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Optimization of Diffusive Transport to Irregular Surfaces with Low Sticking Probability

Published online by Cambridge University Press:  15 February 2011

Peter Pfeifer and
Bernard Sapoval
Peter Pfeifer
Affiliation:
Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211Laboratoire de Physique de la Matière Condensée, Ecole Polytechnique, F-91128 Palaiseau, France
Bernard Sapoval
Affiliation:
Laboratoire de Physique de la Matière Condensée, Ecole Polytechnique, F-91128 Palaiseau, France
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Abstract

We study steady-state diffusion to an irregular membrane or catalyst surface which “annihilates” arriving particles by transfer across the membrane or chemical reaction at the surface. For diffusion in two dimensions and an arbitrary given surface, we present a simple algorithm to compute the total flux across the surface (annihilation rate) when the permeability of the membrane or reaction probability at the surface is small. The resulting flux increases with increasing surfaceirregularity and depends nonlinearly on the transport parameters and on the surface area. It predicts an optimal temperature, dependent on the surface irregularity, at which the flux is maximal. We illustrate this for self-similar surfaces, in which case the flux is a power law of the transport parameters and is governed by the fractal dimension of the surface.

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Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 366: Symposium N – Dynamics in Small Confining Systems , 1994, 271
Copyright
Copyright © Materials Research Society 1995

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