Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session RY: Instability: Interfacial and Thin Film VII |
Hide Abstracts |
Chair: Michael Shearer, North Carolina State University Room: Hyatt Regency Long Beach Regency E |
Tuesday, November 23, 2010 3:05PM - 3:18PM |
RY.00001: ABSTRACT WITHDRAWN |
Tuesday, November 23, 2010 3:18PM - 3:31PM |
RY.00002: Mixed mode buoyancy-driven instability in a Hele-Shaw cell J. Carballido-Landeira, P.M.J. Trevelyan, C. Almarcha, A. De Wit Buoyancy-driven instabilities of a horizontal interface between two different miscible solutions contained in a Hele-Shaw cell are studied both theoretically and experimentally. Our regime of interest is focused on the case when the fastest diffusing species is located in the upper layer. If the upper solution is denser, a Rayleigh-Taylor (RT) instability develops characterized by a deformation of the interface into fingers. If, on the contrary, the denser solution is on the bottom, a Diffusive Layer Convection (DLC) instability is obtained because of differential diffusion effects. Indeed the fast diffusion downwards of the solute initially contained in the upper zone leads to a depletion and an accumulation zone respectively above and below the contact line where locally convection is triggered. In between these two regimes, a mixed mode dynamics intermediate between the RT and DLC regimes is obtained when the density profiles contain a locally stratifically stable region near the interface surrounded by two stratifically unstable regions. Experiments show that such an instability generates new plume-like structures around the interface. [Preview Abstract] |
Tuesday, November 23, 2010 3:31PM - 3:44PM |
RY.00003: Capillary instability driven by a permeability gradient Talal Al-Housseiny, Jesus Hernandez, Jeffrey Aristoff, Suzie Protiere, Howard Stone Viscous fingering, the phenomenon associated with the Saffman- Taylor instability, occurs when a low viscosity fluid penetrates a fluid of higher viscosity. Surface tension generally acts to stabilize the interface of the two fluids. In this work, we study a new surface-tension-induced instability that is driven by a permeability gradient. The instability is even revealed when a fluid of higher viscosity penetrates a fluid of lower viscosity (stable in the Saffman-Taylor sense). This capillary instability is demonstrated in a microfluidic setup composed of two symmetric channels that linearly increase in width, rather than the traditional Hele-Shaw cell. The conditions necessary to achieve this instability are studied. In particular, we determined a critical capillary number below which the instability occurs. The effect of viscosity ratio and permeability gradient are also examined. [Preview Abstract] |
Tuesday, November 23, 2010 3:44PM - 3:57PM |
RY.00004: Inertial effects on viscous fingering in the complex plane Andong He, Andrew Belmonte We present the nonlinear unsteady Darcy's equation, which includes inertial effects for flows in a porous medium or Hele-Shaw cell, and discuss the conditions under which it reduces to the classical Darcy's law. In the absence of surface tension, we derive a generalized Polubarinova-Galin equation in the complex plane, which includes the inertial effects for a circular interface geometry. The linear stability of the base-flow state is examined by perturbing the corresponding conformal map - we show that inertia always has a tendency to stabilize the interface, regardless of whether a less viscous fluid is displacing a more viscous fluid or vice versa. [Preview Abstract] |
Tuesday, November 23, 2010 3:57PM - 4:10PM |
RY.00005: Pattern transition from fingering to fracturing in a reacting Hele-Shaw flow Tomohiro Ujiie, Yuichiro Nagatsu, Mitsumasa Ban, Yoshihito Kato, Yutaka Tada We have experimentally investigated pattern formation obtained when a more viscous aqueous polymer solution is displaced by a less viscous solution including a metal ion in a Hele-Shaw cell. When the two liquids contact, a chemical reaction takes place and a gel is formed. For some concentrations of the polymer and the metal ion, a transition from fingering pattern to fracturing pattern is demonstrated as the injection rate exceeds threshold value. The fingering-fracturing transition is sufficiently abrupt that no gradual transition has been observed. When there is no metal ion in the less viscous solution (non-reactive case), the transition was never observed. These results are similar to those obtained in a Hele-Shaw experiment using an associating polymer solution (Zhao {\&} Maher, \textit{Phys, Rev, E}, 47, 4728, (1993)). We have measured the rheological property of the gel by means of a rheometer and investigated the relationship between the observed fingering-fracturing transition and the measured rheological property. Finally, we discuss the similarity between the present result and the result obtained by Zhao {\&} Maher. [Preview Abstract] |
Tuesday, November 23, 2010 4:10PM - 4:23PM |
RY.00006: Phase-field modeling of viscous fingering in a Hele-Shaw cell Luis Cueto-Felgueroso, Ruben Juanes When a viscous fluid is displaced by a less viscous one in the gap between two parallel plates, or Hele-Shaw cell, the interface between the two fluids is unstable. For low injection rates the system evolves towards a single channel, known as the Saffman-Taylor finger, while for high rates the interface forms a complicated, branched pattern. Here we present a phase-field model for two-phase displacements that captures the viscous instability. The model reproduces the transition from stable displacement to the Saffman-Taylor finger, and from the latter to a dendritic structure, depending on the viscosity contrast and injection rate. The model is a system of two partial differential equations: a nonlinear, fourth-order equation for the transport of the order parameter, and an elliptic equation for the pressure of the mixture. The interface thickness is maintained through a double-well bulk potential. We present numerical simulations and a linear stability analysis of the model. Continuum modeling of wetting phenomena is necessary in many scientific and engineering applications, from microfluidics and multiphase flow, to flow and transport in permeable media. The present model is also the first step towards an extended model of multiphase displacements in porous media. [Preview Abstract] |
Tuesday, November 23, 2010 4:23PM - 4:36PM |
RY.00007: Unstable miscible displacements in Hele-Shaw cells: Three-dimensional Navier-Stokes simulations Rafael Oliveira, Eckart Meiburg We simulate unstable miscible displacements in Hele-Shaw cells based on the three-dimensional, variable viscosity Navier-Stokes equations coupled to a convection-diffusion equation for the concentration field. The simulations exhibit the formation of individual, quasisteady fingers whose properties are characterized as a function of the viscosity ratio and the Peclet number. We observe both traditional tip splitting events, as well as a novel inner splitting mechanism that has not yet been reported in the literature. This tip splitting is associated with fluid transport perpendicular to the plane of the Hele-Shaw cell, and hence cannot be reproduced by gap-averaged approaches. It has the effect of splitting the trailing sections of the finger longitudinally, while the finger tip can largely remain intact. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700