2D Electrorheological Fluid: Field-Induced Chain Formation

Electric Field

Field strength E 2.0 kV/mm

Particle count 70

Carrier fluid drag 1.0×

Shear test force 0%

Live Readouts

Chain order S

0.00

Longest chain

Estimated yield stress τ_y

0.00 kPa

How it works

This is a flat, top-down 2D slice of the same electrorheological (Winslow) effect as the 3D version of this sim: dielectric particles suspended between two electrode plates (here, the top and bottom edges of the plane), polarized by an applied field. With the field off, only Brownian jitter and steric collisions move the particles. Switch it on and each particle behaves like an induced dipole

p = 4πε0·εf·β·a²·E,   β = (εp − εf) / (εp + 2εf)

where β is the Clausius–Mossotti factor and a the particle radius. Two aligned dipoles separated by r at angle θ to the field carry interaction energy

U(r,θ) = (p² / 4πε0εf) · (1 − 3cos²θ) / r³

which is attractive head-to-tail (θ ≈ 0°, along the field) and repulsive side-by-side (θ ≈ 90°). Every frame integrates the exact planar force F = −∇U from this potential for every pair, plus short-range steric repulsion and thermal noise — no scripted animation. Particles spontaneously chain along field lines and bridge the plates, exactly as in the real Winslow effect.

The chained structure resists shear like a solid until the applied stress exceeds the fluid's Bingham yield stress, estimated here from field strength and particle loading as

τy ≈ 3·φ·β·ε0·εf·E²   (φ = particle area fraction)

Drag the Shear test force slider to push the chains sideways — below τy they bend and hold; well above it they shatter back into a disordered suspension, just like a real ER clutch or damper losing lock.

Dielectric particle Chained (field-aligned)