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Instability of a vertical chemical front: Effect of viscosity and density varying with concentration
Published in American Institute of Physics Inc.
2008
Volume: 20
   
Issue: 1
Abstract
In this work we analyze the behavior of a chemical front in a vertical porous medium. A homogeneous autocatalytic reaction occurs in the liquid phase. The column is filled with a chemical species and the reaction is initiated at one end of the vertical column by instantaneously adding the product. The reaction occurs at the interface of the products and the reactants. This causes the reaction front to move down (up) when the product is added to the top (bottom). The front or interface demarcates the domain into two regions: one rich in the reactants and the other rich in products. In this work chemohydrodynamic instabilities are studied, when the density and viscosity of the reactants and products are different and concentration dependent. The dependency of these properties on concentration is explicitly considered. We assume the process to be isothermal and other properties such as diffusivity and permeability to be constant. A traveling wave of chemical concentration is generated in the upward direction (when the products are introduced at the bottom) as the product reacts at the interface. The stability of the interface is determined by the viscosity and density of the two fluids. A shooting method in combination with a Runge-Kutta fourth-order scheme is used for generating the base state of the traveling front. Here, the conditions at which an interfacial instability induced by the density gradients is stabilized due to the viscosity dependence on concentration are determined. Linear stability predictions are determined by inducing perturbations on the traveling wave base state and analyzing their evolution. The effect of various parameters on the stability of the flow was calculated and compared with the nonlinear simulations. The nonlinear problem is modeled using the stream-function, vorticity equations. These equations are solved using a second-order finite difference scheme in space and first-order forward difference scheme in time. The instability predicted from the linear stability analysis is validated with nonlinear simulations. © 2008 American Institute of Physics.
About the journal
JournalData powered by TypesetPhysics of Fluids
PublisherData powered by TypesetAmerican Institute of Physics Inc.
ISSN10706631
Open AccessNo
Concepts (14)
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    Chemicals
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    Computational fluid dynamics
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    Density (specific gravity)
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    Finite difference method
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    Linear stability analysis
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    Numerical methods
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    Porous materials
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    Runge kutta methods
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    Viscosity
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    Vorticity
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    CHEMOHYDRODYNAMICS
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    Flow instability
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    RUNGE-KUTTA FOURTH-ORDER SCHEME
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    Hydrodynamics