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  • American Institute of Physics (AIP)  (5)
  • 1
    Electronic Resource
    Electronic Resource
    Modeling and experimental studies of wave evolution on free falling viscous films (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 12 (2000), S. 2236-2256 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A new simplified model is developed for describing the characteristics of free falling wavy liquid films. The model consists of a set of three partial differential equations (in x and t) for the local film thickness, volumetric flow rate, and wall shear stress. It is shown that the new model is a substantial improvement over all existing simplified models of wavy films such as the long wave equation, the Nakaya model (extended third-order long wave equation), the Shkadov model, and the Kapitza boundary layer model. These prior models predict nonphysical negative wall shear stress when the wave amplitude is large and cannot explain the experimentally observed relationship between the maximum wave amplitude and the Reynolds (Re) and Kapitza (Ka) or Weber (We) numbers. In contrast, the present model yields physically meaningful results and quantitative predictions of large amplitude waves. Local bifurcation analysis of the model for small Re gives the following analytical relations for the velocity (Ce) and maximum amplitude of the solitary waves: hmax−1=0.132 Re5/3 Ka−1=〈fraction SHAPE="CASE"〉16(3−Ce)=1.925 We−1. Experimental studies of free falling viscous films were conducted using water–glycerin solutions for Reynolds numbers in the range of 2–20 and Kapitza numbers in the range of 6–22. Comparison of the experimental data on wave amplitudes with analytical correlations shows excellent agreement. Numerical simulations of the wave profiles generated from the simplified model also match closely with the experimentally observed wave profiles.© 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1287612
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  • 2
    Electronic Resource
    Electronic Resource
    Bifurcation analysis of chemical reactors and reacting flows (1999)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 9 (1999), S. 13-35 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this work we review the local bifurcation techniques for analyzing and classifying the steady-state and dynamic behavior of chemical reactor models described by partial differential equations (PDEs). First, we summarize the formulas for determining the derivatives of the branching equation and the coefficients in the amplitude equations for the most common singularities. We also illustrate the procedure for the numerical computation of these coefficients. Next, the application of these local results to various reactor models described by PDEs is discussed. Specifically, we review the recent literature on the bifurcation features of convection-reaction and convection-diffusion-reaction models in one and more spatial dimensions, with emphasis on the features introduced due to coupling between the flow, heat and mass diffusion and chemical reaction. Finally, we illustrate the use of dynamical systems concepts in developing low dimensional (effective or pseudohomogeneous) models of reactors and reacting flows, and discuss some problems of current interest. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166377
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  • 3
    Electronic Resource
    Electronic Resource
    Analysis of concentration and temperature patterns on catalytic surfaces (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 5338-5352 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A simple mathematical model for pattern formation on isothermal as well as nonisothermal catalytic surfaces is developed and analyzed. The model accounts for diffusion of the species, conduction of heat, convection from the fluid phase, and a bimolecular Langmuir–Hinshelwood type kinetic expression. The isothermal model is shown to exhibit stationary concentration patterns for typical sets of parameters. The nonisothermal model exhibits stationary temperature and concentration patterns only for near stoichiometric composition of the reactants (three equation model). The calculations show that these stationary patterns exist in regions near the ignition and extinction points and are most likely to form during ignition or extinction of the surface. It is also found that moving concentration and temperature patterns exist near the Hopf bifurcation point of the ignited homogeneous branch. The moving patterns predicted for realistic values of the transport and kinetic parameters are concentration patterns with almost constant temperature distribution on the surface. The typical size of the patterns and the period of oscillation are estimated in terms of the physicochemical parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.467198
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  • 4
    Electronic Resource
    Electronic Resource
    Modeling and analysis of moving temperature patterns on catalytic surfaces (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 814-821 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A mathematical model that predicts moving temperature and concentration patterns on nonisothermal catalytic surfaces is developed and analyzed. The model accounts for a slow change of the surface activity of the catalyst, diffusion of the species, conduction of heat, convection from the fluid phase, and a Langmuir–Hinshelwood-type kinetic expression. It is shown that this model predicts ignition, extinction, and homogeneous oscillations for a wide range of parameter values. It is found that the model does not predict stationary temperature patterns for typical values of the transport coefficients. However, the model predicts moving (oscillating) temperature and concentration patterns for typical parameter values. The calculations show that these spatiotemporal patterns exist in regions near the homogeneous Hopf bifurcation point indicating that homogeneous oscillations are unlikely to occur. It is also found that the typical size of these moving patterns is of the order of 1 cm2 and the period of oscillation is smaller but of the same order of magnitude as the period of homogeneous oscillation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468138
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  • 5
    Electronic Resource
    Electronic Resource
    Convective instabilities induced by exothermic reactions occurring in a porous medium (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2907-2922 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A pseudohomogeneous model is developed and used to analyze the onset of reaction-driven convection in an open rectangular box containing a porous medium. For exothermic reactions, the one-dimensional conduction state exhibits multiplicity as well as oscillatory behavior. Singularity theory is used to classify the different possible bifurcation diagrams of conduction states, along with their stabilities. Linear instability theory is used to determine the stability of the conduction states to convective perturbations. The dependence of both simple zero and Hopf bifurcation neutral stability curves on various problem parameters is presented. It is shown that the Lewis number, Le (ratio of thermal to mass diffusivity), has a pronounced effect on the stability boundaries. Increasing the value of Le, shifts the stationary stability boundary toward higher Rayleigh numbers (Ra). It is also shown that in the region of multiple conduction solutions, there exists a critical value of Lewis number, Le1 (resp., Le2) below which the entire ignited (resp., extinguished) conduction branch is stable to convective perturbations for 0〈Ra〈Rac, where Rac is the critical Rayleigh number at the extinction (resp., ignition) point. Moreover, depending on the value of Le, a branch of the neutral stability curve for simple bifurcation is found for negative values of Ra. The results indicate that oscillatory instability is more likely to occur for the case of liquids, while for gases only stationary instability is possible for a practical range of parameter values. Numerically computed global bifurcation diagrams of conductive and convective solutions along with flow patterns, isotherms, and concentration profiles are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868119
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