A ferrofluid is an oily suspension of nanoscale magnetic particles. Below a critical applied field the fluid's surface tension keeps its surface flat; once the field crosses that threshold, the magnetic body force overcomes gravity and surface tension together and the flat surface becomes unstable, buckling into a regular hexagonal-ish array of sharp peaks along the field lines — the Rosensweig (normal-field) instability.
The critical field for an infinite-permeability ferrofluid balances the destabilizing magnetic pressure against gravity and surface tension:
H_c = sqrt( 2·sqrt(ρ·g·γ) / μ₀ )
with ρ the fluid density (≈1400 kg/m³ for a kerosene-based ferrofluid, fixed here), g gravity, γ the surface tension you control, and μ₀ the permeability of free space. Raising γ raises H_c — more surface tension resists deformation, so it takes a stronger field to trigger spikes.
The spike spacing itself is set by the same gravity–tension balance, the classic capillary wavelength:
λ = 2π / sqrt(ρ·g/γ) capillary length ℓ = sqrt(γ/(ρ·g))
Peak height above threshold is reported in multiples of the capillary length ℓ — the natural length scale for this instability — scaled by how far H sits past H_c, which is why the spikes grow smoothly rather than snapping on.
- Field strength H — drag it past H_c to trigger the ring of spikes around the magnet; higher excess field gives taller spikes.
- Surface tension γ — raises H_c and shortens the capillary wavelength, so higher γ means a higher threshold but finer, more closely-packed spikes once triggered.
- Viscosity — a thicker fluid responds more sluggishly to a changing field (does not change the threshold itself).
- Drag the magnet — the instability is local: it only appears in the ring directly above the magnet's field, so moving the magnet moves the spike crown with it.