Trapping and escape in a turbid medium
Abstract
We investigate the absorption of diffusing molecules in a fluidfilled spherical beaker that contains many small reactive traps. The molecules are absorbed either by hitting a trap or by escaping via the beaker walls. In the physical situation where the number N of traps is large and their radii a are small compared to the beaker radius R, the fraction of molecules E that escape to the beaker wall and the complementary fraction T that eventually are absorbed by the traps depend only on the dimensionless parameter combination λ = Na/R. We compute E and T as a function of λ for a spherical beaker and for beakers of other threedimensional shapes. The asymptotic behavior is found to be universal: 1  E ∼ λ for λ → 0 and E ∼ λ^{1/2} for λ → ∞.
 Publication:

Journal of Chemical Physics
 Pub Date:
 December 2017
 DOI:
 10.1063/1.5009425
 arXiv:
 arXiv:1710.05009
 Bibcode:
 2017JChPh.147u4903K
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Physics  Chemical Physics
 EPrint:
 9 pages, 3 figures, 2column revtex format