DYNAMICS OF GRANULAR STRATIFICATION

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-di mensional vertical Hele-Shaw cell-has been recently reported by H. A. Makse et al. [Nature 386, 379 (1997)]. Here we study experimentally th e 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 motio n of the kink and formation of a pair of layers. Using a high-speed vi deo 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 gra ins underneath a sublayer of large rolling grains. This dynamical segr egation process-known as ''kinematic sieving,'' ''free surface segrega tion,'' or simple ''percolation''- contributes to the spontaneous stra tification of grains in the case of thick flows. We characterize the d ynamical process of stratification by measuring all relevant quantitie s: the velocity of the rolling grains, the velocity of the kink, and t he wavelength of the layers. We also measure other phenomenological co nstants such as the rate of collision between rolling and static grain s, and all the angles of repose characterizing the mixture. The wavele ngth of the layers behaves linearly with the thickness of the layer of rolling grains (i.e., with the flow rate), in agreement with theoreti cal predictions. The velocity profile of the grains in the rolling pha se 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 downwa rd-moving grains. We measure the shape and size of the kink, as well a s the profiles of the rolling and static phases of grains, and find ag reement with recent theoretical predictions.