Dynamics of granular stratification

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Abstract
Spontaneous stratification in granular mixtures—i.e., the formation of alternating layers of small-rounded and large-faceted grains when one pours a random mixture of the two types of grains into a quasi-two-dimensional vertical Hele-Shaw cell—has been recently reported by H. A. Makse et al. [Nature 386, 379 (1997)]. Here we study experimentally the dynamical processes leading to spontaneous stratification. We divide the process in three stages: (a) avalanche of grains and segregation in the rolling phase, (b) formation of the “kink”—an uphill wave at which grains are stopped—at the bottom substrate, and (c) uphill motion of the kink and formation of a pair of layers. Using a high-speed video camera, we study a rapid flow regime where the rolling grains size segregate during the avalanche due to the fact that small grains move downward in the rolling phase to form a sublayer of small rolling grains underneath a sublayer of large rolling grains. This dynamical segregation process—known as “kinematic sieving,” “free surface segregation,” or simple “percolation”— contributes to the spontaneous stratification of grains in the case of thick flows. We characterize the dynamical process of stratification by measuring all relevant quantities: the velocity of the rolling grains, the velocity of the kink, and the wavelength of the layers. We also measure other phenomenological constants such as the rate of collision between rolling and static grains, and all the angles of repose characterizing the mixture. The wavelength of the layers behaves linearly with the thickness of the layer of rolling grains (i.e., with the flow rate), in agreement with theoretical predictions. The velocity profile of the grains in the rolling phase is a linear function of the position of the grains along the moving layer, which implies a linear relation between the mean velocity and the thickness of the rolling phase. We also find that the speed of the upward-moving kink has the same value as the mean speed of the downward-moving grains. We measure the shape and size of the kink, as well as the profiles of the rolling and static phases of grains, and find agreement with recent theoretical predictions.
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