Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session FD: Interfacial and Thin Film Instabilities III* |
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Chair: Alex Oron, Technion Room: Tampa Marriott Waterside Hotel and Marina Grand Salon CD |
Monday, November 20, 2006 8:00AM - 8:13AM |
FD.00001: Stability of creeping Couette flow of a power-law fluid past a deformable solid Scott A. Roberts, Satish Kumar The stability of plane Couette flow of a power-law fluid past a deformable solid of finite thickness is considered in this work. The solid is a neo-Hookean or linear elastic material which is incompressible and impermeable to the fluid, and linear stability analysis is applied in the creeping-flow limit. Four key dimensionless parameters govern the problem: an imposed shear rate, a solid-to-fluid thickness ratio, an interfacial tension, and a power-law index. The neo-Hookean solid exhibits a first normal stress difference, not present in linear elastic solids, which is strongly coupled to the imposed shear rate and the power-law index. For large thickness ratios, $H \gg 1$, the shear rate necessary to induce an instability, $\gamma_{\mathrm{c}}$, scales as $\gamma_{\mathrm{c}} \sim H^{-1/n}$, where $n$ is the power-law index. This scaling can be understood in terms of a simple balance between viscous shear stresses in the fluid and elastic shear stresses in the solid. For small thickness ratios, shear-thinning has a stabilizing effect, in contrast to what is observed for thick solids. Whereas a shortwave instability is always observed with Newtonian fluids and neo-Hookean solids when interfacial tension is absent, it can be suppressed with power-law fluids for certain values of $n$. These results are potentially of interest for enhancing mixing in microfluidic devices and understanding the rheology of worm-like micelle solutions. [Preview Abstract] |
Monday, November 20, 2006 8:13AM - 8:26AM |
FD.00002: Annular waves on the surface of impact-formed tektites John Kolinski, Joanna Austin, G. Gioia, Pinaki Chakraborty, Susan Kieffer Tektites are naturally occurring pieces of glass formed by melting of terrestrial rocks during a meteorite impact. The most unusual tektites, known as Australites, were formed by an impact at an unknown site in Austro-Asia, and are found in a large strewn field covering Australia. These tektites solidified on ascent through the earth's atmosphere, and partially remelted during re-entry. The thin remelted layer on the front surface shows distinct flanges with annular wavy structures. We propose that the annular wavy structure is a manifestation of surface waves on the flow of the thin layer. [Preview Abstract] |
Monday, November 20, 2006 8:26AM - 8:39AM |
FD.00003: Stability analysis for air film drag reduction Chinar Aphale, William Schultz, Steven Ceccio A linear stability analysis of an air-water interface is studied for basic understanding of air film physics applied to a ship hull for drag reduction purposes. Three different flows are studied. In the first case, viscosity is considered and is a special case of the problem studied by Yih (1967) when the thickness of two layers is the same and a long-wave stability analysis is performed. The second and third case are inviscid basic flows with unequal thicknesses and inviscid and viscous velocity profiles, respectively. Unstable conditions are determined according to Rayleigh theorem. Interesting inferences are drawn if limits are considered on thicknesses and wave numbers that might be considered for plenums on the hull surface. [Preview Abstract] |
Monday, November 20, 2006 8:39AM - 8:52AM |
FD.00004: Mighty morphing monolayers: How oscillatory flow can influence phase morphology Jonathan Leung, Amir Hirsa Co-existing phase domains are commonly observed in many insoluble monolayers at the air-water interface. Here, vitamin K1, which has been shown to have two very distinct co-existing phase domains, is studied on a flowing system using Brewster angle microscopy. The flow geometry consists of an open-top rectangular cavity in which the flow is driven by the periodic oscillation of the floor in its own plane at large Reynolds numbers (approximately 500). The oscillation of the floor allows for the dilation and compression of any monolayer on the surface while still maintaining an essentially flat interface. An unforced monolayer (no flow) under goes an extensive relaxation at very large time scales (1 or more hours) resulting in a significant decrease in the area of the condensed versus expanded domains. The effect of oscillatory flow (150 oscillations) is to retard the `natural' long time scale relaxation of the monolayer. [Preview Abstract] |
Monday, November 20, 2006 8:52AM - 9:05AM |
FD.00005: Capillary instabilities of liquid films inside a wedge Li Yang, G.M. Homsy We consider a liquid meniscus inside a wedge of included angle $2\beta$ that wets the solid walls with a contact angle $\theta$. The meniscus has a convex interface which satisfies $\pi/2<\theta+\beta<\pi$. The capillary pressure gradient due to a small disturbance in the location of the contact line moves fluid from a neck region to a bulge region, causing instabilities. A dynamic contact-line condition is considered in which the contact angle varies linearly with the slipping speed of the contact line with a slope of $G$: $G=0$ represents perfect slip and fixed contact angle. A nonlinear thin film equation is derived and numerically solved for the shape of the contact line as a function of parameters. The result for $G=0$ shows that the evolution process consists of a successive formation of bulges and necks in decreasing length and time scales, eventually resulting a cascade structure of primary, secondary and tertiary droplets. When $G>0$, there is a similar but slower nonlinear evolution process. The numerical results agree qualitatively with very recent experimental results. [Preview Abstract] |
Monday, November 20, 2006 9:05AM - 9:18AM |
FD.00006: Three-dimensional coherent structures of surface turbulence Serafim Kalliadasis, Evgeny A. Demekhin, Evgeny N. Kalaidin, S.Yu. Vlaskin The evolution of naturally excited disturbances on a thin liquid film falling down an inclined planar substrate undergoes several transitions between different wave regimes starting from two-dimensional (2D) solitary pulses at small Reynolds numbers to the `surface turbulence' stage for sufficiently large Reynolds numbers where the surface is randomly covered by localized three-dimensional (3D) coherent structures. Here we analyze the instability of 2D pulses to 3D disturbances and the transitions of 2D pulses to fully developed 3D waves. The main instability mechanism is the Rayleigh instability of well- separated (isolated) 2D solitary waves. On the other hand, the physical mechanism for the 3D instability of 2D periodic waves is due to wave-wave interaction and mass exchange between neighboring waves. These instabilities are characteristic of small inclination angles but under special conditions can be realized for the vertical flow. [Preview Abstract] |
Monday, November 20, 2006 9:18AM - 9:31AM |
FD.00007: Three-dimensional oscillatory large-scale Marangoni convection in a binary liquid layer Alexander Nepomnyashchy, Sergey Shklyaev, Alex Oron Marangoni convection in a binary liquid layer with nondeformable free surface is considered in the presence of the Soret effect. Both the thermocapillary and solutocapillary effects are taken into account. Oscillatory long-wave convection revealed by Oron and Nepomnyashchy (PRE, 2004) is investigated in detail. A set of amplitude equations describing the nonlinear evolution of three-dimensional perturbations is obtained and studied. Our weakly nonlinear analysis shows that three types of patterns can be stable near the stability threshold, namely: antiphase rectangles (AR), squares (AS), and asynchronous hexagons (AH). These patterns exhibit a superposition of either two (in the case of both AR and AS) or three (in the case of AH) standing waves shifted in phase. In the former case the waves amplitudes are equal to each other and the phase shift equals $\pi/2$. The AH patterns form a two-parametric family with the waves amplitudes depending on their phase shifts. Numerical simulations are carried out for square lattices. It is shown that at finite supercriticality traveling squares and other intermediate regime can be also stable in certain parameter domains. [Preview Abstract] |
Monday, November 20, 2006 9:31AM - 9:44AM |
FD.00008: Capillary oscillations of a liquid sphere pinned on a circle-of-contact. Paul Steen, Eric Theisen, Michael Vogel, Carlos Lopez, Amir Hirsa The vibration of a sphere is a classical example of the competition between liquid inertia and surface tension. In contrast to the violin string, where pinning raises the pitch, constraining the deformable sphere can lower the vibration frequency. This is known. The lower frequency arises from the activation of an oscillation of the center-of-mass relative to the frame of the constraint, a mode with zero frequency for the unconstrained sphere. The dynamics of this center-of-mass mode is the subject of our study and is important in a number of applications since it is the lowest frequency of the system. Our model restricts deformations to spherical-shaped caps. A tractable description of finite-amplitude motions emerges. Regimes of qualitatively different dynamics are predicted that include: i) small-amplitude vibrations about one of either bistable states; ii) large-amplitude limit-cycle oscillations around the two point-attractors. Predictions are compared to experiment and to previous work that employs the classical model. [Preview Abstract] |
Monday, November 20, 2006 9:44AM - 9:57AM |
FD.00009: Spreading, superspreading and autophobing in surfactant-driven films Omar Matar, Richard Craster We study the dynamics of a surfactant-laden film resting on a solid substrate. We use lubrication theory to derive a coupled system of equations for the film thickness and surfactant concentrations; here, the surfactant is allowed to exist in the form of both monomers and micelles which can adsorb at the air-liquid and solid-liquid interfaces. These equations account for capillarity, Marangoni stresses, surface and bulk diffusion and sorption kinetics. Long- and short-range intermolecular forces are also considered and are assumed to depend on surfactant concentration. We examine the behaviour of the system by means of numerical simulations and show that a variety of different responses are possible depending on system parameters. These include, spreading, autophobing followed by dewetting (starting from a perfectly wetting situation) and superspreading (starting from a partially wetting situation). [Preview Abstract] |
Monday, November 20, 2006 9:57AM - 10:10AM |
FD.00010: Transient Hydrodynamic Experiments in a Two-Dimensional Axisymmetric Geometry Aya Diab, Michael Corradini Two dimensional experiments have been undertaken to study the phenomenon of liquid entrainment associated with interfacial hydrodynamic instabilities, specifically the Rayleigh Taylor instability. The current work is part of an effort to understand the phenomenon of Rayleigh Taylor instability associated with a rapid superheated steam bubble expansion that may occur in a CANDU reactor. The experiments aim at quantifying the liquid entrainment in a two dimensional axisymmetric geometry for a range of operating pressures. This experimental work is similar to that undertaken three decades ago at MIT, but the geometry has been modified to decrease the blowdown chute volume in order to reduce the experimental uncertainties. The goal of this work is to characterize the entrainment phenomenon by two parameters that can be used to verify a semi-empirical model that is being developed in a parallel modeling effort. Specifically, the first parameter quantifies the width of the mixing zone and the second parameter quantifies the volumetric ratio between the entrained liquid and the mixing zone. [Preview Abstract] |
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