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 LJ: Surface Tension Effects II |
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Chair: Ranga Narayanan, University of Florida Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 6 |
Tuesday, November 21, 2006 8:00AM - 8:13AM |
LJ.00001: Nibbling Tears of Wine Jeff Aristoff, John Bush The meniscus of an alcohol-rich solution is known to climb upwards due to an evaporation-induced Marangoni stress, thus initiating the tears of wine phenomenon. Rather than merging directly, the tears may bob up and down when they make contact with the underlying reservoir, appearing to nibble at its edge. We present a qualitative description of this flow and propose a simple theoretical model for this behavior. We thus rationalize the observed dependence of the nibbling frequency on the system parameters. [Preview Abstract] |
Tuesday, November 21, 2006 8:13AM - 8:26AM |
LJ.00002: Pattern Formation in Marangoni Convection in an Annular Cell Takashi Mashiko, Satoshi Matsumoto, Hiroaki Ohira, Shinichi Yoda, Yasuhiro Kamotani To elucidate the mechanism of air bubble alignment in Marangoni convection in an annular cell, which was accidentally observed in a microgravity experiment on a space shuttle, we started a series of experiments on the ground. We have three candidates for the main cause of the alignment in mind; surface flow of air bubbles, excluded-volume effect of air bubbles, and formation of some periodic flow structure. Based on this prospect, we designed and have conducted three kinds of experiments; input of liquid droplets into convection, input of solid beads, and observation of the flow pattern using tracer particles. The initial experiments have given us some information, such as a sign of transition of the flow structure, which motivates further investigation. In addition to the flow observation in the above-mentioned initial experiments, we recently set up a new experimental system, in which the temperature distribution on the free surface is measured simultaneously with the flow observation. [Preview Abstract] |
Tuesday, November 21, 2006 8:26AM - 8:39AM |
LJ.00003: Marangoni Convection Experiment in Binary Mixtures J. Zhang, R. Behringer, A. Oron Marangoni instabilities in binary mixtures are believed to be different from pure liquids. In contrast with a large amount of experimental work on Marangoni convection in pure liquids, such experiments in binary mixtures are not available in the literature. Using commonly available binary mixtures such as sodium chloride/water, we have systematically investigated the pattern formation for a set of substrate temperature and solute concentrations. A liquid film is drawn on a silicon wafer which maintains a constant temperature, while its surface opens directly to the air with a fixed room temperature. The flow patterns evolve with time, driven by surface tension fluctuations due to evaporation and the Soret effect, while the air-liquid interface does not deform. A standard shadow graph method is used to keep track of the pattern formation as a function of time. The patterns are mainly composed of quasi-static polygons and rolls. The mean pattern-size gradually increases during the evolution. The evaporation affects the pattern formation mainly at the early stage and the local evaporation tends to become uniform at the film surface. The Soret effect becomes important at the later stage and affects the mixture for a large mean solute concentration where the Soret number is significantly above zero. The strength of convection increases with the initial solute concentration and the substrate temperature. Our findings differ from the theoretical predictions in which evaporation is neglected. [Preview Abstract] |
Tuesday, November 21, 2006 8:39AM - 8:52AM |
LJ.00004: A New Thermodynamic Property of Fluid with a Moving Interface Kausik Das, C. Ward We have investigated the effect of surface energy variation on the energy balance condition across the interface. A new thermodynamic property of the surface, termed surface thermal capacity is defined. It is shown that the effect of the surface thermal capacity on heat transfer (and evaporation) is important for nonzero interface velocities. A thermodynamic description of this new property is provided. [Preview Abstract] |
Tuesday, November 21, 2006 8:52AM - 9:05AM |
LJ.00005: Steady Marangoni flow traveling with chemical fronts Laurence Rongy, Anne De Wit Chemical fronts propagating in a solution with a free surface generate spatiotemporal distributions of heat and mass that can initiate surface tension-driven and buoyancy-driven convections leading to complex experimental dynamics. It is useful to discriminate the influence of the various effects by analyzing model systems where only one type of convective flow is active. The goal of our work is to theoretically investigate the coupling between autocatalytic reactions, diffusion and Marangoni-driven flows to understand the resulting chemo- hydrodynamic patterns. We use the incompressible Navier-Stokes equations coupled to a conservation equation for the autocatalytic product concentration in the absence of gravity and for isothermal conditions. The boundary condition at the free surface introduces a solutal Marangoni number, M, representing the coupling intensity between hydrodynamics and reaction-diffusion processes. We show that such systems reach an asymptotic dynamics characterized by a steady fluid vortex traveling at a constant speed with the front. Increased propagation speed, front deformation and possible transient oscillating dynamics occur when M increases. [Preview Abstract] |
Tuesday, November 21, 2006 9:05AM - 9:18AM |
LJ.00006: Numerical simulation of the surfactant-laden drop deformation and breakup using an ALE method Xiaofeng Yang, Ashley J. James An arbitrary Lagrangian-Eulerian (ALE) method method on an adaptive grid has been developed to simulate interfacial flows with insoluble surfactants. The interface is captured using a coupled level set and volume of fluid method. The surfactant mass in each grid cell is directly tracked by solving a convection-diffusion equation, which ensures the surfactant mass conservation. The surfactant concentration, which determines the local surface tension through an equation of state, is then computed as surfactant mass per interfacial area. To accurately approximate the interfacial area, the fluid interface is reconstructed using piece-wise parabolas. The evolution of the level set function, volume fraction, and surfactant mass is performed using an ALE approach. The flow velocity is obtained by solving the Stokes equations, with the surface tension force incorporated using a continuum-based method. The method is applied to simulate the effect of surfactants on drop deformation and breakup in a Stokes flow. The results are compared with available analytical and experimental results in literature. [Preview Abstract] |
Tuesday, November 21, 2006 9:18AM - 9:31AM |
LJ.00007: Using Remobilizing Surfactants to Increase the Terminal Velocity of Rising Bubbles Ashish Taneja, Demetrius Papageorgiou, Charles Maldarelli The terminal velocity of rising bubbles decreases and the interface is immobilized even if a trace amount of surfactants is present in the bulk liquid. In this work, we identified physiochemical criteria of surfactant, which insures that the interface of the bubble does not become immobile in their presence. Surfactants, which satisfy these criteria, are termed remobilizing surfactants. Remobilizing surfactants should have a very high solubility and are characterized by a rapid rate of kinetic exchange. We will present experimental evidence, which verifies these criteria. We used nitrogen bubbles rising either in water or a 70:30 mixture of glycerol-water and medium chain alcohols as surfactants. With hexanol in glycerol-water mixture 30{\%} remobilization was achieved. However, with butanol in water, negligible amount of remobilization was achieved. This is attributed to the fact that water being a low viscous liquid, rising bubbles have a high terminal velocity and thus a high rate of convection on the surface of these bubbles. This high rate of surface convection is not being counterbalanced by the kinetic exchange. Thus the concentration gradient of surfactant molecules at the interface does not get eliminated and the interface remains immobile. [Preview Abstract] |
Tuesday, November 21, 2006 9:31AM - 9:44AM |
LJ.00008: Marangoni-B\'enard convection in circular and elliptical cylinders Pauline Assemat, Alain Bergeon, Edgar Knobloch The spatial organization of single-fluid Marangoni-B\'enard convection in vertical cylinders with circular and elliptical horizontal cross-section is described. The convection is driven by an imposed heat flux from above and the Marangoni stresses that arise at the free but undeformed surface due to temperature-dependent surface tension. The solutions and their stability characteristics are obtained using branch-following techniques together with direct numerical simulations. The effect of the ellipticity and the symmetries of the grid are discussed. [Preview Abstract] |
Tuesday, November 21, 2006 9:44AM - 9:57AM |
LJ.00009: Dynamics of liquid lenses Richard Craster, Omar Matar The dynamics of a lens of one liquid moving on the surface of another liquid is examined using Lubrication theory. A coupled system of equations for the air-liquid and liquid-liquid interfaces is derived. For highly viscous lenses, extensional stresses are promoted and an additional equation for the lens velocity is derived. The potential singularity at the three-phase line is alleviated by a microscopic precursor layer of the spreading fluid assumed to be present ahead of the macroscopic lens. The results of our numerical simulations show that, for weak gravitational forces, the shape of the lens at equilibrium depends solely on the surface tension ratio for sufficiently deep substrate thicknesses. For thin substrates, the underlying liquid film deforms severely near the point of deposition exhibiting flattening and dimpling. [Preview Abstract] |
Tuesday, November 21, 2006 9:57AM - 10:10AM |
LJ.00010: Ripples in wetting films Vladimir Ajaev, Roumen Tsekov, Olga Vinogradova Wavy shapes of liquid surface are often observed in large-scale flows, i.e. ripples on a surface of a lake, but are rather unusual to find in microscale systems. We show theoretically that deformations in a draining wetting film, created when a bubble is pressed against a solid wall, can result in ripples on the liquid surface. We consider a regime when dynamics of the system is determined by a complex interplay between disjoining pressure and surface tension, while the effect of gravity is negligible. Numerical simulations based on axisymmetric lubrication-type model show evolving shapes with many points of maximum and minimum and allow us to determine the conditions when such shapes can be observed. Experimental evidence of the proposed mechanism will be discussed, including direct comparison with recent observations of the so-called `wimple' shapes (L.Y.Clasohm et al., Langmuir {\bf 21} 8243, 2005) in films of thickness of the order of 100 nm. [Preview Abstract] |
Tuesday, November 21, 2006 10:10AM - 10:23AM |
LJ.00011: Discussion of jump condition at gas-liquid interface Yukihiro Yonemoto, Tomoaki Kunugi A modeling of gas-liquid interface is one of key issues of the numerical research on multiphase flow. Currently, the Continuum Surface Force model (CSF: Brackbill et al., 1992) is popular to model a gas-liquid interface in computational fluid dynamics. However, the CSF model cannot explain the physics of the gas-liquid interface because this model is derived by a mechanical energy balance at the interface. As a practical matter, we must consider the physics of bubble coalescence or breakup, soap bubble and so on. In this study, assuming that the interface is a thin membrane and has a finite thickness, we develop a new mathematical model of the gas-liquid interface based on thermodynamics and mathematical approach. In particular, we derive the equation of free energy based on Lattice gas model including both influences of the electric double layer caused by a contamination and the jump condition at gas-liquid interface treated by thermodynamics. Finally, we compare this thermodynamic jump condition with the conventional one. [Preview Abstract] |
Tuesday, November 21, 2006 10:23AM - 10:36AM |
LJ.00012: Flow resistance computation for a non-wetting fluid in an interior corner Danny Bolleddula, Mark Weislogel Capillary flows in containers or conduits with interior corners are commonplace in nature and industry. The wide majority of investigations addressing such flows have solved the problem numerically in terms of a flow resistance coefficient (friction factor) for cases where spontaneous liquid spreading along the corner occurs for contact angles below the Concus-Finn critical wetting condition for the particular conduit geometry of interest. This research effort provides missing numerical data for the flow resistance coefficient for partially wetting systems above the Concus-Finn condition. In such cases the fluid spontaneously de-wets the interior corner and often retracts into corner-bound drops. A narrowly banded numerical coefficient is desirable for further analysis and is achieved by careful selection of length scales to nondimensionalize the problem. Example solutions to steady and transient flow problems are provided that illustrate application of the results. [Preview Abstract] |
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