Ferrofluid Rosensweig Instability
Magnetic fluid forms hexagonal spike patterns in a vertical magnetic field
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The Rosensweig (normal-field) instability (1965): a ferrofluid in a horizontal dish forms a hexagonal array of peaks when the vertical magnetic field exceeds a critical value B_c = √(2μ₀g·ρ·σ/χ²). Below B_c, surface tension wins and the fluid is flat. Above B_c, the magnetic free energy of a peak exceeds the surface+gravity cost. The hexagonal pattern minimizes energy — same math as Rayleigh-Bénard convection cells.