A grounded, rotating high-voltage roll carries a thin curtain of mineral grains. A corona electrode charges every grain on contact to an initial charge q₀ ∝ roll voltage. Once on the grounded roll, each grain's charge relaxes exponentially — the same RC-discharge law as a leaking capacitor:
q(t) = q0 · exp(−t / τ), τ = ε0 / σ (conductivity-dependent)
Conductive grains (zircon, rutile, ilmenite) have high σ, so τconductor is a few milliseconds — charge, and with it the electrostatic image force pinning the grain to the roll, collapses almost instantly. Insulating grains (quartz/silica) have low σ, so τinsulator is set by the conductivity-contrast slider and can be hundreds of milliseconds.
A grain stays pinned to the roll while the electrostatic adhesion force Fe(t) = C·q(t)² exceeds the outward mechanical force trying to fling it off:
F_out(θ) = m·ω²R − m·g·cos θ
where θ is the angle traveled since the grain landed at the top of the roll and ω is the roll's angular speed. The grain detaches the instant Fe(t) drops below Fout(θ), then flies off ballistically with the roll's tangential velocity at that angle. Because conductors discharge almost immediately, they detach near the top of the roll with a large horizontal launch velocity and are thrown into the far conductor bin. Insulators stay charged and pinned much longer, riding around toward the underside of the roll before gravity finally overcomes the (now much weaker) adhesion — they drop nearly straight down into the near non-conductor bin. Grains that detach in between land in the middling bin and would be re-processed in a real plant.
- Roll voltage — raises q0, raising initial adhesion force for every grain (delays detachment for both species, but insulators still win the contrast).
- Roll speed — raises ω, raising centrifugal force and shortening the time available before the mechanical force overtakes adhesion.
- Conductivity contrast — the ratio τinsulator/τconductor; this is the actual separation knob real plants tune via humidity/temperature. Push it to the minimum and the bins blur together; push it up and the split becomes sharp.