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The size segregation phenomenon of granular materials in a two-dimensional rotating drum is simulated very efficiently using a simplified deterministic model. We demonstrate ergodicity in the sense that the statistical properties of a particle trajectory reflect the behaviour of the whole assembly. Segregation is shown to occur in a bidisperse system even if the radii of the particles are very similar (ratio as big as 0.9). Since Oyama's pioneering experiments in 1939 [l] it has been well known that particles of different sizes tend to accumulate in different regions in a partially fdled cylinder rotating around its horizontal symmetry axis, Recent experiments [2-41 show that radial segregation occurs also in two dimensions. That is, the smaller particles assemble into an inner core of the filling. Clbment, Duran and Rajchenbach[3] recorded the trajectory of a single particle of different size in an otherwise monodisperse granular medium. The experimental set-up for tracing the position of a coloured or illuminating particle by a videocamera, and evaluating the record by digital image processing is easily accessible, and highly automationable. They showed that a single small particle will more likely be found in the middle of the packing than at the container wall, demonstrating that segregation is not a collective effect requiring a certain density of small particles.Many parameters are involved in this process, such as size, shape, mass, friction forces, rotating velocity, filling of the drum, etc. Some of them should be more important than others, thus the question naturally arises: what is the minimal model, which captures the essential physics? Moreover, one would like to know to what extent the trajectory of a tagged particle reflects the behaviour of the whole assembly quantitatively.

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In order to study scaling phenomena in granular materials, simple extensions of a model originally proposed by Jullien, Meakin and Pavlovitch (Phys. Rev. Lett. 69, 640 (1992)) are developed. It is shown that the model reproduces phenomena like the heap formation due to friction at the container walls during vertical shaking, as well as size segregation in a rotating drum. The geometrical mechanisms underlying these phenomena are discussed, as well as preliminary results about the critical behavior.

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