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 ED: Interfacial and Thin-Film Instabilities II |
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Chair: Harry Swinney, University of Texas at Austin Room: Tampa Marriott Waterside Hotel and Marina Grand Salon CD |
Sunday, November 19, 2006 4:15PM - 4:28PM |
ED.00001: Harmonic moments of radial viscous fingering patterns Harry L. Swinney, Alexander Leshchiner, Matthew Thrasher, Mark Mineev-Weinstein We measure the displacement of oil by air in a Hele-Shaw cell constructed of circular glass plates 288 mm in diameter, separated by a gap of 0.38 mm [1]. Oil is removed from the cell perimeter and is replaced by air that enters through a hole in the bottom plate. High resolution digital imaging is used to track the growth of the air bubble, which develops viscous fingers. We determine the pattern's harmonic moments, which are integrals of integer powers of z = x + iy over the oil domain. The results for the harmonic moments are in accord with Richardson's theory [2], which predicts that harmonic moments should be time invariant in the absence of surface tension. Extending the theory to include surface tension, we obtain from measurements of the time evolution of the harmonic moments a value for the surface tension that is within 10 percent of the accepted value. \newline [1] L. Ristroph, M. Thrasher, M. B. Mineev-Weinstein, and H. L. Swinney, Phys. Rev. E 74, 015201 (2006). \newline [2] S. Richardson, J. Fluid Mechanics 56, 609 (1972). [Preview Abstract] |
Sunday, November 19, 2006 4:28PM - 4:41PM |
ED.00002: Spiral viscous fingering. Yuichiro Nagatsu, Atsushi Hayashi, Yoshihito Kato, Yutaka Tada When a less-viscous fluid displaces a more-viscous fluid in a radial Hele-Shaw cell, viscous fingering pattern is believed to develop in a radial direction. We performed experiments on viscous fingering in a radial Hele-Shaw cell when a polymer solution, a sodium polyacrylate (SPA) solution is used as the more-viscous fluid and the trivalent iron (Fe$^{3+})$ solution is as the less-viscous fluid. The experiment was done by varying the concentration of Fe$^{3+}$, $c_{Fe3+}$. We have found that viscous fingering pattern develops spirally when $c_{Fe3+}$ is larger than a threshold value, while the pattern develops in a radial direction for small $c_{Fe3+}$. We confirmed from different experiments that an instantaneous chemical reaction takes place between SPA solution and Fe$^{3+}$ solution. The chemical reaction produces precipitation and significantly reduces the viscosity of the SPA solution. The quantity of the precipitation is increased with $c_{Fe3+}$. We will make a discussion on the relationship between the formation of spiral viscous fingering and the chemical reaction taking place between the two fluids. [Preview Abstract] |
Sunday, November 19, 2006 4:41PM - 4:54PM |
ED.00003: Variable Density and Viscosity Displacements in Horizontal Hele-Shaw Cells: Linear Stability Analysis Laurent Talon, Nisheet Goyal, Eckart Meiburg We investigate the linear stability of a variable density and viscosity, miscible displacement in a horizontal Hele-Shaw cell. The two-dimensional base state is evaluated by means of nonlinear Stokes simulations. We observe the formation of a quasisteady tip, whose vertical equilibrium position is determined by a balance of viscous and gravitational forces. The tip propagates more rapidly as the effects of gravity increase. The linear stability of this base state is studied with regard to spanwise perturbations. We observe a gravity-modulated viscous fingering mode at the displacement front, and a Rayleigh-Taylor mode along the unstably stratified horizontal interface. Their dependence on the viscosity ratio, the gravity parameter and the Peclet number is discussed. [Preview Abstract] |
Sunday, November 19, 2006 4:54PM - 5:07PM |
ED.00004: An experimental study on non-isothermal miscible displacements in Hele-Shaw cells Norihito Fujita, Yuichiro Nagatsu, Yoshihito Kato, Yutaka Tada Non-isothermal miscible displacements in Hele-Shaw cells are experimentally investigated. This is done by the more-viscous liquids at room temperature being displaced by the less-viscous liquids at high temperature, 353K. Fundamental characteristics are presented on how the effects of non-isothermal field on the miscible displacement patterns are varied by the following factors, the viscosity of the less-viscous liquid at ,293K, \textit{$\mu $}$_{l,20}$, the growth rate of the pattern, $R$, the growth time of the pattern, $t$, and the gap width of the cell,$b$. The effects of non-isothermal fields on the pattern (1) do not monotonically varied with \textit{$\mu $}$_{l,20}$, and become significant in a certain limited range of \textit{$\mu $}$_{l,20}$. (2) increase with $R$ in the present experimental condition. (3) decrease with $t$ in the present experimental condition. (4) do not monotonically varied with $b$. The experimental results is able to be explained by the cooling model of the less-viscous liquids due to heat loss to the plates consisting of the cell. [Preview Abstract] |
Sunday, November 19, 2006 5:07PM - 5:20PM |
ED.00005: The effect of evaporation on fingering instabilities Jill Klentzman, Mulugeta Markos, Vladimir Ajaev Fingering instability of a moving contact line has been studied extensively for cases when the flow is driven by gravity, thermocapillary stresses, or a combination of the two. However, in many practical applications, evaporation is also present when the contact line becomes unstable. We use a lubrication-type model to incorporate evaporative mass loss into the evolution equation for a two-dimensional liquid film surface and carry out studies of the effect of evaporation on fingering instability in the framework of this model. Furhermore, in order to verify the validity of the lubrication-type approach, we carry out boundary-integral simulations of gravity-driven films and compare the numerical results with the shapes obtained using a thin-film approximation. [Preview Abstract] |
Sunday, November 19, 2006 5:20PM - 5:33PM |
ED.00006: Miscible Displacement of a Less Viscous Fluid by a More Viscous One in a Vertical Hele-Shaw Cell Surya Harith Vanaparthy, Nisheet Goyal, Eckart Meiburg We investigate miscible displacements of a less viscous fluid by a more viscous one in a vertically oriented Hele-Shaw cell, in order to gain insight into recently observed instabilities in corresponding experiments. As a first step we perform highly resolved two-dimensional Stokes flow simulations in the gap of the Hele-Shaw cell. A quasisteady front is seen to evolve for a range of governing parameters, which have the form of a Peclet number, a gravity parameter and the viscosity ratio. The subsequent linear stability analysis of this quasisteady front yields both the growth rate and the dominant instability modes. [Preview Abstract] |
Sunday, November 19, 2006 5:33PM - 5:46PM |
ED.00007: Scaling laws in large scale simulations of the Saffman-Taylor instability Petri Fast We present new large scale simulations of the Saffman-Taylor instability driven by a constant massflux. In contrast to viscous fingering driven by a constant {\em pressure jump}, we observe at late time simultaneous ramification of the fingers and coarsening of the ``fjords.'' This may explain the new asymptotic scaling regime where the interface dynamics is described by a power-law relation for a measure of interfacial stretching vs. time. We present detailed comparisons with experimental data from the literature. [Preview Abstract] |
Sunday, November 19, 2006 5:46PM - 5:59PM |
ED.00008: Chemically Driven Interfacial Convection P.M.J. Trevelyan, A. De Wit, S. Kalliadasis This study examines chemically driven interfacial convection for a two layer system in a Hele Shaw cell under microgravity conditions. The two immiscible liquids each have a reactant dissolved into them. The two reactants A and B react at the interface to produce a surfactant S through the mechanism A+B $\rightarrow$ S. Tangential stresses due to interfacial gradients of S are induced via the solutal Marangoni effect which generates interfacial motion. A two-dimensional model containing the Navier-Stokes and mass transport equations of the chemical species in the bulk along with the surfactant transport equation on the interface and appropriate boundary conditions is constructed for small amplitude interfacial deformations. For suitable parameters the linear stability analysis predicts an instability. To explore the evolution of the system approximate nonlinear solutions are obtained. [Preview Abstract] |
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