What exactly are the spikes, or peaks and valleys, caused by in pictures such as these
Wikipedia states that "From the point of view of magnetic energy, peaks and valleys are energetically favorable", but I'm not exactly sure what that means, or how it works. Why isn't the fluid just happy being attracted to the magnet in a semi-sphere shape? Could it be that it gains a magnetic charge, so it attempts to repel itself at the same time? Just pulling at straws here.
Answer
The shape is caused by normal-field instability. This is the condition where these small 10nm droplets of ferrofluids are described by Maxwells equations where the divergence of the B field is zero and the curl of H is zero. The imposed magnetic field leads to a stress condition mismatch at the interface between the internal of the droplet and the outside. This excess pressure causes the droplets to elongate in the direction of the magnetic field. The inter-peak spacing is approximately given by the Taylor wave-length for regular hydrodynamic instabilities, but the peak amplitude is a function of field intensity.
This elongation can be seen in a variety of ways. In an example where the ferrofluid is less dense and the field strength is lower you can see the simple elongations occur.
In more dense or higher field conditions you can see the stress and deformations take on a more rugged shape as they crowd together along field lines of equal strength. This gives it a spiked appearance.
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