Trapping and escape in a turbid medium.

Abstract

We investigate the absorption of diffusing molecules in a fluid-filled 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 three-dimensional shapes. The asymptotic behavior is found to be universal: 1 - E ∼ λ for λ → 0 and E ∼ λ-1/2 for λ → ∞.