%0 Book Section %1 statphys23_1090 %A Shimokawa, M. %A Ohta, S. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K angle avalanche kink pile repose sand statphys23 stratification topic-4 %T Dual Stratification of a sand pile formed by Trapped Kink %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1090 %X When a mixture of large rough grains (LRG) and small smooth grains (SSG) is poured into a vertical quasi-two dimensional Hele-Shaw cell, a stratification pattern alternate LRG and SSG emerges spontaneously. The dynamical process of a stratification pattern is divided into three stages: (a) A size segregation occurs in the avalanche. Upper and lower layers of an avalanche are LRG and SSG, respectively. (b) The avalanche stops at the bottom, where a kink appears. The kink is an uphill wave generated on the bottom, which moves toward the top of the pile. (c) The uphill motion of the kink forms a pair of layers. This process repeats and the stratification pattern emerges. It is reported that a kink generates only at the bottom of the pile. Therefore the stripe is formed toward the top from the bottom. We find out a new dual stratification pattern. The dual stratification has two different wavelengths, although it is reported that ordinary stratification has only single wavelength. The wavelength at upper region is about twice as long as that at lower region. In the emergence of the dual stratification, we observe a kink which is generated not only at the bottom but also on the slope. It should be noted that a kink is also generated on the slope. No work is currently available in the published literature on the new kink. We named the new kink ``trapped kink.'' The experiment is performed with a Hele-Shaw cell which consists of two vertical acrylic plates ($6055$ cm$^2$). The two plates are mounted parallel on a horizontal base plate. The distance between the two plates is 0.5 cm. The size of the system is about twice the size of conventional systems. Glass beads (SSG) are uniformly mixed with brown sugar (LRG) by the same volume ratio. The diameter of SSG is 0.1 mm, while that of LRG ranges from 0.2 mm to 0.8 mm. The angles of repose of SSG and LRG are 27 degrees and 38 degrees, respectively. The mixture is poured from the top edge of the Hele-Shaw cell through a funnel. The experiments are performed in the room humidity 41$\pm$4\% since special care have to be taken to prevent cohesion due to moisture. The dynamical process of new dual stratification pattern is as follows: An avalanche stops on the slope. The trapped kink is generated at the position where the avalanche stopped. The trapped kink backs up toward the top of the pile. The next avalanche arises and goes down until it arrives at the bottom. A normal kink is generated and it goes up toward the top. The next avalanche arises when the normal kink arrives at the top. And trapped kink arises again. This process repeats. The frequency of kink generation at the upper region is twice that at the lower region. As mentioned above, that a kink causes a wavelength of alternate LRG and SSG. Wavelength at lower region $łambda_a$ is produced only by the normal kink, while that at upper region $łambda_b$ is produced by the normal kink and the trapped kink. Thus $łambda_b$ is about twice as long as $łambda_a$. We understand that a trapped kink is essential for the formation of a dual stratification. However it cannot be predicted by any ordinary theories. We propose a simple model to explain the generation of the trapped kink. The model shows that the generation position of trapped kink measured from the top of the sand pile is 11.8$\pm$2.6cm, it agrees with the experimental result (13.2cm).

@incollection{statphys23_1090, abstract = {When a mixture of large rough grains (LRG) and small smooth grains (SSG) is poured into a vertical quasi-two dimensional Hele-Shaw cell, a stratification pattern alternate LRG and SSG emerges spontaneously. The dynamical process of a stratification pattern is divided into three stages: (a) A size segregation occurs in the avalanche. Upper and lower layers of an avalanche are LRG and SSG, respectively. (b) The avalanche stops at the bottom, where a kink appears. The kink is an uphill wave generated on the bottom, which moves toward the top of the pile. (c) The uphill motion of the kink forms a pair of layers. This process repeats and the stratification pattern emerges. It is reported that a kink generates only at the bottom of the pile. Therefore the stripe is formed toward the top from the bottom. We find out a new dual stratification pattern. The dual stratification has two different wavelengths, although it is reported that ordinary stratification has only single wavelength. The wavelength at upper region is about twice as long as that at lower region. In the emergence of the dual stratification, we observe a kink which is generated not only at the bottom but also on the slope. It should be noted that a kink is also generated on the slope. No work is currently available in the published literature on the new kink. We named the new kink ``trapped kink.'' The experiment is performed with a Hele-Shaw cell which consists of two vertical acrylic plates ($60\times 55$ cm$^2$). The two plates are mounted parallel on a horizontal base plate. The distance between the two plates is 0.5 cm. The size of the system is about twice the size of conventional systems. Glass beads (SSG) are uniformly mixed with brown sugar (LRG) by the same volume ratio. The diameter of SSG is 0.1 mm, while that of LRG ranges from 0.2 mm to 0.8 mm. The angles of repose of SSG and LRG are 27 degrees and 38 degrees, respectively. The mixture is poured from the top edge of the Hele-Shaw cell through a funnel. The experiments are performed in the room humidity 41$\pm$4\% since special care have to be taken to prevent cohesion due to moisture. The dynamical process of new dual stratification pattern is as follows: An avalanche stops on the slope. The trapped kink is generated at the position where the avalanche stopped. The trapped kink backs up toward the top of the pile. The next avalanche arises and goes down until it arrives at the bottom. A normal kink is generated and it goes up toward the top. The next avalanche arises when the normal kink arrives at the top. And trapped kink arises again. This process repeats. The frequency of kink generation at the upper region is twice that at the lower region. As mentioned above, that a kink causes a wavelength of alternate LRG and SSG. Wavelength at lower region $\lambda_a$ is produced only by the normal kink, while that at upper region $\lambda_b$ is produced by the normal kink and the trapped kink. Thus $\lambda_b$ is about twice as long as $\lambda_a$. We understand that a trapped kink is essential for the formation of a dual stratification. However it cannot be predicted by any ordinary theories. We propose a simple model to explain the generation of the trapped kink. The model shows that the generation position of trapped kink measured from the top of the sand pile is 11.8$\pm$2.6cm, it agrees with the experimental result (13.2cm).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Shimokawa, M. and Ohta, S.}, biburl = {https://www.bibsonomy.org/bibtex/2044322748840f7ee68094fba3c5d1c2e/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {2b5ce8339dd9a8bfb230416344b46c78}, intrahash = {044322748840f7ee68094fba3c5d1c2e}, keywords = {angle avalanche kink pile repose sand statphys23 stratification topic-4}, month = {9-13 July}, timestamp = {2007-06-20T10:16:38.000+0200}, title = {Dual Stratification of a sand pile formed by Trapped Kink}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1090}, year = 2007 }