Packing induced bistable phenomenon in granular flow: analysis from complex network perspective

doi:10.1007/s10483-014-1886-6

Abstract

Abstract: The effects of packing configurations on the phase transition of straight granular chute flow with two bottlenecks are studied. The granular flow shows a diluteto-dense flow transition when the channel width is varied, accompanied with a peculiar bistable phenomenon. The bistable phenomenon is induced by the initial packing configuration of particles. When the packing is dense, the initial flux is small and will induce a dense flow. When the packing is loose, the initial flux is large and will induce a dilute flow. The fabric network of granular packing is analyzed from a complex network perspective. The degree distribution shows quantitatively different characteristics for the configurations. A two-dimensional (2D) packing clustering coefficient is defined to better quantify the fabric network.

Key words: granular flow, complex network, phase transition, bistable phenomenon

2010 MSC Number:

O369

Mao-bin HU;Qi-yi LIU;Wang-ping SUN;Rui JIANG;Qing-song WU. Packing induced bistable phenomenon in granular flow: analysis from complex network perspective. Applied Mathematics and Mechanics (English Edition), 2014, 35(12): 1565-1572.

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References

[1] Majmudar, T. S. and Behringer, R. P. Contact force measurements and stress-induced anisotropy in granular materials. nature, 435, 1079-1082 (2005)
[2] Sun, Q. C., Zhang, G. H., and Jin, F. The stress distribution in polydisperse granular packings in two dimensions. Chinese Physics Letters, 30, 028301 (2013)
[3] Eshuis, P., van der Weele, K., van der Meer, D., Bos, R., and Lohse, D. Phase diagram of vertically shaken granular matter. Physics of Fluids, 19, 123301 (2007)
[4] Van Gerner, H. J., van der Hoef, M. A., van der Meer, D., and van der Weele, K. Inversion of Chladni patterns by tuning the vibrational acceleration. Physical Review E, 82, 012301 (2010)
[5] Yan, X., Shi, Q., Hou, M., Lu, K., and Chan, C. K. Effects of air on the segregation of particles in a shaken granular bed. Physical Review Letters, 91, 014302 (2003)
[6] Shi, Q., Sun, G., Hou, M., and Lu, K. Density-driven segregation in vertically vibrated binary granular mixtures. Physical Review E, 75, 061302 (2007)
[7] Xia, J. H., You, Y.W., Wang, P. P., Wang, W. L., and Liu, C. S. A molecular dynamics simulation of segregation behaviors of horizontally vibrated binary granular mixture. Chinese Physics B, 19, 056404 (2010)
[8] O'Hern, C. S., Silbert, L. E., Liu, A. J., and Nagel, S. R. Jamming at zero temperature and zero applied stress: the epitome of disorder. Physical Review E, 68, 011306 (2003)
[9] To, K., Lai, P. Y., and Pak, H. K. Jamming of granular flow in a two-dimensional Hopper. Physical Review Letters, 86, 71-74 (2001)
[10] Xu, N., Vitelli, V., Wyart, M., Liu, A. J., and Nagelet, S. R. Energy transport in jammed sphere packings. Physical Review Letters, 102, 038001 (2009)
[11] Bi, D., Zhang, J., Chakraborty, B., and Behringer, R. P. Jamming by shear. nature, 480, 355-358 (2011)
[12] Chen, W., Hou, M., Lu, K., Jiang, Z., and Lam, L. Granular flows through vertical pipes controlled by an electric field. Physical Review E, 64, 061305 (2001)
[13] Hou, M., Chen, W., Zhang, T., and Lu, K. Electric field controlled dilute-dense flow transition in granular flow through a vertical pipe. Powder Technology, 135, 105-111 (2003)
[14] Hou, M., Chen,W., Zhang, T., Lu, K., and Chan, C. K. Global nature of dilute-to-dense transition of granular flows in a 2D channel. Physical Review Letters, 91, 204301 (2003)
[15] Huang, D., Sun, G., and Lu, K. Relationship between the flow rate and the packing fraction in the choke area of the two-dimensional granular flow. Physical Review E, 74, 061306 (2006)
[16] Huang, D., Sun, G., Hou, M. Y., and Lu, K. Q. The effect of the granule velocity on the dilute-dense flow transition in granular system. Acta Physica Sinica, 55, 4754-4759 (2006)
[17] Hou, M., Tu, H., Liu, R., Li, Y., Lu, K., Lai, P. Y. and Chan, C. K. Temperature oscillations in a compartmentalized bidisperse granular gas. Physical Review Letters, 100, 068001 (2008)
[18] Li, Y., Liu, R., and Hou, M. Gluing bifurcation and noise-induced hopping in the oscillatory phenomena of compartmentalized bidisperse granular gases. Physical Review Letters, 109, 198001 (2012)
[19] Li, Y. C., Zhang, Z. B., Tu, H. G., Liu, R., Hu, H. Y., and Hou, M. Y. The flux profile of granular gas in compartmentalized system. Acta Physica Sinica, 58, 13-19 (2009)
[20] Chen, Y. P., Evesque, P., and Hou, M. Y. Experimental study on the local equation of state for vibrated granular gases. Acta Physica Sinica, 62, 164503 (2013)
[21] Zheng, H. P., Jiang, Y. M., and Peng, Z. Stress distribution and surface instability of an inclined granular layer. Chinese Physics B, 22, 040511 (2013)
[22] Cai, Q. D., Chen, S. Y., and Sheng, X. W. Numerical simulation of two-dimensional granular shearing flows and the friction force of a moving slab on the granular media. Chinese Physics B, 20, 024502 (2011)
[23] Lu, K. Q., Hou, M. Y., Jiang, Z. H., Wang, Q., Sun, G., and Liu, J. X. To understand earth-quake from the granular physics point of view-causes of earthquakes, earthquake precursors and prediction. Acta Physica Sinica, 61, 119103 (2012)
[24] Peng, Z. and Jiang, Y. M. Maximum ceasing angle of inclination and flux formula for granular orifice flow. Acta Physica Sinica, 60, 054501 (2011)
[25] Jop, P., Forterre, Y., and Pouliquen, O. A constitutive law for dense granular flows. nature, 441, 727-730 (2006)
[26] Delannay, R., Louge, M., Richard, P., Taberlet, N., and Valance, A. Towards a theoretical picture of dense granular flows down inclines. Nature Materials, 6, 99-108 (2007)
[27] Jiang, Y. M. and Mario, L. Hydrodynamic theory of grains, water and air. Acta Physica Sinica, 62, 204501 (2013)
[28] Rericha, E. C., Bizon, C., Shattuck, M. D., and Swinney, H. L. Shocks in supersonic sand. Physical Review Letters, 88, 014302 (2002)
[29] Drozd, J. J. and Denniston, C. Velocity fluctuations in dense granular flows. Physical Review E, 78, 041304 (2008)
[30] Tripathi, A. and Khakhar, D. V. Steady flow of smooth, inelastic particles on a bumpy inclined plane: hard and soft particle simulations. Physical Review E, 81, 041307 (2010)
[31] Kumaran, V. and Maheshwari, S. Transition due to base roughness in a dense granular flow down an inclined plane. Physics of Fluids, 24, 053302 (2012)
[32] Sun, Q. C. and Ji, S. Y. A pair correlation function characterizing the anisotropy of force networks. Chinese Physics Letters, 28, 064501 (2011)
[33] Arevalo, R., Zuriguel, I., and Maza, D. Topological properties of the contact network of granular materials. International Journal of Bifurcation and Chaos, 19, 695-702 (2009)
[34] Ben-Nun, O., Einav, I., and Tordesillas, A. Force attractor in confined comminution of granular materials. Physical Review Letters, 104, 108001 (2010)
[35] Walker, D. M. and Tordesillas, A. Topological evolution in dense granular materials: a complex networks perspective. International Journal of Solids and Structures, 47, 624-639 (2010)
[36] Tordesillas, A., Walker, D. M., and Lin, Q. Force cycles and force chains. Physical Review E, 81, 011302 (2010)
[37] Hu, M. B., Jiang, R., and Wu, Q. S. Complex force network in marginally and deeply jammed. Chinese Physics B, 22, 066301 (2013)
[38] Liu, Q. Y., Yang, G. C., Hu, M. B., Jiang, R., Wu, Q. S., and Wu, Y. H. Optimization of granular chute flow with two bottlenecks. Applied Mechanics and Materials, 487, 532-535 (2014)
[39] Hajra, S. K., Shi, D., and McCarthy, J. J. Granular mixing and segregation in zigzag chute flow. Physical Review E, 86, 061318 (2012)
[40] Alonso-Marroquin, F., Azeezullah, S. I., Galindo-Torres, S. A., and Olsen-Kettle, L. M. Bottle-necks in granular flow: when does an obstacle increase the flow rate in an hourglass. Physical Review E, 85, 020301(R) (2012)