  Spontaneous stratification of granular mixtures has been reported by Makse et
al. [Nature 386, 379 (1997)] when a mixture of grains differing in size and
shape is poured in a quasi-two-dimensional heap. We study this phenomenon using
two different approaches. First, we introduce a cellular automaton model that
illustrates clearly the physical mechanism; the model displays stratification
whenever the large grains are rougher than the small grains, in agreement with
the experiments. Moreover, the dynamics are close to those of the experiments,
where the layers are built through a ``kink'' at which the rolling grains are
stopped. Second, we develop a continuum approach, based on a recently
introduced set of coupled equations for surface flows of granular mixtures that
allows us to make quantitative predictions for relevant quantities. We study
the continuum model in two limit regimes: the large flux or thick flow regime,
where the percolation effect (i.e., segregation of the rolling grains in the
flow) is important, and the small flux or thin flow regime, where all the
rolling grains are in contact with the surface of the sandpile. We find that
the wavelength of the layers behaves linearly with the flux of grains. We
obtain analytical predictions for the shape of the kink giving rise to
stratification as well as the profile of the rolling and static species when
segregation of the species is observed.
