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Dimensional Crossover in the Growth of Depletion Zone in a Rectangular Capillary: Experiments and Monte Carlo Simulations

Published online by Cambridge University Press:  01 February 2011

Sung Hyun Park ,
Hailin Peng ,
Panos Argyrakis ,
Haim Taitelbaum  and
Raoul Kopelman
Sung Hyun Park
Affiliation:
Department of Chemistry, University of Michigan, Ann Arbor, MI 48109–1055, U.S.A.
Hailin Peng
Affiliation:
Department of Chemistry, University of Michigan, Ann Arbor, MI 48109–1055, U.S.A.
Panos Argyrakis
Affiliation:
Department of Physics, University of Thessaloniki, 54124 Thessaloniki, Greece
Haim Taitelbaum
Affiliation:
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
Raoul Kopelman
Affiliation:
Department of Chemistry, University of Michigan, Ann Arbor, MI 48109–1055, U.S.A.
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Abstract

The diffusion-limited kinetics of the growth of depletion zone around a static point trap in a thin, long stripe geometry was studied using a laser photobleaching experiment of fluorescein dye inside a rectangular capillary. The dynamics of the depletion zone was monitored by the θ-distance, defined as the distance from the trap to the point where the reactant concentration has been depleted to the specific fraction of its initial bulk value. A dimensional crossover from two dimensions to one dimension, due to the finite width of the reaction zone, was observed. The crossover seems to occur for all θ values concurrently when the depletion zone touches the boundary for the first time, suggesting that the boundary information spreads faster than diffusion. Monte Carlo simulations were performed to support the experimental results. The crossover time (τc) is found to scale with the width (L) of the rectangular reaction zone as τc ∼ L2, as expected from the Einstein's diffusion law.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 790: Symposium P – Dynamics in Small Confining Systems–2003 , 2003 , P7.23
Copyright
Copyright © Materials Research Society 2004

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References

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