Screening & Classification

Separating particles by size. Learn screens (vibrating, grizzly, banana), screen efficiency, hydrocyclones and the cut size d₅₀, Stokes' law settling, equal-settling particles, partition curves, and circulating load in closed grinding circuits.

Size control keeps crushers and mills efficient and delivers the right particle size to separation. Screens handle coarse particles (> ≈ 1 mm); hydrocyclones classify fine particles in water by settling rate, which depends on both size and density.

An analogy

A screen is a kitchen sieve; a hydrocyclone is a whirlpool that throws heavy, coarse particles to the wall and lets fine, light ones escape through the middle.

Screens

Grizzlies scalp coarse rock before crushers; vibrating screens (single/double deck) size crushed ore; banana screens handle high tonnage; wet screens remove fines. Blinding, pegging and wear reduce efficiency.

Settling and hydrocyclones

In a cyclone, slurry spins; coarse/dense particles move to the wall and exit the underflow (spigot), fines report to overflow (vortex finder). Because settling depends on density, fine heavy particles (e.g. gold, galena) often report to the underflow and get overground.

Closed circuits

Ball mills discharge to cyclones; underflow returns to the mill. Circulating loads of 150–350 % are typical — higher loads reduce overgrinding but need more pumping.

Partition curves

The partition (Tromp) curve shows the fraction of each size reporting to underflow; the imperfection or sharpness index describes efficiency. Fine screens (Derrick stack sizers) can replace cyclones for sharper cuts.

Formulas

• Stokes' law: v_t = g d² (ρ_s − ρ_f) / (18 μ)
• Circulating load (by size): CL = (o − f) / (f − u) (fractions passing a size in overflow, feed, underflow)
• Screen efficiency: E = undersize passed / undersize in feed

Worked example: Stokes settling

Given: 50 µm quartz-like particle, ρ 2700; Water μ 0.001 Pa·s

Find: v_t.

• v = 9.81 × (50 × 10⁻⁶)² × 1700/(18 × 0.001)
• = 2.32 × 10⁻³ m/s

Answer: 2.3 mm/s

Worked example: Circulating load

Given: % −75 µm: overflow 80, feed 45, underflow 25

Find: CL.

• CL = (80 − 45)/(45 − 25) = 1.75

Answer: 175 %

Common mistakes

• Wrong: Applying Stokes' law to coarse particles. — Right: Stokes is valid only at low Reynolds number (fine particles).
• Wrong: Ignoring density in classification. — Right: Heavy minerals concentrate in the circulating load.

Applications

• Grinding circuits: Cyclone clusters controlling product size.
• Aggregate plants: Screens produce sized construction products.
• Gravity recovery: Capturing heavy minerals in cyclone underflow.

Key takeaways

• Screens for coarse, cyclones for fine.
• v_t = gd²Δρ/(18μ).
• CL = (o − f)/(f − u).
• Density affects classification.

Going further

• Plitt model: Empirical cyclone d₅₀ and sharpness prediction.
• Fine screening: Stack sizers replacing cyclones.
• Mass balancing: Least-squares reconciliation of plant surveys.