Advertisement

Translocation of a granular chain in a horizontally vibrated saw-tooth channel

  • Fariba Mortazavi
  • Mehdi Habibi
  • Ehsan Nedaaee Oskoee
Open Access
Regular Article

Abstract.

We study the translocation mechanism of a granular chain in a horizontally vibrated saw-tooth channel using MD simulations and macro-scale experiments and show that the translocation speed is independent of the chain length as long as the chain length is larger than the spatial period of the saw-tooth. With the help of simulation, we explore the effect of geometry of the container and frequency and amplitude of vibration as well as chain flexibility on the chain drift speed. We observe that the most efficient transport is achieved when one of the channel walls is shifted with respect to the other wall by an amount equal to half the spatial period of the saw-tooth. We define a persistence length for the chain and show that the translocation speed depends on the ratio of persistence length over the spatial period of the saw-tooth. The optimum translocation occurs when this ratio is about 0.4. We also determine the optimum saw-tooth angle for the translocation of the chain as well as the optimum distance between the two walls. Some properties of this system are similar to those of polymer systems.

Graphical abstract

Keywords

Flowing Matter: Granular Matter 

References

  1. 1.
    M. Muthukumar, Phys. Rev. Lett. 86, 3188 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    David Löf, Karin Schillén, Bengt Jönsson, Alex Evilevitch, J. Mol. Biol. 368, 55 (2007)CrossRefGoogle Scholar
  3. 3.
    Davide Marenduzzo, Cristian Micheletti, Enzo Orlandini, J. Phys. Condens. Matter 22, 283102 (2010)CrossRefGoogle Scholar
  4. 4.
    Marta De Frutos, Lucienne Letellier, Eric Raspaud, Biophys. J. 88, 1364 (2005)CrossRefGoogle Scholar
  5. 5.
    Martin Castelnovo, Alex Evilevitch, Eur. Phys. J. E 24, 9 (2007)CrossRefGoogle Scholar
  6. 6.
    Derek Stein, Frank H.J. van der Heyden, Wiepke J.A. Koopmans, Cees Dekker, Proc. Natl. Acad. Sci. U.S.A. 103, 15853 (2006)ADSCrossRefGoogle Scholar
  7. 7.
    Joshua David Cross, Elizabeth A. Strychalski, H.G. Craighead, J. Appl. Phys. 102, 4701 (2007)Google Scholar
  8. 8.
    Jonas O. Tegenfeldt, Christelle Prinz, Han Cao, Steven Chou, Walter W. Reisner, Robert Riehn, Yan Mei Wang, Edward C. Cox, James C. Sturm, Pascal Silberzan et al., Proc. Natl. Acad. Sci. U.S.A. 101, 10979 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    Walter Reisner, Keith J. Morton, Robert Riehn, Yan Mei Wang, Zhaoning Yu, Michael Rosen, James C. Sturm, Stephen Y. Chou, Erwin Frey, Robert H. Austin, Phys. Rev. Lett. 94, 196101 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    Fredrik Persson, Pawel Utko, Walter Reisner, Niels B. Larsen, Anders Kristensen, Nano Lett. 9, 1382 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    Paul Grayson, Lin Han, Tabita Winther, Rob Phillips, Proc. Natl. Acad. Sci. U.S.A. 104, 14652 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    I. Derényi, P. Tegzes, T. Vicsek, Chaos 8, 657 (1998)ADSCrossRefGoogle Scholar
  13. 13.
    Z. Farkas, P. Tegzes, A. Vukics, T. Vicsek, Phys. Rev. E 60, 7022 (1999)ADSCrossRefGoogle Scholar
  14. 14.
    M. Levanon, D.C. Rapaport, Phys. Rev. E 64, 011304 (2001)ADSCrossRefGoogle Scholar
  15. 15.
    Zénó Farkas, Ferenc Szalai, Dietrich E. Wolf, Tamás Vicsek, Phys. Rev. E 65, 022301 (2002)ADSCrossRefGoogle Scholar
  16. 16.
    J.F. Wambaugh, Charles Reichhardt, C.J. Olson, Phys. Rev. E 65, 031308 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    A.J. Bae, W.A.M. Morgado, J.J.P. Veerman, G.L. Vasconcelos, Physica A 342, 22 (2004)ADSCrossRefGoogle Scholar
  18. 18.
    Michael Heckel, Patric Müller, Thorsten Pöschel, Jason A.C. Gallas, Phys. Rev. E 86, 061310 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    J.A.C. Gallas, H.J. Herrmann, S. Sokołowski, Physica A 189, 437 (1992)ADSCrossRefGoogle Scholar
  20. 20.
    R. Grochowski, P. Walzel, M. Rouijaa, C.A. Kruelle, I. Rehberg, Appl. Phys. Lett. 84, 1019 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    Johannes Blaschke, Jürgen Vollmer, Phys. Rev. E 87, 040201 (2013)CrossRefGoogle Scholar
  22. 22.
    Shahin Mobarakabadi, Ehsan Nedaaee Oskoee, Matthias Schröter, Mehdi Habibi, Phys. Rev. E 88, 042201 (2013)CrossRefGoogle Scholar
  23. 23.
    James M. Polson, Brian Bylhouwer, Martin J. Zuckermann, Arthur J. Horton, William M. Scott, Phys. Rev. E 82, 051931 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    Matthew T. Downton, Martin J. Zuckermann, Erin M. Craig, Michael Plischke, Heiner Linke, Phys. Rev. E 73, 011909 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    Martin Kenward, Gary W. Slater, Phys. Rev. E 78, 051806 (2008)ADSCrossRefGoogle Scholar
  26. 26.
    Joel S. Bader, Richard W. Hammond, Steven A. Henck, Michael W. Deem, Gregory A. McDermott, James M. Bustillo, John W. Simpson, Gregory T. Mulhern, Jonathan M. Rothberg, Proc. Natl. Acad. Sci. U.S.A. 96, 13165 (1999)ADSCrossRefGoogle Scholar
  27. 27.
    Steven A. Henck, Michael W. Deem, Gregory A. McDermott, James M. Bustillo, Jonathan M. Rothberg, Electrophoresis 21, 74 (2000)CrossRefGoogle Scholar
  28. 28.
    J.S. Bader, M.W. Deem, R.W. Hammond, S.A. Henck, J.W. Simpson, J.M. Rothberg, Appl. Phys. A 75, 275 (2002)ADSCrossRefGoogle Scholar
  29. 29.
    Kevin Safford, Yacov Kantor, Mehran Kardar, Arshad Kudrolli, Phys. Rev. E 79, 061304 (2009)ADSCrossRefGoogle Scholar
  30. 30.
    Z.A. Daya, E. Ben-Naim, R.E. Ecke, Eur. Phys. J. E 21, 1 (2006)CrossRefGoogle Scholar
  31. 31.
    M.B. Hastings, Z.A. Daya, E. Ben-Naim, R.E. Ecke, Phys. Rev. E 66, 025102 (2002)ADSCrossRefGoogle Scholar
  32. 32.
    J. Galanis, R. Nossal, D. Harries, Soft Matter 6, 1026 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    C.R.K. Windows-Yule, B.J. Scheper, W.K. den Otter, D.J. Parker, A.R. Thornton, Phys. Rev. E 93, 020901 (2016)ADSCrossRefGoogle Scholar
  34. 34.
    S.F. Edwardes, Granular Matter: An Interdisciplinary Approach, edited by A. Mehta (Springer, New York, 1994)Google Scholar
  35. 35.
    T.A. Witten, Rev. Mod. Phys. 70, 1531 (1998)ADSCrossRefGoogle Scholar
  36. 36.
    Eli Ben-Naim, Z.A. Daya, Peter Vorobieff, Robert E. Ecke, Phys. Rev. Lett. 86, 1414 (2001)ADSCrossRefGoogle Scholar
  37. 37.
    Jeffrey J. Prentis, Daniel R. Sisan, Phys. Rev. E 65, 031306 (2002)ADSCrossRefGoogle Scholar
  38. 38.
    V. Yadav, A. Kudrolli, Eur. Phys. J. E 35, 104 (2012)CrossRefGoogle Scholar
  39. 39.
    Ping-Ping Wen, Ning Zheng, Liang-Sheng Li, Heng Li, Gang Sun, Qing-Fan Shi, Phys. Rev. E 85, 031301 (2012)ADSCrossRefGoogle Scholar
  40. 40.
    Ling-Nan Zou, Xiang Cheng, Mark L. Rivers, Heinrich M. Jaeger, Sidney R. Nagel, Science 326, 408 (2009)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    KuanHua Chen, Y.C. Chou, Kiwing To, Phys. Rev. E 87, 012711 (2013)CrossRefGoogle Scholar
  42. 42.
    W.-T. Lin, Y.-C. Sun, C.-C. Chang, Y.-C. Lin, C.-W. Peng, W.-T. Juan, J.-C. Tsai, Phys. Rev. Lett. 112, 058001 (2014)ADSCrossRefGoogle Scholar
  43. 43.
    Masao Doi, Sam F. Edwards, The Theory of Polymer Dynamics, Vol. 73 (Oxford University Press, 1988)Google Scholar
  44. 44.
    H. Hertz, J. Reine Angew. Math. 92, 156 (1881)MathSciNetGoogle Scholar
  45. 45.
    Nikolai V. Brilliantov, Frank Spahn, Jan-Martin Hertzsch, Thorsten Pöschel, Phys. Rev. E 53, 5382 (1996)ADSCrossRefGoogle Scholar
  46. 46.
    Thorsten Pöschel, Thomas Schwager, Computational Granular Dynamics: Models and Algorithms (Springer Science & Business Media, 2005)Google Scholar
  47. 47.
    Ljubinko Kondic, Phys. Rev. E 60, 751 (1999)CrossRefGoogle Scholar
  48. 48.
    Andrew Belmonte, Michael J. Shelley, Shaden T. Eldakar, Chris H. Wiggins, Phys. Rev. Lett. 87, 114301 (2001)ADSCrossRefGoogle Scholar
  49. 49.
    Narges Nikoofard, Hamidreza Khalilian, Hossein Fazli, J. Chem. Phys. 139, 074901 (2013)ADSCrossRefGoogle Scholar
  50. 50.
    Sarah E. Henrickson, Martin Misakian, Baldwin Robertson, John J. Kasianowicz, Phys. Rev. Lett. 85, 3057 (2000)ADSCrossRefGoogle Scholar
  51. 51.
    I. Ali, D. Marenduzzo, J.M. Yeomans, Phys. Rev. Lett. 96, 208102 (2006)ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2016

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Fariba Mortazavi
    • 1
  • Mehdi Habibi
    • 1
    • 2
  • Ehsan Nedaaee Oskoee
    • 1
  1. 1.Institute for Advanced Studies in Basic SciencesZanjanIran
  2. 2.Van der Waals-Zeeman InstituteUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations