Scaling approach to study diffusion and reaction processes on fractal catalysts

TY - JOUR

T1 - Scaling approach to study diffusion and reaction processes on fractal catalysts

AU - Gutfraind, Ricardo

AU - Sheintuch, Moshe

N1 - Funding Information: Acknowledgements-This research was supported by the Technion’s VPR Fund-Henri Gutwirth Promotion of Research. We thank Prof. David Avnir for very useful clarifications.

PY - 1992/12

Y1 - 1992/12

N2 - We use simple scaling arguments to predict the behaviour of diffusion and reaction processes taking place in porous fractal object, modelled by fractal surface, or over isolated catalyst crysallite, using a fractal subset to represent the distribution of active sites. These scalings are tested then by exact numerical simulations. The analysed processes and scaling are: (a) In a process of reaction and diffusion inside a catalyst with fractal external surface exposed to a fixed reactant concentration the overall reaction rate scales as k(D/k)(d-Df)/2, where D is the diffusion coefficient, k is the rate constant of a first-order reaction and d is the dimension of the embedding Euclidean space. (b) In a process of diffusion from the bulk, through a stagnant film, towards a fractal surface over which an instantaneous reaction occurs, the overall rate scales as δ-Df, where Df is the surface fractal dimension and δ is the film thickness. This holds for a fractal rough surface as modelled by the Koch curve (Df>1) or for a fractal subset as modelled by the Cantor set (CS). (c) In a process of adsorption on the gaps of a Cantor set (CS) and surface diffusion towards the CS points where instantaneous reaction occurs the rate scales as ka(Ds/ka)(1-Df)/2 , where Ds is the surface diffusion coefficient and ka is the adsorption constant.

AB - We use simple scaling arguments to predict the behaviour of diffusion and reaction processes taking place in porous fractal object, modelled by fractal surface, or over isolated catalyst crysallite, using a fractal subset to represent the distribution of active sites. These scalings are tested then by exact numerical simulations. The analysed processes and scaling are: (a) In a process of reaction and diffusion inside a catalyst with fractal external surface exposed to a fixed reactant concentration the overall reaction rate scales as k(D/k)(d-Df)/2, where D is the diffusion coefficient, k is the rate constant of a first-order reaction and d is the dimension of the embedding Euclidean space. (b) In a process of diffusion from the bulk, through a stagnant film, towards a fractal surface over which an instantaneous reaction occurs, the overall rate scales as δ-Df, where Df is the surface fractal dimension and δ is the film thickness. This holds for a fractal rough surface as modelled by the Koch curve (Df>1) or for a fractal subset as modelled by the Cantor set (CS). (c) In a process of adsorption on the gaps of a Cantor set (CS) and surface diffusion towards the CS points where instantaneous reaction occurs the rate scales as ka(Ds/ka)(1-Df)/2 , where Ds is the surface diffusion coefficient and ka is the adsorption constant.

UR - http://www.scopus.com/inward/record.url?scp=0026987113&partnerID=8YFLogxK

U2 - 10.1016/0009-2509(92)85120-Z

DO - 10.1016/0009-2509(92)85120-Z

M3 - 文章

AN - SCOPUS:0026987113

SN - 0009-2509

VL - 47

SP - 4425

EP - 4433

JO - Chemical Engineering Science

JF - Chemical Engineering Science

IS - 17-18

ER -