Each particle's terminal settling velocity follows Stokes' law (valid for the low-Reynolds-number regime these grain sizes sit in), corrected for hindered settling in a concentrated slurry by the Richardson–Zaki relation:
v_t = 2·r²·(ρ_p − ρ_w)·g / (9·μ)
v_h = v_t · (1 − φ)^4.65 (φ = slurry solids fraction)
A particle reports to the underflow (washed product) if its hindered settling velocity exceeds the upward wash-water velocity, and to the overflow (slime/loss stream) otherwise:
net = v_h − v_wash
net > 0 → underflow (kept)
net < 0 → overflow (discarded)
Clay grains (2–15 µm) settle orders of magnitude slower than bauxite grains (60–350 µm) at the same density, so raising the wash velocity clears clay to overflow — but push it too far and it starts entraining fine, valuable bauxite too, which shows up as Al₂O₃ loss. The cut size d₅₀ is solved from the same equation for the wash velocity in use: the grain radius exactly balanced by the current flow.