Pattern formation in a sandpile of ternary granular mixtures

Pattern formation in a sandpile is investigated by pouring a ternary mixture of grains into a vertical narrow cell. Size segregation in avalanches causes the formation of patterns. Four kinds of patterns emerge: stratification, segregation, upper stratification-lower segregation, and upper segregation-lower stratification. A phase diagram is constructed in a parameter space of θ11/θ33 and θ22/θ33, where θ11,θ22, and θ33 are the repose angles of small, intermediate, and large grains, respectively. To qualitatively understand pattern formation, a phenomenological model based on a roll-or-stay rule is proposed. A similar pattern formation is found in a numerical simulation of the phenomenological model. These results suggest that the ratios of the repose angles of three kinds of grains are important for pattern formation in a sandpile.