Ex-situ soil washing exploits one fact: contaminant mass is not spread evenly across a soil sample — it concentrates on the fine (clay/silt) particles, because adsorption scales with specific surface area, which grows as particle diameter shrinks:
q(d) = q₀ · (d_ref / d)^a (specific loading, mg contaminant per kg particle)
where a is the contaminant's fines-affinity exponent (higher for strongly-sorbing PAHs/heavy metals, lower for TPH). A hydrocyclone classifier then splits particles into a coarse underflow and a fine overflow using a partition curve centred on the cut size d₅₀:
E_coarse(d) = 1 / (1 + (d₅₀ / d)^n) (Plitt-type reduced efficiency curve)
Particles larger than d₅₀ preferentially report to the coarse underflow; particles smaller than d₅₀ preferentially report to the fine overflow. Attrition scrubbing mechanically abrades fine contaminated coatings off the surface of sand grains before classification, liberating that mass into the fines stream. Each wash pass then applies a further rinse to whatever remains attached:
C' = C · (1 − η), η = η_max · scrub · (1 − (1 − rinse)^passes)
Note on this build: the original 3D version of this plant states that raising the cut size sends more mass to the clean coarse output. That is backwards from its own partition formula (and from real hydrocyclones): raising d₅₀ makes the coarse cut harder to qualify for, so fewer particles cross the threshold and coarse recovery drops. This 2D build's direction below was checked against the formula numerically and corrected.
- Cut size d₅₀ — raise it and a particle must be bigger to report to the clean coarse stream, so less mid-size silt qualifies: coarse recovery drops but the coarse output that remains is cleaner. Lower it and more mid-size silt now clears the (smaller) bar into coarse: more mass recovered, but more residual contamination in it.
- Scrub intensity — how aggressively coatings are stripped off coarse grains before separation; low intensity leaves contaminated films on "clean" sand.
- Wash passes — repeated rinsing of the coarse fraction, each pass removing a further fraction of what is still attached.
The coarse underflow (typically 70–90% of the original soil mass) can often be returned to site as clean fill; the fine overflow slurry is dewatered and sent for further treatment or licensed disposal — this is why soil washing works best on sandy/gravelly soils and struggles on soils that are mostly clay.
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