Experiments on transient magnetic liquid ridges.

EXPERIMENTS  ON  TRANSIENT  MAGNETIC  LIQUID  RIDGES.

 

Bert Reimann 1, Reinhard Richter 1, Ingo Rehberg 1 and Adrian Lange 1.

 

1.      Experimental Physik V, Universitat Bayreuth, D-95440 Bayreuth.

2.      Otto-von-Guericke Universitet Magdeburg, D-39016 Magdeburg.

 

A horizontal layer of magnetic fluid develops a pattern of liquid crests, as soon as a threshold BC of the vertically orientated magnetic induction is surpassed [1]. This well known Rosenszweig or normal field instability has commonly been investigated by increasing the magnetic induction in a quasi static manner, creating in this way a stable hexagonal pattern of liquid crests.

In contrast, we increase the magnetic induction in a jump like manner. This gives access to the marginal unstable solutions of liquid ridges. Their unstable branch is situated under the branch of the stable hexagonal solution [2, 3]. In the experiment we observe a transient pattern of concentric ridges, which finally decays into a stable hexagonal pattern. The wave number of this concentric pattern has been found to increase linearly with the magnetic induction, in accordance with the predictions of linear stability theory [4].

Here we investigate the properties of the liquid ridges in greater detail. After the first jump to a supercritical induction BSUP and the consecutive formation of the liquid ridges, we switch to a subcritical induction BSUP. In this way the ridges are prevented to end up in the hexagonal state. Instead they decay in an oscillatory manner. Figure 1 display the state prepared by the first jump (a), the intermediate, nearly flat surface (b), and the recovery of the liquid ridge after a half oscillation period (c).

We present the critical scaling behavior of the oscillation frequency as function of the subcritical induction BSUB. More over results of the propagation velocity of the surface waves versus BSUB are referred. Both experimental curves are compared with results obtained by linear stability theory.

 

 

Figure 1: Series of frames showing the well established system

of concentric ridges (a), nearly flat surface (B), and the reestablished ridges (c).

 

Financial support by the Deutsche Forschungsgemeinschaft through Grant Ri1054 / 1 1 is gratefully acknowledged.

 

References:

 

1.      M. D. Cowley and R. E. Rosenszweig // J. Fluid Mech. 30 (1967) 671.

2.      V. M. Zaitsev and M. I. Shliomis // Doclady of Academy Sciences USSR, 188 (1969) 12611.

3.      A. Gailitis // J. Fluid Mech. 82 (1977) 401.

4.      A. Lange, B. Reimann and R. Richter // Phys. Rev. E 61 (2000) 5528.