Ilmenite (ρ≈4700 kg/m³)
Quartz sand (ρ≈2650 kg/m³)
This 2D companion strips the spiral gravity concentrator down to the physics that actually drives it: each grain's own Stokes settling velocity, v = (ρparticle−ρwater)·g·d²/(18μ). Denser ilmenite grains settle faster and relax toward the trough's slow inner band; lighter quartz grains stay suspended in the faster outer flow and drift outward. A movable splitter at the trough exit cuts the stream into concentrate and tailings, and every grain that crosses it is tallied live into a recovery and grade readout.
Ilmenite (dark, ρ≈4700 kg/m³) and quartz sand (pale, ρ≈2650 kg/m³) grains enter together at the outer edge of a 5-turn spiral trough and separate purely from density, grain size and flow speed — no scripted paths, just a settling-velocity calculation run per grain, per frame.
Raise Water flow speed and watch even heavy grains get carried outward (recovery drops); raise Grain size and separation sharpens (denser grains settle faster, relatively). Slide the Splitter inward for a purer, smaller concentrate, or outward to recover more ilmenite at the cost of grade — the same operating trade-off real plant operators tune.
Real Humphreys and Reichert spiral concentrators use exactly this principle at industrial scale: no chemicals, no electricity beyond a pump — just gravity, density difference and a carefully shaped trough, separating tonnes of heavy mineral sand a day.
The 3D version is a facility walkthrough — a stylised process-plant tour with preset stage names and a scripted particle path. This 2D version instead simulates the actual separation mechanism: each grain's radial position on the spiral is computed every frame from its Stokes settling velocity, so recovery and grade genuinely respond to the flow, grain-size and splitter controls rather than following a fixed animation.
Stokes' law gives the terminal settling velocity of a small sphere in a viscous fluid: v = (ρp−ρf)·g·d²/(18μ). It depends on the density difference between grain and water, gravity, and the square of the grain diameter. A denser or larger grain settles faster, so it spends more time in the trough's slow inner band — which is exactly the mechanism a spiral concentrator exploits.
Faster water raises the reference velocity a grain must beat to settle into the inner band. Grains whose Stokes velocity no longer clears that bar get swept toward the faster outer flow regardless of density, so fewer ilmenite grains make it past the splitter into the concentrate.
Moving the splitter outward widens the "concentrate" zone, capturing more of the ilmenite that only partially settled — but it also lets in more quartz that drifted just inside the cut, lowering the TiO₂ grade. Moving it inward keeps the concentrate purer but leaves more ilmenite behind in the tailings. No single splitter position maximises both at once.
It estimates the TiO₂ content of the material crossing the splitter into the concentrate, assuming ilmenite carries about 52% TiO₂ by mass and quartz carries none — a simplification of real ore assays, but it captures how purity shifts as you change the controls.