Two-dimensional density-driven segregation in vertically vibrated binary granular mixtures

Two-dimensional segregation effect in vertically vibrated binary granular mixtures with same size is studied by molecular dynamic simulation. The results show that the lighter and mixed state, in which the lighter particles tend to rise and form a pure layer on top of the system while the heavier particles and some of the lighter ones stay at the bottom and form a mixed layer, also exists in the two-dimensional system. The validity of the scheme of the lighter and mixed state is testified by comparing the distribution profiles implied by the scheme with that of the real simulated state. We further propose to use twice the ratio of the thickness of the top layer to that of the whole system as an order parameter to describe the degree of the segregation quantitatively, and present a method that can accurately calculate the order parameter in the simulation. By use of the order parameter, we show that the order parameter is a convex monotonic function of the density ratio between the heavier and lighter particles.