Heaping instabilities in a layered Bi-disperse granular bed

Heap formations in a layered bi-disperse granular bed under vertical vibration with strength Γ have been studied experimentally. With the volume ratio (χ) between the two different types of grains and Γ as control parameters, different heap patterns can be created and details of the heap formation can be investigated. In particular, a periodic state in which the heap is being created and destroyed more or less periodically has been realized. This periodic heaping state is found to be related to two instabilities controlled by χ and Γ; namely the instability of a horizontal granular interface and the instability of a heap in a layered granular system. This latter instability would occur only in a layered system. A nonlinear phenomenological model is developed to understand these two instabilities and the predictions of the model are found to be in good agreement with experiments.