TY - JOUR
T1 - Boundary homogenization for trapping by patchy surfaces
AU - Berezhkovskii, Alexander M.
AU - Makhnovskii, Yurii A.
AU - Monine, Michael I.
AU - Zitserman, Vladimir Yu
AU - Shvartsman, Stanislav Y.
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2004/12/8
Y1 - 2004/12/8
N2 - 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.
AB - 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.
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U2 - 10.1063/1.1814351
DO - 10.1063/1.1814351
M3 - Article
C2 - 15634098
AN - SCOPUS:11144273343
VL - 121
SP - 11390
EP - 11394
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
SN - 0021-9606
IS - 22
M1 - 5
ER -