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 GF: Hele-Shaw Flows: Interfacial & TFI |
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Chair: Eckart Meiburg, University of California, Berkeley Room: Hilton Chicago Continental C |
Monday, November 21, 2005 10:34AM - 10:47AM |
GF.00001: Characteristics of miscible viscous fingering involving liquid viscosity changes due to variations in chemical species concentrations by chemical reaction Yuichiro Nagatsu, Kenji Matsuda, Yoshihito Kato, Yutaka Tada Reactive miscible viscous fingering occurs when a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell. In the present study, we have succeeded to experimentally show reactive miscible viscous fingering in a Hele-Shaw cell involving changes of displaced liquid viscosity due to variations in chemical species concentrations by chemical reaction by making use of dependence of viscosity of polymer solution on pH. When the displaced liquid viscosity is increased by the reaction, a fractal dimension of miscible viscous fingering pattern with the reaction is larger than that without the reaction. In contrast, when the displaced liquid viscosity is decreased by the reaction, the fractal dimension of miscible viscous fingering pattern with the reaction is smaller than that without the reaction. A physical model to explain these changes of fingering pattern by the reaction is proposed. [Preview Abstract] |
Monday, November 21, 2005 10:47AM - 11:00AM |
GF.00002: Miscible fingering instabilities in vertical Hele-Shaw cells: A Stokes based analysis Hannes Pichler, Nisheet Goyal, Eckart Meiburg We study the downward displacement of a heavier/lighter more viscous fluid by a lighter/heavier less viscous fluid in a vertically arranged Hele-Shaw cell. Two-dimensional Stokes flow simulations in the gap of the Hele-Shaw cell are employed to obtain the quasisteady base state, whose linear stability is subsequently analyzed. The base state properties depend on the relative magnitude of gravitational and viscous forces, as well as on the dimensionless displacement velocity. In the gravitationally stable configuration, the front thickness decreases with the viscosity ratio, while the reverse holds true for gravitationally unstable situations. The growth rates of the dominant perturbation modes show a similar dependence on the viscosity contrast. For fluids with highly disparate viscosities, gravitational effects are seen to become negligible. Conversely, for mild viscosity contrasts, the base states and the features of the dispersion relations are dominated by gravitational forces. [Preview Abstract] |
Monday, November 21, 2005 11:00AM - 11:13AM |
GF.00003: Miscible displacements in a Hele-Shaw cell: Linear stability analysis based on the three-dimensional Stokes equations Nisheet Goyal, Eckart Meiburg We investigate the miscible fingering instability of neutrally buoyant fluids in a Hele-Shaw cell. As a first step we perform highly resolved two-dimensional Stokes flow simulations in the gap of the Hele-Shaw cell. A quasisteady displacement front is seen to evolve, whose front thickness is seen to scale with $Pe^{-1/2}$, while it depends only weakly on the viscosity ratio. An exponential viscosity-concentration relationship leads to an increase in the tip velocity with the Peclet number for high viscosity contrasts, while a linear relationship has the reverse effect. The simulation results suggest that in the limit of high $Pe$ and large viscosity contrast, the width and tip velocity of the displacement front asymptote to the same values as their immiscible counterparts in the limit of large capillary numbers. The subsequent linear stability analysis of this front clarifies the influence of the Peclet number and the viscosity ratio on the growth rate and wavelength of the dominant instability modes. These findings are compared to corresponding Darcy counterparts, and to experimental data by other authors. [Preview Abstract] |
Monday, November 21, 2005 11:13AM - 11:26AM |
GF.00004: Effect of surfactants on stability of a moving interface in a Hele-Shaw cell. Carolyn Gramlich, G.M. Homsy Viscous fingering of immiscible fluids in a Hele-Shaw cell has been seen experimentally to be influenced by effects of surfactants on the interface between the fluids. A reasonable hypothesis is that Marangoni stresses due to a spanwise gradient in surfactant concentration are responsible. We analyze the problem of soluble surfactant transport in the Hele- Shaw cell and use matched expansions to derive effective boundary conditions including surfactant effects. These are then used to analyze the linear stability of a displacement flow. We find that Marangoni stresses due to differential adsorption of surfactant induce a secondary flow causing wavelength-dependent destabilization of the interface. [Preview Abstract] |
Monday, November 21, 2005 11:26AM - 11:39AM |
GF.00005: Meanders in a Hele-Shaw cell Nolwenn Le Grand, Adrian Daerr, Laurent Limat If a rivulet is injected at the top of a Hele-Shaw cell, it is not necessarily straight. Above a critical flow rate, and if under conditions of total wetting, the rivulet can meander and one can see the pattern travel. Experiments were performed with several surfactant solutions (dishwashing Fairy liquid, SDS, Triton-X) and also with silicone oils. We have found that the behavior of the waves was not the same, depending on weather the surfactant has a rigid or mobile interface. Downward and above all upward traveling meanders have been seen for rigid interfaces, whereas there are only downward traveling interfaces for mobile interfaces. We have also investigated on the consequences of a change in surfactant concentration. If too concentrated, the meanders have smaller amplitudes, suggesting a possible effect of the gradients of surface tension. Finally, the experiments with silicone oil also exhibited meanders, though traveling much faster than the surfactant ones, and always downward. With these oils, there is no surface tension gradient, wetting meanders are created by purely hydrodynamic means. [Preview Abstract] |
Monday, November 21, 2005 11:39AM - 11:52AM |
GF.00006: Fingering of interfacial micellar gels Andrew Belmonte, Thomas Podgorski, Michael Sostarecz, Sylvain Zorman We present an experimental study of the instabilities of a gel-like material which forms at the interface between two aqueous solutions of a surfactant and an organic salt in a Hele-Shaw cell; these two solutions will form a highly elastic micellar fluid when mixed homogeneously. By injecting one fluid into the other at different rates, a variety of fingering patterns are observed in both radial and linear geometries. Because the interfacial gel thickens with time, rapidly moving fronts are stable, and instabilities occur only for slower flows. We observe a regime of unconfined stationary or wavy fingers for which width selection seems to occur independent of the bounding walls, unlike the Saffman-Taylor fingering case. [Preview Abstract] |
Monday, November 21, 2005 11:52AM - 12:05PM |
GF.00007: Viscosity contrast effects on fingering formation in rotating Hele-Shaw flows Jos\'{e} Miranda, Hermes Gad\^{e}lha, Enrique Alvarez-Lacalle The different finger morphologies that arise at the interface separating two immiscible fluids in a rotating Hele-Shaw cell are studied analytically and numerically. The whole range of viscosity contrast is analyzed and a variety of fingering patterns systematically introduced, including the case in which the inner fluid is less viscous than the outer one. Our results demonstrate that both the magnitude and the sign of the viscosity contrast strongly affect the shape of the emerging fingers, and also their length distribution. We have also found that the occurrence and location of pinch-off singularities are remarkably modified when the inner fluid is less viscous: instead of generating an isolated detaching drop, a full finger is disconnected from the interface. Finally, we have verified that the finger competition phenomena revealed by our simulations are correctly predicted by a weakly nonlinear analysis of the pattern development, showing that such important finger competition dynamics is already set at relatively early stages of interfacial evolution. [Preview Abstract] |
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