Jackson, D.P. Hysteresis and Multiple Stable Configurations in a Magnetic Fluid System. Journal of Physics: Condensed Matter 20, no. 20 (2008): e204140 https://iopscience.iop.org/article/10.1088/0953-8984/20/20/204140

A magnetic liquid in a horizontal Hele–Shaw cell is subjected to a vertical magnetic field. The width of the magnetic fluid finger is measured as a function of applied field and compared to a theoretical model. The theoretical model uses an energy minimization procedure and predicts a double energy minimum, hysteresis, and discontinuous transitions between a circle and a finger. The experimental data set agrees very well with the theory for a well-defined magnetic fluid finger. Near the transitions, the experiments show hysteresis and support for a double energy minimum; however, the agreement is not quite so good. The discrepancy between theory and experiment near the transition region is likely due to the simplified finger model used in the theory.

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