Drag-induced particle segregation with vibrating boundaries

We consider a system composed of two different types of particles that have different radii, but equal density. Both particles experience gravity and a linear drag force from the interstitial fluid. They are excited by a boundary that vibrates with high frequency and adds sufficient energy that the particles near the boundary become highly dilated. For moderate energy input rates we show that a single large particle introduced into a large number of small particles will rapidly move to a fixed height and remain approximately stationary. In particular, the large particle will never come into contact with the vibrating base. If there are a large number of large particles, then this behavior leads to a very distinct segregation in which the large particles are sandwiched between two layers of small particles. We show that this behavior occurs as a direct result of non-equilibrium effects and develop a simple phenomenological model that gives good predictions of the height at which the sandwiched layer occurs.