  The influence of size differences, shape, mass and persistent motion on phase
separation in binary mixtures has been intensively studied. Here we focus on
the exclusive role of diffusivity differences in binary mixtures of equal-sized
particles. We find an effective attraction between the less diffusive
particles, which are essentially caged in the surrounding species with the
higher diffusion constant. This effect leads to phase separation for systems
above a critical size: A single close-packed cluster made up of the less
diffusive species emerges. Experiments for testing of our predictions are
outlined.
