Presets
Playback
Field and roll
The corona charges every grain; conductors give the charge back to the roll, non-conductors keep it.
Feed and splitters
Grain size and moisture change both the weight and the leakage time of the charge.
Model checks
The science
Charge, grip and release
Ions from the corona electrode charge each grain until it holds the Pauthenier saturation charge qs = 4πε0 p a2 E, where p = 1 + 2(εr - 1)/(εr + 2) (3 for a conductor) and the charge grows as q(t) = qs t/(t + τ), τ = 4ε0E/j for ion current density j. On the grounded roll the charge leaks away as exp(-t/τleak): milliseconds for a conductor, minutes for dry quartz. A charged grain is pressed to the roll by its image charge, F = q2/(16πε0a2), so it sticks until a brush removes it; a discharged grain leaves when the centrifugal force beats gravity, at cos φ = ω2R/g. A conductor in the field of the static electrode also picks up an induced charge (π2/6)·4πε0a2E of opposite sign and is pulled outward, which flings it further.
What the simulation does
Each grain rides the roll at angular speed ω; at every time step the radial force balance (centrifugal, gravity, image force, electrode force) is evaluated. When the net force points outward the grain leaves along the tangent and flies on a parabola (with the electrode pull for conductors) into one of three bins set by two adjustable splitters. Moisture shortens the leakage time of the non-conductors and middlings, which is why damp feed separates badly.
Honest simplifications
- One roll of 12 cm radius, round grains of three fixed materials, no grain-to-grain collisions, no dust, no air drag and no ion-wind effects.
- Fields are taken as voltage divided by an effective gap (10 cm for the corona and 12 cm for the static electrode); the real field is non-uniform and depends on the electrode shape.
- Charge leakage is a single exponential and the middling class is one representative semi-conductor, so the numbers are illustrative, not plant data.
What to try
- Load Too fast roll: even non-conductors are thrown off early because centrifugal force beats the image force, and purity collapses.
- Load Damp feed: the non-conductor charge leaks away within a second and the clean separation is lost.
- Raise the grain size: weight grows as d cubed but the charge only as d squared, so coarse grains fall off the roll.