Effective Perrin theory for the anisotropic diffusion of a strongly hindered rod

Slender rods in concentrated suspensions constitute strongly
interacting systems with rich dynamics: transport slows down
drastically and the anisotropy of the motion becomes arbitrarily
large. We develop a mesoscopic description of the dynamics down to
the length scale of the interparticle distance. Our theory is based
on the exact solution of the Smoluchowski-Perrin equation; it is in
quantitative agreement with extensive Brownian dynamics simulations
in the dense regime. In particular, we show that the tube
confinement is characterised by a power law decay of the
intermediate scattering function with exponent 1/2