MaximaLabs

Dense-medium separator simulation

ore (+ medium) -> sinks + floats (Tromp partition on particle density)

Governing equations

The exact equations the solver works for a dense-medium separator — the same math shown in the app's "Theory" panel, not a black box.

P(ρ)=11+exp⁡(ln⁡3 (ρ50−ρ)/Ep)P(\rho) = \frac{1}{1 + \exp\big(\ln 3\,(\rho_{50} - \rho)/E_p\big)}
Ep=12(ρ75−ρ25),Ep(d)=Ep (dref/d)nE_p = \tfrac{1}{2}(\rho_{75} - \rho_{25}),\quad E_p(d) = E_p\,(d_{ref}/d)^{n}
ρparticle=(∑mwm/ρm)−1\rho_{particle} = \Big(\sum_m w_m/\rho_m\Big)^{-1}
P(ρ)P(\rho)
fraction of particles of density ρ reporting to the sinks
ρ50\rho_{50}
cut density — half the particles report to the sinks [kg/m^3]
EpE_p
écart probable [kg/m^3]
ρ25,ρ75\rho_{25}, \rho_{75}
densities with 25% and 75% to the sinks [kg/m^3]
dref,nd_{ref}, n
reference size [m] and exponent of the Ep size scaling
wm,ρmw_m, \rho_m
mass share and density of mineral m in a particle
ρparticle\rho_{particle}
particle density [kg/m^3]

Parameters

cut_density_kg_m3 [kg/m^3, required — the Tromp ρ50], ecart_probable_kg_m3 [kg/m^3, required — Ep = (ρ75 − ρ25)/2; 0 = perfect]; optional ep_reference_size_m [m] + ep_size_exponent [-] (Ep(d) = Ep·(d_ref/d)^n), mineral_densities_kg_m3 [{mineral: kg/m^3} — else the feed's mineral_texture, else the cited table], valuable_mineral + grain_size_m [m] (liberation: composites sort on their own density), liquid_to_sinks [0..1, required with a liquid inlet], assay [{name: {mineral: mass fraction}} — e.g. p2o5 publishes P2O5 and BPL grades]. Needs solids.psd + psd_minerals

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