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Pattern formation in a horizontally shaken granular submonolayer

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Abstract

We study the mechanism leading to the formation of stripe-like patterns in a rectangular container filled with a sub-monolayer of frictional spherical particles when it is subjected to horizontal oscillations. By means of Molecular Dynamics simulations we could reproduce the experimental results. Systematic simulations allow to identify friction to be responsible for the pattern formation, that is, the tangential interaction between contacting particles and between the particles and the floor of the container. When particles are in contact with the floor and other adjacent particles simultaneously, there emerges a frustrated situation in which the particles are prevented from rolling on the floor. This effect leads to local jamming and eventually to stripe-like pattern formation. In the long time evolution, the stripes are unstable. Stripes may merge as well as disintegrate.

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References

  1. Cooke, M.H., Stephens, D.J., Bridgwater, J.: Powder mixing—a literature survey. Powder Technol. 15, 1–20 (1976)

    Article  Google Scholar 

  2. Kudrolli, A.: Size separation in vibrated granular matter. Rep. Prog. Phys. 67, 209–247 (2004)

    Article  ADS  Google Scholar 

  3. Pöschel, T.: Dynamik Granularer Systeme. Logos, Berlin (2001)

    Google Scholar 

  4. Ristow, G.: Pattern Formation in Granular Materials, volume of 164 of Springer Tracts in Modern Physics, Springer (1999)

  5. Aranson, I.S., Tsimring, L.S.: Patterns and collective behaviour in granular media: theoretical concepts. Rev. Mod. Phys. 78, 641–692 (2006)

    Article  ADS  Google Scholar 

  6. Aranson, I.S., Tsimring, L.S.: Granular Patterns. Oxford University Press, Oxford (2009)

    Google Scholar 

  7. Allen, J.R.: Asymmetrical ripple marks and the origin of cross-stratification. Nature 194, 167–169 (1962)

    Article  ADS  Google Scholar 

  8. Anderson, R.S., Bunas, K.L.: Grain size segregation and stratigraphy in aeolian ripples modelled with a cellular automaton. Nature 365, 740–743 (1993)

    Article  ADS  Google Scholar 

  9. Koeppe, J., Enz, M., Kakalios, J.: Avalanche segregation of granular media. In: Behringer, R.P., Jenkins, J.T. (eds.) Powders and Grains’97, pp. 443–446. Rotterdam, Balkema (1997)

  10. Julien, P.Y., Lan, Y.Q., Raslan, Y.: Experimental mechanics of sand stratification. In: Behringer, R.P., Jenkins, J.T. (eds.) Powders and Grains’97, pp. 487–490. Rotterdam, Balkema (1997)

  11. Makse, H.A., Havlin, S., King, P.R., Stanley, H.E.: Novel pattern formation in granular matter. In: Schimansky-Geier, L., Pöschel, T. (eds.) Stochastic Dynamics. Lecture Notes in Physics, pp. 319–333. Springer, Berlin (1997)

  12. Makse, H.A.: Stratification instability in granular flows. Phys. Rev. E 56, 7008–7016 (1997)

    Article  ADS  Google Scholar 

  13. Makse, H.A., Havlin, S., King, P.R., Stanley, H.E.: Spontaneous stratification in granular mixtures. Nature 386, 379–382 (1997)

    Article  ADS  Google Scholar 

  14. Makse, H.A., Havlin, S., Ivanov, PCh., King, P.R., Prakash, S., Stanley, H.E.: Pattern formation in sedimentary rocks: connectivity, permeability, and spatial correlations. Phys. A 233, 587–605 (1996)

    Article  Google Scholar 

  15. Makse, H.A., Cizeau, P., Stanley, H.E.: Possible stratification mechanism in granular mixtures. Phys. Rev. Lett. 78, 3298–3301 (1997)

    Article  ADS  Google Scholar 

  16. Makse, H.A., Cizeau, P., Stanley, H.E.: Modeling stratification in two-dimensional sandpiles. Phys. A 249, 391–396 (1998)

    Article  Google Scholar 

  17. Makse, H.A., Herrmann, H.-J.: Microscopic model for granular stratification and segregation. Europhys. Lett. 43, 1–6 (1998)

    Article  ADS  Google Scholar 

  18. Gray, J.M.N.T., Hutter, K.: Pattern formation in granular avalanches. Cont. Mech. Thermodyn. 9, 341–345 (1997)

    Article  Google Scholar 

  19. Gray, J.M.N.T., Hutter, K.: Physik granularer Lawinen. Physikalische Blätter 54, 37–43 (1998)

    Article  Google Scholar 

  20. Grasselli, Y., Herrmann, H.-J.: Experimental study of granular stratification. Granul. Matter 1, 43–47 (1998)

    Article  MATH  Google Scholar 

  21. Boutreux, T., De Gennes, P.G.: Surface flow of granular mixtures. In: Behringer, R. P., Jenkins, J. T. (eds.) Powders and Grains’97, pp. 439–442. Rotterdam, Balkema (1997)

  22. Boutreux, T., De Gennes, P.G.: Surface flows if granular mixtures: I. General principles and minimal model. J. Physique I 6, 1295–1304 (1996)

    Article  ADS  Google Scholar 

  23. Meakin, P.: A simple two-dimensional model for particle segregation. Phys. A 163, 733–746 (1990)

    Article  Google Scholar 

  24. Sorby, H.C.: On the structures produced by the currents present during the deposition of stratified rocks. Geologist 2, 137–147 (1859)

    Google Scholar 

  25. Head, D.A., Rodgers, G.J.: Slowly driven formation with granular mixtures. Phys. Rev. E 56, 1976–1980 (1997)

    Article  ADS  Google Scholar 

  26. Werner, B.T., Hallet, B.: Numerical simulation of selforganized stone stripes. Nature 361, 142–145 (1993)

    Article  ADS  Google Scholar 

  27. Washburn, A.L.: Classification of patterned ground and review of suggested origins. Geol. Soc. Am. Bull. 67, 823–866 (1956)

    Article  ADS  Google Scholar 

  28. Olafsen, J.S., Urbach, J.S.: Clustering, order, and collapse in a driven granular monolayer. Phys. Rev. Lett. 81, 4369–4372 (1998)

    Article  ADS  Google Scholar 

  29. Prevost, A., Melby, P., Egolf, D.A., Urbach, J.S.: Nonequilibrium two-phase coexistence in a confined granular layer. Phys. Rev. E 70, 050301(R) (2004)

    Article  ADS  Google Scholar 

  30. Melby, P., Vega Reyes, F., Prevost, A., Robertson, R., Kumar, P., Egolf, D.A., Urbach, J.S.: The dynamics of thin vibrated granular layers. J. Phys.: Condens. Matter 17, S2689–S2704 (2005)

    Article  ADS  Google Scholar 

  31. Sapozhnikov, M.V., Aranson, I.S., Olafsen, J.S.: Coarsening of granular clusters: two types of scaling behaviors. Phys. Rev. E 67, 010302(R) (2003)

    Article  ADS  Google Scholar 

  32. Losert, W., Cooper, D.G.W., Gollub, J.P.: Propagating front in an excited granular layer. Phys. Rev. E 59, 5855–5861 (1999)

    Article  ADS  Google Scholar 

  33. Olafsen, J.S., Urbach, J.S.: Velocity distributions and density fluctuations in a granular gas. Phys. Rev. E 60, R2468–R2471 (1999)

    Article  ADS  Google Scholar 

  34. Nie, X., Ben-Naim, E., Chen, S.Y.: Dynamics of vibrated granular monolayers. Europhys. Lett. 51, 679–684 (2000)

    Article  ADS  Google Scholar 

  35. Cafiero, R., Luding, S., Herrmann, H.-J.: Two-dimensional granular gas of inelastic spheres with multiplicative driving. Phys. Rev. Lett. 84, 6014–6017 (2000)

    Article  ADS  Google Scholar 

  36. Rivas, N., Cordero, P., Risso, D., Soto, R.: Segregation in quasi-two-dimensional granular systems. New J. Phys. 13, 055018 (2011)

    Article  ADS  Google Scholar 

  37. Rivas, N., Ponce, S., Gallet, B., Risso, D., Soto, R., Cordero, P., Mujica, N.: Sudden chain energy transfer events in vibrated granular media. Phys. Rev. Lett. 106, 088001 (2011)

    Article  ADS  Google Scholar 

  38. Aranson, I.S., Blair, D., Kalatsky, V.A., Crabtree, G.W., Kwok, W.-K., Vinokur, V.M., Welp, U.: Electrostatically driven granular media: phase transitions and coarsening. Phys. Rev. Lett. 84, 3306–3309 (2000)

    Article  ADS  Google Scholar 

  39. Mullin, T.: Coarsening of self-organized clusters in binary mixtures of particles. Phys. Rev. Lett. 84, 4741–4744 (2000)

    Article  ADS  Google Scholar 

  40. Mullin, T.: Mixing and de-mixing. Science 295, 1851 (2002)

    Article  Google Scholar 

  41. Reis, P.M., Ehrhardt, G., Stephenson, A., Mullin, T.: Gases, liquids and crystals in granular segregation. Europhys. Lett. 66, 357–363 (2004)

    Article  ADS  Google Scholar 

  42. Reis, P.M., Sykes, T., Mullin, T.: Phases of granular segregation in a binary mixture. Phys. Rev. E 74, 051306 (2006)

    Article  ADS  Google Scholar 

  43. Reis, P., Mullin, T.: Granular segregation as a critical phenomenon. Phys. Rev. Lett. 89, 244301 (2002)

    Article  ADS  Google Scholar 

  44. Pica Ciamarra, M., Coniglio, A., Nicodemi, M.: Dynamically induced effective interaction in periodically driven granular mixtures. Phys. Rev. Lett. 97, 038001 (Jul 2006)

    Google Scholar 

  45. Pica Ciamarra, M., Coniglio, A., Nicodemi, M.: Phenomenology and theory of horizontally oscillated granular mixtures. Eur. Phys. J. E. 22, 227–234 (2007)

    Article  Google Scholar 

  46. Strassburger, G., Betat, A., Scherer, M.A., Rehberg, I.: Pattern formation by horizontal vibration of granular material. In: Wolf, D.E., Schreckenberg, M., Bachem, A. (eds.) Workshop on Traffic and Granular Flow, pp. 329–334. World Scientific, October 9–11 (1995)

  47. Betat, A., Dury, C., Rehberg, I., Ristow, G., Scherer, M., Schröter, M., Straßburger, G.: Formation of patterns in granular materials. In: Busse, F.H., Müller, S.C. (eds.) Evolution of Spontaneous Structures in Dissipative Continuous Systems, pp. 495–545. Springer, Berlin (1998)

    Chapter  Google Scholar 

  48. Scherer, M.A., Buchholtz, V., Pöschel, T., Rehberg, I.: Swirling granular matter: from rotation to reptation. Phys. Rev. E 54, R4560–R4563 (Nov 1996)

  49. Scherer, M.A., Kötter, K., Markus, M., Goles, E., Rehberg, I.: Swirling granular solidlike clusters. Phys. Rev. E 61, 4069–4077 (Apr 2000)

  50. Aumaître, S., Kruelle, C.A., Rehberg, I.: Segregation in granular matter under horizontal swirling excitation. Phys. Rev. E 64, 041305 (2001)

    Article  ADS  Google Scholar 

  51. Schnautz, T., Brito, R., Kruelle, C.A., Rehberg, I.: A horizontal brazil-nut effect and its reverse. Phys. Rev. Lett. 95, 028001 (2005)

    Article  ADS  Google Scholar 

  52. Kudrolli, A., Wolpert, M., Gollub, J.P.: Cluster formation due to collisions in granular material. Phys. Rev. Lett. 78, 1383–1386 (1997)

    Article  ADS  Google Scholar 

  53. Goldhirsch, I., Zanetti, G.: Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619–1622 (1993)

    Article  ADS  Google Scholar 

  54. Brilliantov, N.V., Salueña, C., Schwager, T., Pöschel, T.: Transient structures in granular gases. Phys. Rev. Lett. 93, 134301 (2004)

    Article  ADS  Google Scholar 

  55. Orza, J.A.C., Brito, R., van Noije, T.P.C., Ernst, M.H.: Patterns and long range correlations in idealized granular flows. J. Mod. Phys. C 8, 953–967 (1997)

    Article  ADS  Google Scholar 

  56. Efrati, E., Livne, E., Meerson, B.: Hydrodynamic singularities and clustering in a freely cooling inelastic gas. Phys. Rev. Lett 94, 088001 (2005)

    Article  ADS  Google Scholar 

  57. Kondic, L., Hartley, R.R., Tennakoon, S.G.K., Painter, B., Behringer, R.P.: Segregation by friction. Europhys. Lett. 61, 742–748 (2003)

    Article  ADS  Google Scholar 

  58. Kondic, L.: Friction based segregation of 2d granular assembly. MRS Proc. 543, 357–362 (1998)

    Article  Google Scholar 

  59. Painter, B., Behringer, R.P.: Dynamics of two-particle granular collisions on a surface. Phys. Rev. E 62, 2380–2387 (2000)

    Article  ADS  Google Scholar 

  60. Dutt, M., Behringer, R.P.: Effects of surface friction on a two-dimensional granular system: cooling bound system. Phys. Rev. E 70, 061304 (2004)

    Article  ADS  Google Scholar 

  61. Radjai, F., Roux, S.: Friction-induced self-organization of a one-dimensional array of particles. Phys. Rev. E 51, 6177–6187 (Jun 1995)

    Google Scholar 

  62. Brilliantov, N.V., Spahn, F., Hertzsch, J.-M., Pöschel, T.: A model for collisions in granular gases. Phys. Rev. E 53, 5382–5392 (1996)

    Google Scholar 

  63. Haff, P.K., Werner, B.T.: Computer simulation of the mechanical sorting of grains. Powder Technol. 48, 239–245 (1986)

    Article  Google Scholar 

  64. Brilliantov, N.V., Pöschel, T.: Rolling friction of a viscous sphere on a hard plane. Europhys. Lett. 42, 511–516 (1998)

    Google Scholar 

  65. Pöschel, T., Brilliantov, N.V.: Rolling as a continuing collision. Eur. Phys. J. B. 12, 299–301 (1999)

    Article  ADS  Google Scholar 

  66. Esipov, S.E., Pöschel, T.: The granular phase diagram. J. Stat. Phys. 86, 1385–1395 (1997)

    Article  ADS  MATH  Google Scholar 

  67. Meerson, B., Dez-Minguito, M., Schwager, T., Pöschel, T.: Close-packed granular clusters: hydrostatics and persistent Gaussian fluctuations. Granual. Matter 10, 21–27 (2007)

    Article  MATH  Google Scholar 

  68. Meerson, B., Pöschel, T., Sasorov, P.V., Schwager, T.: Giant fluctuations at a granular phase separation threshold. Phys. Rev. E 69, 021302 (2004)

    Article  ADS  Google Scholar 

  69. Clerc, M.G., Cordero, P., Dunstan, J., Huff, K., Mujica, N., Risso, D., Varas, G.: Liquidsolid-like transition in quasi-one-dimensional driven granular media. Nat. Phys. 4, 249–254 (2008)

    Article  Google Scholar 

  70. Kondic, L.: Dynamics of spherical particles on a surface: collision-induced sliding and other effects. Phys. Rev. E 60, 751–770 (Jul 1999)

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Acknowledgments

The authors gratefully acknowledge the support of the Cluster of Excellence ‘Engineering of Advanced Materials’ at the University of Erlangen-Nuremberg, which is funded by the German Research Foundation (DFG) within the framework of its ‘Excellence Initiative’.

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Correspondence to Thorsten Pöschel.

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Krengel, D., Strobl, S., Sack, A. et al. Pattern formation in a horizontally shaken granular submonolayer. Granular Matter 15, 377–387 (2013). https://doi.org/10.1007/s10035-013-0411-2

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