STRATIFICATION INSTABILITY IN GRANULAR FLOWS

When a mixture of two kinds of grains differing in size and shape is p oured in a vertical two-dimensional cell, the mixture spontaneously st ratifies in alternating layers of small and large grains, whenever the large grains are more faceted than the small grains. Otherwise, the m ixture spontaneously segregates in different regions of the cell when the large grains are more rounded than the small grains. We address th e question of the origin of the instability mechanism leading to strat ification using a recently proposed set of equations for surface flow of granular mixtures. We show that the stable solution of the system i s a segregation solution due to size (large grains tend to segregate d ownhill near the substrate and small grains tend to segregate uphill) and shape (rounded grains tend to segregate downhill and more faceted grains tend to segregate uphill). As a result, the segregation solutio n of the system is realized for mixtures of large-rounded grains and s mall cubic grains with the large-rounded grains segregating near the b ottom of the pile. Stability analysis reveals the instability mechanis m driving the system to stratification as a competition between size s egregation and shape segregation taking place for mixtures of large cu bic grains and small-rounded grains. The large cubic grains tend to si ze segregate at the bottom of the pile, while at the same time, they t end to shape segregate near the pouring point. Thus, the segregation s olution becomes unstable, and the system evolves spontaneously to stra tification.