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Reaction-diffusion on a periodic array of penetrable spherical sinks

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  • Venema, P.
  • Bedeaux, D.

Abstract

In this paper an analysis is given of the reaction-diffusion process on a periodic array of penetrable spherical sinks. The effective rate coefficient is calculated for these lattices as a function of the several parameters in the system, such as the volume fraction, the reactivity of the sinks and the ratio of the diffusion constants inside and outside the sinks. In the analysis the distribution of the absorption inside and on the surface of the sinks is expanded in multipole moments. For the calculation only a finite number of these multipoles is taken into account. A careful analysis of the convergence is made by increasing the number of multipoles until the result stabilizes. This is in particular important at volume fractions close to dense packing. Earlier results by Felderhof [1] who uses a similar method for the special case of perfectly absorbing sinks are found to deviate up to 15% compared to the fully converged results. We also compare our results with the so-called spherical approximation which is found to be a good approximation for all volume fractions when the process is reaction-controlled while in the limit of perfectly absorbing sinks this approximation is only correct at low volume fractions.

Suggested Citation

  • Venema, P. & Bedeaux, D., 1989. "Reaction-diffusion on a periodic array of penetrable spherical sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 156(3), pages 835-852.
    • Handle: RePEc:eee:phsmap:v:156:y:1989:i:3:p:835-852
    DOI: 10.1016/0378-4371(89)90023-X
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    References listed on IDEAS

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    1. Denos Gazis & Robert Herman & Alexei Maradudin, 1960. "The Problem of the Amber Signal Light in Traffic Flow," Operations Research, INFORMS, vol. 8(1), pages 112-132, February.
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