Pattern formation in a sandpile of ternary granular mixtures
Michiko Shimokawa, Fukuoka Institute of Technology, Japan.

Size segregation in avalanches causes pattern formation in a sandpile; when binary mixtures of grains are poured into a narrow vertical cell, a segregation or a stratification pattern is formed spontaneously. It was reported that the pattern was determined by the angles of repose and the sizes of the two grains. In contrast to binary mixtures, pattern formation in a sandpile of ternary granular mixtures has not yet to be investigated in detail. Thus, pattern formation in a sandpile is investigated by pouring a ternary mixture of grains. In our experiments, not only stratification and segregation patterns, observed in experiments with binary mixtures, but also new type of upper stratification--lower segregation, and upper segregation--lower stratification emerges. A phase diagram is constructed in a parameter space of \theta¸_11/\theta 33 and \theta_22/\theta_33 where \theta_11, \theta_22, and \theta_33 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. This study is collaborated with Prof. Sakaguchi in Kyushu university.

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