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Analytical representations of the spread harmonic measure density

Denis S. Grebenkov*

  • Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS–Ecole Polytechnique, 91128 Palaiseau, France and St. Petersburg National Research University of Information Technologies, Mechanics and Optics, 197101 St. Petersburg, Russia

  • *denis.grebenkov@polytechnique.edu
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Phys. Rev. E 91, 052108 – Published 7 May, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.052108

Abstract

We study the spread harmonic measure that characterizes the spatial distribution of reaction events on a partially reactive surface. For Euclidean domains in which Brownian motion can be split into independent lateral and transverse displacements, we derive analytical formulas for the spread harmonic measure density and analyze its asymptotic behavior. This analysis is applicable to slab domains, general cylindrical domains, and a half-space. We investigate the spreading effect due to multiple reflections on the surface, and the underlying role of finite reactivity. We discuss further extensions and applications of analytical results to describe Laplacian transfer phenomena such as permeation through semipermeable membranes, secondary current distribution on partially blocking electrodes, and surface relaxation in nuclear magnetic resonance.

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Phys. Rev. E 91, 052108– Published 7 May, 2015
  • Received 27 January 2015

©2015 American Physical Society

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