Flux to a trap

Abstract

The flux of particles to a single trap is investigated for two systems: (1) particles in 3D space which jump a fixed step length l (the Rayleigh flight) and are adsorbed by a spherical surface, and (2) particles on a lattice, jumping to nearest neighbor sites, with a single adsorbing site. Initially, the particles are uniformly distributed outside the traps. When the jump length goes to zero, both processes go over to regular diffusion, and the first case yields the diffusive flux to a sphere as solved by Smoluchowski. For nonzero step length, the flux for large times is given by a modified form of Smoluchowski's result, with the effective radius replaced by R-cl , where c =0.29795219 and cl is the Milne extrapolation length for this problem. For the second problem, a similar expression for the flux is found, with the effective trap radius a function of the lattice (sc, bcc, fcc) being considered.