  We study the interface dynamics of a binary particle mixture in a rotating
cylinder numerically. By considering only the particle motion in axial
direction, it is shown that the initial dynamics can be well described by a
one-dimensional diffusion process. This allows us to calculate a macroscopic
diffusion constant and we study its dependence on the inter-particle friction
coefficient, the rotation speed of the cylinder and the density ratio of the
two components. It is found that radial segregation reduces the drift velocity
of the interface. We then perform a microscopic calculation of the diffusion
coefficient and investigate its dependence on the position along the cylinder
axis and the density ratio of the two particle components. The latter
dependence can be explained by looking at the different hydrostatic pressures
of the two particle components at the interface. We find that the
microscopically calculated diffusion coefficient agrees well with the value
from the macroscopic definition when taken in the middle of the cylinder.
