The problem of trapping of diffusing particles by identical, perfectly absorbing rings periodically distributed along an otherwise reflecting infinite cylindrical tube is very difficult for analytical treatment due to the mixed boundary conditions on the tube surface. Analytical solutions to this problem are considered in two recent papers.1,2 Among other results reported in these works, the authors propose approximate expressions for the mean lifetime τ of a particle whose starting point is uniformly distributed over the tube surface, and the tube is surrounded by an outer concentric tube which is a reflecting boundary for diffusing particles. These expressions can be written in a unified form as
where ρ and L are the radius and half-period of the inner tube, R is the outer tube radius, and D is the particle diffusivity. The factor...
