The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2241–2252 | Cite as

Granular electrostatics: Progress and outstanding questions

  • T. Shinbrot
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications


Every physicist studies electrostatics in the first year of graduate study, and learns that the electric field is a linear superposition of contributions from charges, each of which obeys a 1/r 2 law. Every physicist also studies classical mechanics, and learns that the problem of three or more bodies in a 1/r 2 field is intrinsically nonlinear. The contradiction between these two teachings is seldom commented upon. In this paper, I overview what is known, what is believed, and what remains entirely unknown about the behaviors of multiple electrically polarized or charged particles. I show that the nonlinearity recognized in classical mechanics leads to highly complex dynamics when particles are permitted to act in the presence of electric fields. I describe several simple problems that lead to effects that are not understood in any way, and I conclude with the proposition that what we know and believe are insignificant compared with the effects that we know to exist but cannot explain.


Particle Charge European Physical Journal Special Topic Volcanic Plume Dielectrophoretic Force Sakurajima Volcano 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P.F.H. Baddeley, Whirlwinds and Dust-storms of India (Bell & Daldy, London, 1860)Google Scholar
  2. 2.
    T. Shinbrot, H.J. , Herrmann, Nature 451, 773 (2008)CrossRefADSGoogle Scholar
  3. 3.
    H.C. Verakis, J. Nagy, “A brief history of dust explosions,” Industrial dust explosions, edited by K.L. Cashdollar, M. Herzberg (Am. Soc. Test. & Mater. Phila, 1987), p. 342Google Scholar
  4. 4.
    W. Gilbert, De Magnete, Translated by PF Mottelay (Dover Pub’s, NY, 1991) [translated in 1893 from original completed in 1600]Google Scholar
  5. 5.
    W.R. Harper, Contact and Frictional Electrification (Oxford University Press, 1967)Google Scholar
  6. 6.
    J. Lowell, W.S. Truscott, J. Phys. D: Applied Phys. 19, 1273 (1986)CrossRefADSGoogle Scholar
  7. 7.
    K.M. Forward, D.J. Lacks, R.M. Sankaran, Phys. Rev. Lett. 102, 028001 (2009)CrossRefADSGoogle Scholar
  8. 8.
    J.F. Kok, D.J. Lacks, Phys. Rev. E 79, 051304 (2009)CrossRefADSGoogle Scholar
  9. 9.
    M. Sow, D.J. Lacks, R.M. Sankaran, J. Electrostatics 71, 396 (2013)CrossRefGoogle Scholar
  10. 10.
    T. Shinbrot, T.S. Komatsu, Q. Zhao, Europhys. Lett. 83, 24004 (2008)CrossRefADSGoogle Scholar
  11. 11.
    M.M. Apodaca, P.J. Wesson, K.J.M. Bishop, M.A. Ratner, B.A. Grzybowski, Angew. Chemie 49, 946 (2010)CrossRefGoogle Scholar
  12. 12.
    A. Mehrotra, F.J. Muzzio, T. Shinbrot, Phys. Rev. Lett. 99, 058001 (2007)CrossRefADSGoogle Scholar
  13. 13.
    R. Anderson, S. Bjornsson, D.C. Blancdhard, S. Gathman, J. Hughes, S. Jonasson, C.B. Moore, H.J. Survilas, B. Vonnegut, Science 148, 1179 (1965)CrossRefADSGoogle Scholar
  14. 14.
    J. Kozák, V. Cermák, The Illustrated History of Natural Disasters (Springer, NY, 2010)Google Scholar
  15. 15.
    I.M.P. Houghton, K.L. Aplin, K.A. Nicoll, Phys. Rev. Lett. 111, 118501 (2013)CrossRefADSGoogle Scholar
  16. 16.
    C. Cimarelli, M.A. Alatorre-Ibargüengoitia, U. Kueppers, B. Scheu, D.B. Dingwell, Geology 42, 79 (2013)CrossRefGoogle Scholar
  17. 17.
    R.J. Thomas, P.R. Krehbiel, W. Rison, H.E. Edens, G.D. Aulich, W.P. Winn, S.R. McNutt, G. Tytgat, E. Clark, Science 315, 1097 (2007)CrossRefADSGoogle Scholar
  18. 18.
    T. Pähtz, H.J. Herrmann, T. Shinbrot, Nat. Phys. 6, 364 (2010)CrossRefGoogle Scholar
  19. 19.
    I. Peterson, Newton’s Clock: Chaos in the Solar System (Freeman, NY, 1993)Google Scholar
  20. 20.
    J.R. Dorfman, M.H. Ernst, D. Jacobs, J. Stat. Phys. 81, 497 (1995)MathSciNetCrossRefzbMATHADSGoogle Scholar
  21. 21.
    M. Pietroni, Eur. Phys. J. 168, 149 (2009)Google Scholar
  22. 22.
    T. Shinbrot, K. LaMarche, B.J. Glasser, Phys. Rev. Lett. 96, 178002 (2006)CrossRefADSGoogle Scholar
  23. 23.
    T. Shinbrot, N.H. Kim, N.N. Thyagu, Proc. Natl. Acad. Sci., USA 109, 10806 (2012)CrossRefADSGoogle Scholar
  24. 24.
    Manuscript under preparation Google Scholar
  25. 25.
    K.E. Daniels, C. Bauer, T. Shinbrot, Granular Matter 16, 217 (2014)CrossRefGoogle Scholar
  26. 26.
    J.R. Leeman, M.M. Scuderi, C. Marone, D.M. Saffer, T. Shinbrot, J. Geophys. Res. 119, 4253 (2014)CrossRefADSGoogle Scholar
  27. 27.
    F. Lechenault, C.L. Rountree, F. Cousin, J.-P. Bouchaud, L. Ponson, E. Bouchaud, Phys. Rev. Lett. 106, 165504 (2001)CrossRefADSGoogle Scholar
  28. 28.
    B.P. Chandra, J.I. Zink, Phys. Rev. B 21, 816 (1980)CrossRefADSGoogle Scholar
  29. 29.
    G.N. Chapman, A.J. Walton, J. Appl. Phys. 54, 5961 (1983)CrossRefADSGoogle Scholar
  30. 30.
    Y. Mori, Y. Obata, J. Pavelka, J. Sikula, T. Lokajicek, J. Acoustic Emission 22, 167 (2004)Google Scholar
  31. 31.
    J.I. Bernoulli, Histoire Acad. Roy. Paris, 5 (1700)Google Scholar
  32. 32.
    J.I. Bernoulli, Histoire Acad. Roy. Paris, 1 (1701)Google Scholar
  33. 33.
    I.S. Aranson, L.S. Tsimring, Rev. Mod. Phys. 78, 641 (2006)CrossRefADSGoogle Scholar
  34. 34.
    A.K. Kamra, Nature 240, 143 (1972)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Rutgers UniversityPiscatawayUSA

Personalised recommendations