Apply a vertical magnetic field and watch hexagonal spikes spontaneously emerge above the critical field Bc. A competition between magnetic energy and surface tension/gravity.
A ferrofluid is a colloid of nanoscale magnetic particles suspended in a carrier liquid. When a uniform vertical magnetic field B is applied, the fluid surface remains flat below a critical field Bc. Above Bc, the surface spontaneously develops a regular hexagonal array of sharp spikes — the Rosensweig instability (1967). This is a first-order phase transition: the flat state becomes unstable, and the hexagonal pattern minimizes the total energy by balancing magnetic energy (favoring spikes to concentrate the field), surface tension (favoring a flat surface), and gravity.
The instability has a characteristic wavelength λc = 2π·√(σ/(ρg)), the capillary-gravity wavelength, which sets the spacing between spikes (≈ 9–10 mm for a typical ferrofluid). The critical field Bc = √(2μ₀·√(σρg))/χ marks the threshold: below it the surface is flat, above it spikes emerge with amplitude A ∝ √(1 − Bc/B), the classic supercritical pitchfork bifurcation. The pattern is hexagonal because the nonlinear coupling of the three wavevectors at 0°, 60°, 120° produces the lowest-energy triangular lattice of spikes.
Ferrofluids are used in dynamic rotary seals, loudspeaker voice-coil cooling and damping, biomedical targeted drug delivery, and heat transfer. The Rosensweig instability is studied in pattern formation and nonlinear dynamics. Artists like Sachiko Kodama have created kinetic ferrofluid sculptures responsive to sound and motion.
Drag the Field Strength B slider. Below Bc the 3D surface stays flat; as B crosses Bc, hexagonal spikes suddenly emerge — the phase transition. Increase B further for taller, sharper spikes. Adjust χ to change Bc (higher χ → lower threshold). Adjust σ to change spike spacing λc. Toggle container shape to see boundary effects. Auto Sweep slowly ramps B from 0 to showcase emergence.