free vortex sheet and the channel walls by bound vortex sheets. Another approach models walls as source sheets. The behavior of the interface between fluids with small density variation (Boussinesq regime) as well as with full density jump is studied numerically using the vortex blob method. The goal is to simulate the flow in the inclined channel and compare the numerical results within two models as well as with the experimental results obtained by Thorpe [J. Fluid Mech. 46 (1971) 299--319]. [Preview Abstract] |
Tuesday, November 22, 2005 9:18AM - 9:31AM |
LF.00007: On instability of large amplitude long interfacial waves Tae-Chang Jo, Wooyoung Choi The evolution of large amplitude interfacial waves in a system of two layers of different densities is investigated using a strongly nonlinear long wave model. A local stability analysis is presented to show that the solitary wave solution of this ‘inviscid’ model suffers from a Kelvin- Helmholtz type instability due to a velocity discontinuity across the interface between two layers. A numerical filter is used to eliminate the short-wave instability (that is absent in real observations) and its effects on long-term numerical simulations are discussed. [Preview Abstract] |
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