Effect of noise on the stability of electrodynamically levitated one or many charged droplets

  • 30 Accesses


The theory of the effect of external fluctuations on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using a classical pseudo-potential approach. The theory is supplemented with numerical simulations where the non-homogeneous modified Mathieu equation is solved for single-droplet as well as many-droplet systems. In this essentially non-equilibrium system a pseudo-potential is identified, and a Boltzmann-like pseudo-equilibrium distribution is suggested that describes the variance of the deterministic configuration of particles levitated in a quadrupolar trap. This formalism seems to explain the numerical results in a fairly close and convincing manner. A transition from a well-ordered Coulombic crystal to a randomly distributed liquid-like structure is observed above a threshold value of noise. A surprising finding of the present work is the observation that the strength of the threshold noise for the transition of a 2-particle system into a noise-dominated regime is identical to the critical noise required for a solid melting transition in a 100-particle system. The simulations could prove useful in analysing an ordered assembly of levitated micro- and nano-particles from the air streams using a contactless membrane.

Graphical abstract

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.


  1. 1

    D. Wineland, P. Ekstrom, H. Dehmelt, Phys. Rev. Lett. 31, 1279 (1973)

  2. 2

    L.S. Brown, G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)

  3. 3

    H.G. Dehmelt, Adv. At. Mol. Phys. 3, 72 (1968)

  4. 4

    W. Paul, Rev. Mod. Phys. 62, 531 (1990)

  5. 5

    H. Winter, H.W. Ortjohann, Am. J. Phys. 59, 813 (1991)

  6. 6

    R.F. Wuerker, H. Shelton, R.V. Langmuir, J. Appl. Phys. 30, 349 (1959)

  7. 7

    M. Singh, Y.S. Mayya, J. Gaware, R.M. Thaokar, J. Appl. Phys. 121, 054503 (2017)

  8. 8

    S. Arnold, L.M. Folan, A. Korn, J. Appl. Phys. 74, 4297 (1993)

  9. 9

    S. Arnold, J.H. Li, S. Holler, A. Korn, A.F. Izmailov, J. Appl. Phys. 78, 3571 (1995)

  10. 10

    R. Blatt, P. Zoller, G. Holzmuller, I. Siemers, Z. Phys. D: At. Mol. Clust. 4, 126 (1986)

  11. 11

    C. Zerbe, P. Jung, P. Hänggi, Phys. Rev. E 49, 3626 (1994)

  12. 12

    E. Joos, A. Lindner, Z. Phys. D: At. Mol. Clust. 11, 300 (1989)

  13. 13

    C.L. Aardahl, R. Vehring, E.J. Davis, G. Schweiger, B.D. Swanson, J. Aerosol Sci. 28, 1505 (1997)

  14. 14

    G. Tepper, J. Fenn, R. Kessick, D. Pestov, J. Anderson, in 2006 Sixth IEEE Conference on Nanotechnology, Vol. 2 (IEEE, 2006) p. 782

  15. 15

    S. Arnold, N. Hessel, Rev. Sci. Instrum. 56, 2069 (1985)

  16. 16

    M. Singh, R. Thaokar, A. Khan, Y.S. Mayya, Phys. Rev. E 98, 032202 (2018)

Download references

Author information

Mohit Singh wrote the manuscript, did numerical simulations, analyzed the results and prepared all figures. Rochish Thaokar and Y.S. Mayya analyzed the results, proposed the physical idea and revised the article. All authors reviewed the manuscript.

Correspondence to Rochish Thaokar.

Additional information

Publisher's Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Singh, M., Mayya, Y.S. & Thaokar, R. Effect of noise on the stability of electrodynamically levitated one or many charged droplets. Eur. Phys. J. E 42, 152 (2019) doi:10.1140/epje/i2019-11919-3

Download citation


  • Soft Matter: Self-organisation and Supramolecular Assemblies