Anomalous scaling of diffusion and reaction processes on fractal catalysts

R. Gutfraind; M. Sheintuch

doi:10.1016/0009-2509(92)87130-I

Anomalous scaling of diffusion and reaction processes on fractal catalysts

R. Gutfraind^*, M. Sheintuch

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The geometry of a heterogeneous catalyst is a crucial parameter in determining its performance. Many catalytic systems can be described well in terms of fractal geometry. Here we study the rate dependence of various operating conditions in diffusion-reaction processes occuring on fractal rough surfaces, such as catalyst supports, and fractal subsets such as steps and kinks that constitute the active sites in metal crystallites. In a process of diffusion and reaction in a catalyst with external fractal surface, exposed to a fixed reactant concentration, the catalyst exhibits an increasingly larger area for faster reactions; the overall rate scales as k(D_s/k)^2-D_f/², where k is the first-order reaction rate constant and D_s is the diffusivity in the solid. A subfractal, like a Cantor Set, to which molecules diffuse through a stagnant fluid layer of thickness δ and react instantaneously with the catalytic set, exhibits an overall rate that scales like δ^-D_f; i.e., this subset is less sensitive to mass transfer resistance than a smooth surface. With finite k, the inverse overall rate can be approximated as the sum of the inverse rates at the two asymptotes of very slow and very fast reactions. A fractal line exposed to a fixed reactant concentration at its enveloping boundary, represent a pore network which is an optimal configuration since porosity is higher at the larger pores.

Original language	English
Pages (from-to)	2787-2792
Number of pages	6
Journal	Chemical Engineering Science
Volume	47
Issue number	9-11
DOIs	https://doi.org/10.1016/0009-2509(92)87130-I
State	Published - 8 Jun 1992
Externally published	Yes

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10.1016/0009-2509(92)87130-I

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@article{4cea118c4673498dbd434409201c14b7,

title = "Anomalous scaling of diffusion and reaction processes on fractal catalysts",

abstract = "The geometry of a heterogeneous catalyst is a crucial parameter in determining its performance. Many catalytic systems can be described well in terms of fractal geometry. Here we study the rate dependence of various operating conditions in diffusion-reaction processes occuring on fractal rough surfaces, such as catalyst supports, and fractal subsets such as steps and kinks that constitute the active sites in metal crystallites. In a process of diffusion and reaction in a catalyst with external fractal surface, exposed to a fixed reactant concentration, the catalyst exhibits an increasingly larger area for faster reactions; the overall rate scales as k(Ds/k)2-Df/2, where k is the first-order reaction rate constant and Ds is the diffusivity in the solid. A subfractal, like a Cantor Set, to which molecules diffuse through a stagnant fluid layer of thickness δ and react instantaneously with the catalytic set, exhibits an overall rate that scales like δ-Df; i.e., this subset is less sensitive to mass transfer resistance than a smooth surface. With finite k, the inverse overall rate can be approximated as the sum of the inverse rates at the two asymptotes of very slow and very fast reactions. A fractal line exposed to a fixed reactant concentration at its enveloping boundary, represent a pore network which is an optimal configuration since porosity is higher at the larger pores.",

author = "R. Gutfraind and M. Sheintuch",

note = "Funding Information: CONCLUSIONS We showed that coherent scaling laws apply for diffusion limited reactions: in permeation through a fractal line the rate scales with k and D (and probably with reactant concentration in nonlinear kinetics) while in diffusion through a boundary layer, to an infinitely-active CS or a fractal line, the rate scales with 6. In reaction limited process the rate is linear with k, while no apparents cale exists in the intermediater ange. This range is of commercial importancea nd calls for the formulation of optimal solutions. Future work will develop approximate Solutions such processes. ACKNOWLEDGEMENT Work supportedb y the Fund for the Promotion of Research in the Technion. REFERENCES Burkov, SE. (1985), J. Phys (Paris), 46, 317. de Gennes, P-G. (1982) CR. Acad. Sci. Pa& II, 295, 1061. Farin,D. and Avnir, D. (1990) New J. Cium., 14, 197. Gutfraind, R. and Sheintuch, M. (1992) Chem. Eng. Sci. (to appear). Pajkossy, T. and Niykos, L. (1989) Electtochetn. Acta, 34, 171-179. Pfeifer, P. and Obret. M. (1989) in The Fractal approach to Heterogeneous Chemistry 03. Avnir Ed.),Wiley. Seri-Levy, A. and Avnir, D. (1991). Sur. Sci.. 248,258-270.",

year = "1992",

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doi = "10.1016/0009-2509(92)87130-I",

language = "英语",

volume = "47",

pages = "2787--2792",

journal = "Chemical Engineering Science",

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publisher = "Elsevier BV",

number = "9-11",

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T1 - Anomalous scaling of diffusion and reaction processes on fractal catalysts

AU - Gutfraind, R.

AU - Sheintuch, M.

N1 - Funding Information: CONCLUSIONS We showed that coherent scaling laws apply for diffusion limited reactions: in permeation through a fractal line the rate scales with k and D (and probably with reactant concentration in nonlinear kinetics) while in diffusion through a boundary layer, to an infinitely-active CS or a fractal line, the rate scales with 6. In reaction limited process the rate is linear with k, while no apparents cale exists in the intermediater ange. This range is of commercial importancea nd calls for the formulation of optimal solutions. Future work will develop approximate Solutions such processes. ACKNOWLEDGEMENT Work supportedb y the Fund for the Promotion of Research in the Technion. REFERENCES Burkov, SE. (1985), J. Phys (Paris), 46, 317. de Gennes, P-G. (1982) CR. Acad. Sci. Pa& II, 295, 1061. Farin,D. and Avnir, D. (1990) New J. Cium., 14, 197. Gutfraind, R. and Sheintuch, M. (1992) Chem. Eng. Sci. (to appear). Pajkossy, T. and Niykos, L. (1989) Electtochetn. Acta, 34, 171-179. Pfeifer, P. and Obret. M. (1989) in The Fractal approach to Heterogeneous Chemistry 03. Avnir Ed.),Wiley. Seri-Levy, A. and Avnir, D. (1991). Sur. Sci.. 248,258-270.

PY - 1992/6/8

Y1 - 1992/6/8

N2 - The geometry of a heterogeneous catalyst is a crucial parameter in determining its performance. Many catalytic systems can be described well in terms of fractal geometry. Here we study the rate dependence of various operating conditions in diffusion-reaction processes occuring on fractal rough surfaces, such as catalyst supports, and fractal subsets such as steps and kinks that constitute the active sites in metal crystallites. In a process of diffusion and reaction in a catalyst with external fractal surface, exposed to a fixed reactant concentration, the catalyst exhibits an increasingly larger area for faster reactions; the overall rate scales as k(Ds/k)2-Df/2, where k is the first-order reaction rate constant and Ds is the diffusivity in the solid. A subfractal, like a Cantor Set, to which molecules diffuse through a stagnant fluid layer of thickness δ and react instantaneously with the catalytic set, exhibits an overall rate that scales like δ-Df; i.e., this subset is less sensitive to mass transfer resistance than a smooth surface. With finite k, the inverse overall rate can be approximated as the sum of the inverse rates at the two asymptotes of very slow and very fast reactions. A fractal line exposed to a fixed reactant concentration at its enveloping boundary, represent a pore network which is an optimal configuration since porosity is higher at the larger pores.

AB - The geometry of a heterogeneous catalyst is a crucial parameter in determining its performance. Many catalytic systems can be described well in terms of fractal geometry. Here we study the rate dependence of various operating conditions in diffusion-reaction processes occuring on fractal rough surfaces, such as catalyst supports, and fractal subsets such as steps and kinks that constitute the active sites in metal crystallites. In a process of diffusion and reaction in a catalyst with external fractal surface, exposed to a fixed reactant concentration, the catalyst exhibits an increasingly larger area for faster reactions; the overall rate scales as k(Ds/k)2-Df/2, where k is the first-order reaction rate constant and Ds is the diffusivity in the solid. A subfractal, like a Cantor Set, to which molecules diffuse through a stagnant fluid layer of thickness δ and react instantaneously with the catalytic set, exhibits an overall rate that scales like δ-Df; i.e., this subset is less sensitive to mass transfer resistance than a smooth surface. With finite k, the inverse overall rate can be approximated as the sum of the inverse rates at the two asymptotes of very slow and very fast reactions. A fractal line exposed to a fixed reactant concentration at its enveloping boundary, represent a pore network which is an optimal configuration since porosity is higher at the larger pores.

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DO - 10.1016/0009-2509(92)87130-I

M3 - 文章

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VL - 47

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EP - 2792

JO - Chemical Engineering Science

JF - Chemical Engineering Science

IS - 9-11

ER -

Anomalous scaling of diffusion and reaction processes on fractal catalysts

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