Boundary homogenization for trapping by patchy surfaces

Alexander M. Berezhkovskii, Yurii A. Makhnovskii, Michael I. Monine, Vladimir Yu Zitserman, Stanislav Y. Shvartsman

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Abstract

We analyze trapping of diffusing particles by nonoverlapping partially absorbing disks randomly located on a reflecting surface, the problem that arises in many branches of chemical and biological physics. We approach the problem by replacing the heterogeneous boundary condition on the patchy surface by the homogenized partially absorbing boundary condition, which is uniform over the surface. The latter can be used to analyze any problem (internal and external, steady state, and time dependent) in which diffusing particles are trapped by the surface. Our main result is an expression for the effective trapping rate of the homogenized boundary as a function of the fraction of the surface covered by the disks, the disk radius and trapping efficiency, and the particle diffusion constant. We demonstrate excellent accuracy of this expression by testing it against the results of Brownian dynamics simulations.

Original languageEnglish (US)
Article number5
Pages (from-to)11390-11394
Number of pages5
JournalJournal of Chemical Physics
Volume121
Issue number22
DOIs
StatePublished - Dec 8 2004

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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    Berezhkovskii, A. M., Makhnovskii, Y. A., Monine, M. I., Zitserman, V. Y., & Shvartsman, S. Y. (2004). Boundary homogenization for trapping by patchy surfaces. Journal of Chemical Physics, 121(22), 11390-11394. [5]. https://doi.org/10.1063/1.1814351