Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session GQ: Instability: Interfacial and Thin-Film IV |
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Chair: Prabir Daripa, Texas A&M University Room: 200E |
Monday, November 23, 2009 8:00AM - 8:13AM |
GQ.00001: Fingering Instability During Debonding: From a Viscous Liquid to a Soft Elastic Solid Julia Nase, Anke Lindner, Costantino Creton We investigate the fingering instability during debonding of a confined viscoelastic layer in a circular lifted Hele-Shaw cell.\footnote{J. Nase, A. Lindner, C. Creton, PRL \textbf{101}, 074503 (2008)} We use PDMS with different degrees of crosslinking, ensuring a continuous transition from a viscous liquid to a soft elastic solid. During debonding, a fingering instability with characteristic initial wavelength $\lambda$ evolves. When going from a liquid to a solid, we observe a transition from bulk to interfacial mechanisms. We predict this transition from linear viscoelastic and surface properties. We show that for the interfacial mechanism, $\lambda$ depends solely on the film thickness, whereas for the bulk mechanism, $\lambda$ depends on the material parameters. $lambda$ is in both cases in quantitative agreement with linear stability analysis. For a Newtonian oil, we discuss in detail the coarsening of the pattern during debonding. Adapting a recent 3D technique, we visualize for the first time in situ the contact line between viscoelastic material and air in three dimensions, providing direct access to the boundary conditions. [Preview Abstract] |
Monday, November 23, 2009 8:13AM - 8:26AM |
GQ.00002: The effects of viscosity and pressure on the bursting of a drop in a Hele-Shaw cell Andrew White, Thomas Ward As one fluid is injected into another fluid of greater viscosity, instabilities occur in the form of fingers which extend radially from the injection point (Saffman \& Taylor, Proc. R. Soc. Lon. A, 1958). As the lower-viscosity fluid reaches the free surface it rapidly bursts through the higher- viscosity fluid (times are typically less that 50 ms for our system) and a pressure drop occurs. This pressure drop induces the shrinking of the non-bursting fingers. By varying the air pressure and water-glycerol viscosity we study this process by analyzing sequences of images prior and after the bursting event inside a Hele-Shaw cell with a gap spacing of between 10 and 500 micrometers. It has been shown that in a micro-scale environment the effects of gravity are negligible as fluid flow is dominated by capillary forces, thus such a setup would behave in space just as it does on Earth. Therefore it may then be possible to use hot air injected into a Hele-Shaw cell filled with water to generate steam in a microgravity environment. [Preview Abstract] |
Monday, November 23, 2009 8:26AM - 8:39AM |
GQ.00003: Two-phase hydrodynamic model for air entrainment at moving contact line Tak Shing Chan, Jacco Snoeijer The moving contact line problems are challenging because they involve multiple length scales. One interesting case arises when an advancing liquid of high viscosity entrains the surrounding phase, such as air. In this presentation, we introduce a hydrodynamic model that generalizes the lubrication theory in order to take into account the velocity fields of the two phases. Assuming that the curvature of the interface is small we derive a differential equation for the interface profile at stationary state. We found that there is a critical capillary number above which no steady meniscus can exist and instability will occur. For example, air bubbles will be entrained into the liquid at the advancing contact line. However, we found no instability when neglecting the viscosity of the surrounding phase, illustrating the two-phase nature of the problem. [Preview Abstract] |
Monday, November 23, 2009 8:39AM - 8:52AM |
GQ.00004: Surfactant effect on the motion of long bubbles in capillary tubes Prabir Daripa In this talk, we give a theoretical proof of the thickening effect of surfactant by considering a small concentration of surfactant $\Gamma$ and variable surface tension on a long bubble interface which is moving slowly and steadily in a capillary tube filled with a liquid of viscosity $\mu$. The contact angle is taken as zero at the walls and the gravitational effect is neglected. This problem was originally considered by Bretherton and later studied numerically by Park (1990) and Ratulowski and Chang (1991). The main result we obtain is a formula of the film thickness in terms of $M$ and $\Gamma$ where $M$ is the Marangoni number. A comparison with Bretherton's ``clean'' case shows the thickening effect of surfactant. This talk is partially based on an going work with Gelu Pasa. [Preview Abstract] |
Monday, November 23, 2009 8:52AM - 9:05AM |
GQ.00005: Stability of liquid sheet edges Rouslan Krechetnikov Accelerating edges of thin liquid sheets are ubiquitous and are known to experience a longitudinal (along-the-edge) instability, which often leads to their break-up and atomization. The fundamental physical mechanisms of this instability are studied analytically in the form of a concise model. It is discovered that the classical Rayleigh-Taylor mechanism is substantially modified which leads to a stability picture different from that for flat interfaces, in part due to an interplay with Rayleigh-Plateau mechanisms. In particular, as the Bond number increases, first only one critical wave number is excited, but for higher values of the Bond number several critical wavenumbers can coexist with the same growth rates. This allows for the transition from the regular picture, in which one wavelength sets the pattern, to the frustrated picture, in which a few wavenumbers compete with each other. [Preview Abstract] |
Monday, November 23, 2009 9:05AM - 9:18AM |
GQ.00006: A Phase-field Model of Wetting in Porous Media -- Origin of Gravity Fingering During Infiltration Ruben Juanes, Luis Cueto-Felgueroso We present a new continuum mathematical model of wetting into dry soil. The inspiration for the new model is the flow of thin films (like water down a plane), which also displays fingering instability. The key idea is very simple: the macroscopic equations must reflect the presence of a macroscopic interface---the wetting front. We then cast the model in the rigorous framework of phase-field models and nonlocal thermodynamics. The new model is appealing. It is a simple extension of the traditional model---Richards' equation---with a new term (a fourth-order derivative in space) but without any new parameters. It reproduces the two key features of unsaturated flow: a nonmonotonic saturation profile, and gravity fingering. It explains why, when, and how, fingers form. It shows excellent quantitative agreement with experiments in terms of tip saturation, tip velocity and finger width. The most attractive aspect is, however, that the new model offers a starting point for fundamentally new formulations of multiphase flow in porous media. [Preview Abstract] |
Monday, November 23, 2009 9:18AM - 9:31AM |
GQ.00007: Transient numerical simulation of miscible channel flow with heat transfer and viscous heating Kirti Sahu, Prashant Valluri, Hang Ding, Omar Matar Pressure-driven miscible channel flow undergoing heat transfer and viscous heating, focusing on the displacement of a highly viscous fluid by a less viscous one, is studied by direct numerical simulations using the finite volume method. The flow dynamics are governed by the continuity and Navier-Stokes equations, coupled to an energy equation and a convective- diffusion equation for the concentration of the more viscous fluid through a concentration- and temperature- dependent viscosity. The effect of temperature difference, Nahme, Prandtl, and Schmidt numbers on the propagation of the front separating the two fluids and temporal evolution of the mass of the less viscous fluid is examined. [Preview Abstract] |
Monday, November 23, 2009 9:31AM - 9:44AM |
GQ.00008: Numerical simulations of two-fluid channel flow with wall deposition and ageing effects Daniele Sileri, Kirti Sahu, Omar Matar We study the dynamics of two immiscible fluids with a high viscosity contrast in pressure-driven channel flow using direct numerical simulations at moderate Reynolds numbers. The equations of mass, momentum and energy conservation in both fluids are solved using a procedure based on the diffuse interface method. A Cahn-Hilliard equation is also solved for the volume fraction. Numerical solutions are obtained subject to no-slip and no-penetration conditions at the walls, and constant flow rate conditions at the channel inlet; outflow conditions are imposed at the outlet. This model accounts for a thermal instability in the bulk, through a chemical equilibrium model based on the Gibbs free energy, which leads to the formation of the highly viscous phase and its deposition at the channel walls. We also account for the evolution of the rheology of the deposited phase through ``ageing.'' We present results showing typical flow dynamics and the effect of system parameters on the average deposit thickness. [Preview Abstract] |
Monday, November 23, 2009 9:44AM - 9:57AM |
GQ.00009: Displacement flows between Newtonian fluids at moderate Reynolds numbers in rectangular channels Prashant Valluri, Hang Ding, Peter Spelt, Omar Matar Displacement flows between two Newtonian fluids in rectangular channels is studied by numerical and analytical means. Two-stages are clearly seen in the displacement process: first, a core of the displaced fluid is removed by a finger of the displacing fluid with width less than the channel height; then, the film of the displaced fluid adjacent to the wall left behind is then removed via interfacial instabilities that grow spatio-temporally. The shape of the finger dictated by a meniscus in the front and a tail of nearly asymptotic height; the latter is a function of the viscosity and density ratios, Weber number and Reynolds number. This dependence is studied by means of highly resolved direct numerical simulations using the diffuse-interface method. The interface shapes obtained is compared with analytical steady state solutions of the meniscus shapes in the downstream region and the asymptotic film thickness in the upstream region. [Preview Abstract] |
Monday, November 23, 2009 9:57AM - 10:10AM |
GQ.00010: Effect of film thickness on EHD-driven instability of superimposed flows Payam Sharifi, Asghar Esmaeeli This study aims to investigate the effect of fluid layer thickness on EHD-driven instability of superimposed fluids using Direct Numerical Simulations (DNS). The geometric setup consists of two fluids having different electrical properties confined between two horizontal electrods, where the lighter fluid is overlaid on top of the heavier one. A front tracking/finite difference scheme is used, in conjunction with Taylor's leaky dielectric model, to solve the governing electrohydrodynamics equations in both fluids at finite Reynolds numbers and the dynamics of the interface and incipience of instability is investigated as a function of the thickness of the lower layer. [Preview Abstract] |
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