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.
|Number of pages||10|
|Journal||Chemical Engineering Science|
|State||Published - Feb 2000|