Diffusion and Heat Exchange in Chemical Kinetics

Frank-Kamenetskii, D. A.

doi:10.1515/9781400877195

Cited by 1,122 publications

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“…The viscosity itself is described by the Arrhenius law (Karato and Li, 1992; 90 Karato and Wu, 1993) and here approximated by a linearized Frank-Kamentskii approach 91 (Frank-Kamenetskii, 1969). This approach is based on the constant rheological gradient γ 92 that describes the dependence on T' and -in case of pressure dependence -a pressure 93…”

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confidence: 99%

Regime classification and planform scaling for internally heated mantle convection

Hüttig¹,

Breuer²

2011

Physics of the Earth and Planetary Interiors

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Abstract:8 Internally heated 3-D mantle convection models in a spherical shell with temperature and 9 pressure dependent viscosity have been performed to provide new insights into the various 10 convection regimes, the transition from steady state convection to time-dependent convection 11 and the associated convection pattern. The analysis of a total of 91 simulations reveals four 12 regime types, i.e., a mobile-lid regime, a sluggish regime, a low-degree regime, and a 13 stagnant-lid regime. The occurrence of these regimes depends on the viscosity contrast and 14 the internal Rayleigh number. The low-degree regime occurs close to the boundary of the 15 stagnant-lid regime in case of temperature dependent viscosity. In case of additional pressure 16 dependence, the range of the low-degree regime is smaller and a narrow range of the sluggish-17 lid regime exists in the weakly convecting part. Furthermore, the transition to the stagnant-lid 18 regime occurs at a lower viscosity contrast.

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confidence: 99%

Regime classification and planform scaling for internally heated mantle convection

Hüttig¹,

Breuer²

2011

Physics of the Earth and Planetary Interiors

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“…An example of this approach is to describe the processes such as gas-phase reactions on supported liquid catalysts, catalytic hydrogenation and oxidation of liquid hydrocarbons, electrochemical decomposition of the liquid reactants with the evolution of gaseous products, and drying the impregnated porous materials a multiphase filtering. Under this approach, it was possible to calculate the coefficients of the effective component transport in the porous material, and explain many experimental effects, e.g., removal of the dissolved components on the outer surface, and in macropores during the drying process [4].…”

Section: Volume 44mentioning

confidence: 99%

“…So K 3 describes the kinetics of the sol-gel transition. In its turn the kinetic equations with modified a rate K 4 and K 5 allow you to simulate the transition to gelation with non-classical critical index [17]. In these kernels:  -is a "geometric" index characterizing the surface area of large aggregates, while it is related with the fractal dimension of aggregates, which are formed in the process of such aggregation.…”

Section: International Letters Of Chemistry Physics and Astronomy Vomentioning

confidence: 99%

Simulation of Hardening Processes, in Silicate Systems

Kudryavtsev

Figovsky²

2015

ILCPA

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In this paper we consider the Quasi-homogeneous Approximation to Describe the Properties of Disperse Systems. We have used the statistical polymer method is based on the consideration of averaged structures of all possible macromolecules of the same weight. One has derived equations allowing evaluation of all additive parameters of macromolecules and their systems. The statistical polymer method allows modeling of branched crosslinked macromolecules and their systems in equilibrium or non-equilibrium. The fractal consideration of statistical polymer allows modeling of all kinds of random fractal and other objects studied by fractal theory. The statistical polymer method is applicable not only to polymers but also to composites, gels, associates in polar liquids and other aggregates. In this paper Description of the state of colloidal solutions of silicon oxide from the viewpoint of statistical physics is based on the idea lies in the fact that a colloidal solution of silicasilica sol consists of a very large number of interacting with each other particles that are in continuous motion. It is devoted to the study of an idealized system of colliding, but non-interacting particles of sol. Analysis was conducted of the behavior of silica sol, in terms of Maxwell-Boltzmann distribution and was calculated the mean free path of the colloidal particles. Based on these data, it was calculated the number of particles capable to overcome the potential barrier in a collision. To modeling of the solgel transition kinetics had considered various approaches.

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“…The boundary layer diffusion is modeled in a manner similar to that used by Mitchell et al [15], taking Stefan flow into account [18]. A v factor is often used as a criterion of whether the combustion rate is controlled by boundary layer diffusion [1]:…”

Section: Boundary Layer Diffusionmentioning

confidence: 99%

Modeling high-pressure char oxidation using langmuir kinetics with an effectiveness factor

Hong

Hecker

Fletcher

2000

Proceedings of the Combustion Institute

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The global nth order rate equation has been criticized for lack of theoretical basis and has been shown to be inadequate for modeling char oxidation rates as a function of total gas pressure. The simple Langmuir rate equation is believed to have more potential for modeling high pressure char oxidation. The intrinsic Langmuir rate equation is applied to graphite flake oxidation data and agrees well with reaction rates at three temperatures over the entire range of oxygen pressure (1-64 atm). It also explains the change of reaction order with temperature.In this work, the intrinsic Langmuir rate equation is combined with (1) an effectiveness factor to account for pore diffusion effects and (2) a random pore structure model to calculate effective diffusivity.The resulting model is able to predict the reaction rates of large (ca. 8 mm) coal char particles as a function of gas velocity, total pressure, oxygen partial pressure, oxygen mole fraction, initial particle size, and gas temperature. This approach is also able to correlate the particle burnouts of pulverized (70 lm) coal char particles in a drop tube reactor as a function of total pressure, oxygen mole fraction, gas and wall temperatures, and residence time. The ability of the model to correlate data over wide range of temperature and pressure is promising.

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Diffusion and Heat Exchange in Chemical Kinetics

Cited by 1,122 publications

References 0 publications

Regime classification and planform scaling for internally heated mantle convection

Regime classification and planform scaling for internally heated mantle convection

Simulation of Hardening Processes, in Silicate Systems

Modeling high-pressure char oxidation using langmuir kinetics with an effectiveness factor

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