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Ferrofluid drops in rotating magnetic fields

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Published 6 June 2003 • Published under licence by IOP Publishing Ltd
, , Focus on Pattern Formation Citation Alexander V Lebedev et al 2003 New J. Phys. 5 57 DOI 10.1088/1367-2630/5/1/357

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1 Institute of Continuous Media Mechanics, 1 Korolev Street, 614013 Perm, Russia

2 Universität Magdeburg, Institut für Theoretische Physik, PSF 4120, 39106 Magdeburg, Germany

Dates

  1. Received 3 January 2003
  2. Published

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1367-2630/5/1/57

Abstract

Drops of a ferrofluid floating in a non-magnetic liquid of the same density and spun by a rotating magnetic field are investigated experimentally and theoretically. The parameters for the experiment are chosen such that different stationary drop shapes including non-axis-symmetric configurations could be observed. Within an approximate theoretical analysis the character of the occurring shape bifurcations, the different stationary drop forms, as well as the slow rotational motion of the drop is investigated. The results are in qualitative, and often quantitative agreement, with the experimental findings. It is also shown that a small eccentricity of the rotating field may have a substantial impact on the rotational motion of the drop.

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(movie1) (movie2)

(movie1) (movie2)

(movie3) (movie4) Figure 1. (2.9 MB, 1.8 MB, 1.8 MB, 1.8 MB MPEGs) The top view of two typical shapes of the rotating drop. On the left (movie2) we show an elongated form well approximated by a three-axis ellipsoid. On the right (movie4) we show a flat spheroid with peaks at the periphery at large values of the magnetic field amplitude. The movies show the slow rotation of the drop in real time. The complete evolution of the drop shape for increasing field strength is available (movie1) with a time-lapse factor of 5. The amplitude G of the magnetic field is shown at the bottom and also graphically displayed by the blue bar on the left. The parameters of this particular experiment are collected in table 1. A particularly intriguing phenomenon occurs after 55 s (4 min 33 s real time) when the external field is switched off. The relaxation to the spherical drop occurs via an intermediate non-axis-symmetrical shape. Switching on the field to the same value again the drop returns immediately to the `starfish' configuration it showed before. This rather peculiar behaviour is shown in real time in movie3.

(movie3) (movie4) Figure 1. (2.9 MB, 1.8 MB, 1.8 MB, 1.8 MB MPEGs) The top view of two typical shapes of the rotating drop. On the left (movie2) we show an elongated form well approximated by a three-axis ellipsoid. On the right (movie4) we show a flat spheroid with peaks at the periphery at large values of the magnetic field amplitude. The movies show the slow rotation of the drop in real time. The complete evolution of the drop shape for increasing field strength is available (movie1) with a time-lapse factor of 5. The amplitude G of the magnetic field is shown at the bottom and also graphically displayed by the blue bar on the left. The parameters of this particular experiment are collected in table 1. A particularly intriguing phenomenon occurs after 55 s (4 min 33 s real time) when the external field is switched off. The relaxation to the spherical drop occurs via an intermediate non-axis-symmetrical shape. Switching on the field to the same value again the drop returns immediately to the `starfish' configuration it showed before. This rather peculiar behaviour is shown in real time in movie3.

Figure 5. (1.0 MB MPEG) An animated version of the theoretical results for the rotation frequency and the internal flow. The parameters are the same as in figure 4, the magnetic bond number is B = 66. The movie shows clearly the difference between the rotation of the drop shape and the vorticity of the internal flow of the fluid. The mass elements of the ferrofluid are coded by the colour and exhibit a rotational flow in the rest frame of the shape.

Figure 6. (1.8 MB MPEG) The top view of a non-axis-symmetric drop in an elliptically polarized magnetic field. The relevant parameter values are collected in the third row of table 1. The relative strength of the field in the x (horizontal in the figure) and y directions, respectively, is shown by the bars on the left. For the values given in the figure the drop had just stopped its rotation. . Note that in the experiment G0y is negative. The drop hence rotates clockwise and the stopping angle is θ = 3π/4 or equivalently θ = 7π/4.

10.1088/1367-2630/5/1/357