Group 6

Nonlinear Dynamical Analysis of Ferrofluid

Ferrofluids exibit nonlinear dynamical behavior in response to both static and oscillating external magnetic fields. An experiment will be developed to isolate a single peak response of ferrofluid to an electromagnetic field generated by a hertzien coil. The apparatus will be configured such that a single peak will be isolated. The response will be observed with a high-speed camera. First a static magnetic field will be applied. This is expected to result in nonlinear surface behavior accompanied by a hysteresis effect. Spontaneous peak formation will be observed at a critical field magnitude. We will examine this response and relate an established qualitative model. A critical magnitude in which spontaneous peak formation is induced (normal field instability), will be observed and analytically correlated to the model. The expected subcritical instability will be observed and the resulting peaks peak characteristics will be analyzed. Next, a thermal component will be introduced and a corresponding term added to the dynamical equation to account for this effect. This nonlinear surface oscillating bifurcation is rarely studied or observed.

Experimental Apparatus

Overall Apparatus

The overall apparatus will consist of the following parts list and configured according to Figure 1. The Teflon fluid holder is used to obtain a flat fluid surface taking advantage of the low surface tension of the material. The Teflon holder will be fabricated by drilling a 3mm diameter and 12mm deep hole into the bulk Teflon and then creating a 30 degree countersink. The ferrofluid is then injected into the hole. The current controlled power supply will drive the magnetic field generated within the herzian coils and the event monitored using a high-speed camera. Computer software will be used to correlate the height of the peak by a pixel/length relationship.

Parts list 1. Hertzion Coil 2. Teflon Fluid Holder 3. Power Supply 4. High-speed Camera 5. Ferrofluid - EFH-1

Parts list

1. Hertzion Coil
2. Teflon Fluid Holder
3. Power Supply
4. High-speed Camera
5. Ferrofluid - EFH-1

Experimental Procedure

References

T. Mahr and I. Rehberg, "Nonlinear dynamics of a single ferrofluid-peak in an oscillating magnetic field," Physica D, vol. 111, pp. 335-346, Jan 1998.