06 / Ferrofluid · separate the mechanisms

A field can translate, align and shape matter

Drag the gold pole; the paired pole moves with it. Switch between field direction, a force proxy, and directional stress to see why these are different controls.

Source strengthMaterial probe xMaterial probe y

A nearly uniform field can have a clear direction yet a weak gradient force. The stress view shows tension along the field and transverse squeeze at the probe. Native ferrofluid adds viscous pressure, temperature-dependent response and explicit interface traction to turn these ingredients into moving material.

—Field strength at probe

—Force-proxy magnitude

—Saturated alignment cue

Equations and model boundary

H(x) = Σₖ sₖ (x − pₖ)/(|x − pₖ|² + ε²)
fproxy = ½∇|H|²
τdirectional ∝ ĥĥᵀ − ½I

A regularized analytic pole-pair illustration with a computed field gradient, not the native iterative magnetization/self-field solve. The stress glyph is a directional model. The native ferro-spike bench also uses occupancy gates and authored surface corrugation; its visible spikes are not evidence of a fully emergent instability.