On the intermediate asymptote of diffusion-limited reactions in a fractal porous catalyst

TY - JOUR

T1 - On the intermediate asymptote of diffusion-limited reactions in a fractal porous catalyst

AU - Sheintuch, Moshe

N1 - Funding Information: This research was supported by Technion VPR Fund-New York Metropolitan Research Fund and by Du-Pont Educational Aid Fund. MS is a member of the Minerva Center of Nonlinear Dynamics and Complex Systems.

PY - 2000/2

Y1 - 2000/2

N2 - One of the main numerical results of studies of reaction and diffusion in pore-fractal geometries is the existence of an intermediate low-slope asymptote, in the plot of log (rate) vs. log k, which separates the known asymptotes of kinetics- and diffusion-controlled rates. Moreover, comparison of the rates in a fractal catalyst with those in a uniform-pore object, showed that the former is superior in the k-insensitive domain. We derive here analytical solutions to the reaction and diffusion process in three pore-fractal geometries: A simple pore-tree with a clear hierarchy exhibits an intermediate asymptote, when all pore-generations are diffusion limited; this asymptote depends on geometric parameters only and its domain of existence is larger with trees of a large number of generations. A pore-tree with mixed hierarchies do not admit such an asymptote but its rate dependence on k does admit three domains with a weak dependence in the intermediate domain. An ordered pore-fractal 'catalyst', like the Sierpinsky gasket, for which numerical results are available, is more complex than the two previous structures as it contains closed-loops: At low k's it can be modeled as self-nesting catalytic squares while with large k's the loops are not important and the object can be viewed as a combination of pore trees with mixed hierarchies.

AB - One of the main numerical results of studies of reaction and diffusion in pore-fractal geometries is the existence of an intermediate low-slope asymptote, in the plot of log (rate) vs. log k, which separates the known asymptotes of kinetics- and diffusion-controlled rates. Moreover, comparison of the rates in a fractal catalyst with those in a uniform-pore object, showed that the former is superior in the k-insensitive domain. We derive here analytical solutions to the reaction and diffusion process in three pore-fractal geometries: A simple pore-tree with a clear hierarchy exhibits an intermediate asymptote, when all pore-generations are diffusion limited; this asymptote depends on geometric parameters only and its domain of existence is larger with trees of a large number of generations. A pore-tree with mixed hierarchies do not admit such an asymptote but its rate dependence on k does admit three domains with a weak dependence in the intermediate domain. An ordered pore-fractal 'catalyst', like the Sierpinsky gasket, for which numerical results are available, is more complex than the two previous structures as it contains closed-loops: At low k's it can be modeled as self-nesting catalytic squares while with large k's the loops are not important and the object can be viewed as a combination of pore trees with mixed hierarchies.

KW - Catalysis

KW - Fractals

KW - Reaction-diffusion

UR - http://www.scopus.com/inward/record.url?scp=0342288643&partnerID=8YFLogxK

U2 - 10.1016/S0009-2509(99)00172-4

DO - 10.1016/S0009-2509(99)00172-4

M3 - 文章

AN - SCOPUS:0342288643

SN - 0009-2509

VL - 55

SP - 615

EP - 624

JO - Chemical Engineering Science

JF - Chemical Engineering Science

IS - 3

ER -