  We use the Self Consisten Generalized Langevin Equation theory (SCGLE) to
study the dynamic arrest transitions of a system of three species of hard
sphere colloidal system in the size ratio 1:3:9. We find that the inclusion of
the smallest species has a depletion effect that drives the system to a second
glass-liquid-glass re-entrance in a similar way that the inclusion of a small
species in an otherwise monodisperse system leads to a (first) re-entrance. And
we also find that the new glass after the second reentrance has very small
localization length. Additionally we compare the kinetic phase diagram of a
binary hard sphere mixture with size asymmetry 1:5, obtained with Mode Coupling
Theory (MCT) and SCGLE theory and exhibit the significant differences between
the two theories.
