New Light on Some Old Problems:  Revisiting the Stefan Tube, Graham's Law, and the Bosanquet Equation

Kerkhof, P.J.A.M.

doi:10.1021/ie960542i

Cited by 25 publications

(13 citation statements)

References 22 publications

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“…The alternative ''binary friction model'' developed by Kerkhof [78,94,95] on the foundation of the Lightfoot friction model [97] relates the pore-averaged fluxes to driving forces by introducing friction coefficients associated with individual viscosity contributions. Friction forces between the diffusing molecules and friction forces between the molecules and the wall are included.…”

Section: Bulk Diffusion Knudsen Diffusion and Pressure-driven Viscoumentioning

confidence: 99%

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Simultaneous Heat and Mass Transfer and Chemical Reaction

Dittmeyer

Emig

2008

Handbook of Heterogeneous Catalysis

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The sections in this article are Introduction Mathematical Description Single Reactions (Conversion Problem) Pore Diffusion in an Isothermal Pellet Film and Pore Diffusion in an Isothermal Pellet Film and Pore Diffusion Together with Interphase Heat Transfer Film and Pore Diffusion Together with Interphase and Intraparticle Heat Transfer External Heat and Mass Transfer Use of Complex Rate Expressions Simple Reversible Reactions Simple Irreversible Reactions with L angmuir– H inshelwood‐Type Kinetics Simple Reversible Reactions with L angmuir– H inshelwood‐Type Kinetics Temperature Dependence and Reaction Order of Transport‐Limited Reactions Intraparticle Diffusion Interphase Mass Transfer Diagnostic Criteria and Experimental Methods for Estimating the Influence of Heat and Mass Transfer on the Effective Reaction Rate Experimental Criteria Theoretical Criteria Experimental Methods for Estimating the Influence of Heat and Mass Transfer Effects Multiple Reactions (Selectivity Problem) Type I Selectivity Type II Selectivity Type III Selectivity Mathematical Description of the Diffusional Transport F ick's Law with Constant Effective Diffusivities Bulk Diffusion and K nudsen Diffusion Pressure‐Driven Viscous Flow and Surface Diffusion M axwell– S tefan Equations and Related Models Bulk Diffusion, K nudsen Diffusion and Pressure‐Driven Viscous Flow Surface Diffusion Control of Selectivity in the Disproportionation of Ethylbenzene to Benzene and Diethylbenzenes on an HZSM ‐5 Catalyst by Utilizing Diffusion Effects Shape‐Selective Catalysis Microkinetics Macrokinetics Modeling of Shape Selectivity Effects Simplifying Assumptions Model Equations Simulation Results A Product Shape Selectivity (Unaffected by Other Factors) B Product Shape Selectivity and Reactant Diffusion Limitation (Combined Effect) C Product Shape Selectivity and Selective Adsorption (Combined Effect) D Product Shape Selectivity and Restricted Transition State Shape Selectivity (Combined Effect) Controlled Modification of the Pore Structure Concluding Remarks

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Section: Bulk Diffusion Knudsen Diffusion and Pressure-driven Viscoumentioning

confidence: 99%

“…Equation (210) can be directly compared with Eq. (210) can be simplified by neglecting ij [78]. The coefficients κ i representing the fractional viscous contributions to the overall friction between component i and the wall were already given in Eq.…”

Section: Bulk Diffusion Knudsen Diffusion and Pressure-driven Viscoumentioning

confidence: 99%

Simultaneous Heat and Mass Transfer and Chemical Reaction

Dittmeyer

Emig

2008

Handbook of Heterogeneous Catalysis

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“…It is interesting to note that the dimensionless ratio of Knudsen flux to viscous flux is, in a straight pore (Kerkhof, 1997;Froment and Bischoff, 1979) :…”

Section: The Knudsen Transport Coefficient D Kmentioning

confidence: 99%

Rarefied Pure Gas Transport in Non-isothermal Porous Media: Effective Transport Properties from Homogenization of the Kinetic Equation

et al. 2007

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Abstract. Viscous flow, effusion, and thermal transpiration are the main gas transport modalities for a rarefied gas in a macro-porous medium. They have been well quantified only in the case of simple geometries. This paper develops a model based on the homogenization of kinetic equations producing effective transport properties (permeability, Knudsen diffusivity, thermal transpiration ratio) in any porous medium sample, as described e. g. by a digitized 3D image. The homogenization procedureneglecting the effect of gas density gradients on heat transfer through the solid -leads to macroscopic transfer relations, and to closure problems in R 6 for the obtention of effective properties. Coherence of the approach with previous literature on the subject is discussed. The asymptotic limits of the model (rarefied and continuum regimes) are also studied. One of the main results is that the effect of the geometry on thermal transpiration has to be described by a tensor which is distinct from the permeability and Knudsen diffusion tensors.

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“…13 The model is controversial in some aspects, but not at the level of detail considered here. 5,6 With gas near room temperature and pressure flowing through m  -scale particles, the Knudsen number (ratio of mean free path to pore diameter) is 0.01  and therefore proper treatment of free molecular flow is needed for suitable accuracy.…”

Section: Introductionmentioning

confidence: 99%

A simple model of gas flow in a porous powder compact

Shugard

Robinson

2014

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This report describes a simple model for ideal gas flow from a vessel through a bed of porous material into another vessel. It assumes constant temperature and uniform porosity. Transport is treated as a combination of viscous and molecular flow, with no inertial contribution (low Reynolds number). This model can be used to fit data to obtain permeability values, determine flow rates, understand the relative contributions of viscous and molecular flow, and verify volume calibrations. It draws upon the Dusty Gas Model and other detailed studies of gas flow through porous media. 4 ACKNOWLEDGMENTS

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New Light on Some Old Problems: Revisiting the Stefan Tube, Graham's Law, and the Bosanquet Equation

Cited by 25 publications

References 22 publications

Simultaneous Heat and Mass Transfer and Chemical Reaction

Simultaneous Heat and Mass Transfer and Chemical Reaction

Rarefied Pure Gas Transport in Non-isothermal Porous Media: Effective Transport Properties from Homogenization of the Kinetic Equation

A simple model of gas flow in a porous powder compact

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