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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 814-821 
    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
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 5338-5352 
    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
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  • 3
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 9 (1999), S. 13-35 
    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
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2907-2922 
    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
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 12 (2000), S. 2236-2256 
    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
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  • 6
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 34 (1988), S. 353-365 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Spontaneous combustion may occur in a coal stockpile when the heat generated within the pile cannot be dissipated at near ambient temperature. Under practical conditions, natural convection enhances the rate of heat removal from the bed and shifts the ignition to lower particle sizes (higher reactivities). Analysis of three limiting cases of a one-dimensional model yields criteria predicting the conditions under which ignition occurs as well as those for which a low-temperature (extinguished) state exists for all particle sizes. A simple asymptotic relation predicts the ignition point at large Rayleigh numbers.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 373-384 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Steady states with different flow rates and temperature profiles may exist in different tubes of a multitube packed-bed reactor due to the coupling among the species, energy and momentum balances, and the change of physical properties with temperature and pressure. Under typical operating conditions if no axial conduction of heat occurs thermoflow multiplicity can be found only for unrealistically high heats of reaction and/or over a very narrow range of exit pressures. However, accounting for the finite but small heat conduction in the reactor tubes leads to multiplicity for typical parameters and a reasonable range of exit pressures. Cooling tends to decrease the region of parameters for which the multiplicity occurs.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1509-1520 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Differences in the dispersion and/or catalytic pellet size between laboratory and commercial reactors, operating at the same average residence time, may lead to differences in the yield of a desired product. Bounds are developed for predicting the maximal design uncertainty introduced by these phenomena for a network consisting of an arbitrary number of irreversible first-order reactions. A major advantage of these bounds is that they do not require any knowledge of the rate constants. It is shown that in a packed-bed reactor, the fractional yield loss is smaller than: \documentclass{article}\pagestyle{empty}\begin{document}$$ 0.5{\rm }(m - 1){\rm }\left[{\sigma _\theta ^{\rm 2} + \left({1.2 + \frac{2}{{Bi_m }}} \right)p^2 } \right] $$\end{document} where m - 1 is the number of reaction steps involved in converting a reactant to the desired product, σθ2 is the dimensionless variance of the residence time density function, Bim is the Biot number, p2 = [(Vp/Sx)2(1/Deτ)], and τ is the average residence time.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 397-408 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The coupling between the momentum and energy balances and the change of physical properties with temperature can give rise to situations in which the pressure drop vs. flow rate curve is nonmonotonic. This can lead to thermoflow multiplicity - the existence of different flow rates in a tube under the same overall pressure drop. A two-dimensional model is used to analyze the conditions leading to thermoflow multiplicity for an incompressible non-Newtonian fluid flowing in a cooled tube. First, the multiplicity features of various limiting models are determined. These results are later used to gain an understanding of the asymptotic multiplicity features of the general model. The results show that the temperature sensitivity of the viscosity necessary for thermoflow multiplicity to occur decreases with increasing Brinkman number or β (modified Stanton number), or with decreasing cooling temperature, Biot number, or power law parameter. Multiple flow rates for a prescribed pressure drop are unlikely to occur in heat exchangers in which the Brinkman numbers are usually low and Biot numbers are high but may be found in polymer processing applications.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 37 (1991), S. 1780-1788 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Most existing criteria for predicting parametric sensitivity or runaway in a catalytic reactor are based on a single-phase model that does not account for interparticle heat and mass transfer resistances and intraparticle diffusion. Accounting for these effects, the simple criterion \documentclass{article}\pagestyle{empty}\begin{document}$$\frac{E}{{RT_f }}\frac{{(- \Delta H)r(T_f,C_f)}}{{T_f }}\left[{\frac{{d_t }}{{4U}} + \frac{{d_p }}{{6h}}} \right] 〈 0.368f(\phi _0)$$\end{document} defines the boundary of operating conditions, in which a catalytic reactor is insensitive to small perturbations. Here, r(Tf,Cf) is the intrinsic reaction rate at inlet conditions, dt(dp) and U(h) are the diameter of reactor tube (catalyst particle) and heat transfer coefficient between the fluid and tube wall (catalyst particle), respectively. The function f(φ0), where φ0 is the normalized Thiele modulus at inlet conditions, accounts for the effects of intraparticle diffusion. For the common case of equal coolant and feed temperatures, f(φ0) = 1 for φ0 〈 0.5 and f(φ0) = 2 φ0 for φ0〉0.5. The conservatism associated with the above criterion is comparable to the uncertainty involved in determining the parameters of the packed bed.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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