8.2 Particle Screening, Hydrocyclone Classification & Sizing

PRC Mining Engineer Licensure Examination Philippines

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1 Chapter 1: Surface Mining Methods & Pit Optimization

1.1 Surface Mining Unit Operations & Method Selection 1.2 Bench Geometry, Slope Stability & Geotechnical Pit Design 1.3 Cut-Off Grade Optimization & Lerchs-Grossmann Pit Limits

2 Chapter 2: Underground Mining Methods & Strata Control

2.1 Underground Mining Method Classification & Selection 2.2 Rock Mechanics, Stress Analysis & Strata Control 2.3 Underground Ground Support Systems & Excavation Design

3 Chapter 3: Materials Handling, Equipment & Mine Economics

3.1 Drilling, Blasting & Explosives Engineering 3.2 Mine Loading, Haulage & Materials Handling Systems 3.3 Mine Capital (CAPEX), Operating Costs (OPEX) & Financial Evaluation

4 Chapter 4: Mine Safety, Ventilation & Philippine Mining Laws

4.1 Mine Ventilation Network Analysis & Environmental Quality 4.2 Philippine Mine Safety Rules, Health & Disaster Prevention 4.3 Philippine Mining Act of 1995 (RA 7942), DAO 2010-21 & Mining Ethics

5 Chapter 5: Physical Geology, Mineralogy & Philippine Deposit Types

5.1 Structural Geology, Tectonics & Ore Controls 5.2 Igneous, Metamorphic & Sedimentary Ore Mineralogy 5.3 Major Philippine Ore Deposit Models

6 Chapter 6: Mineral Exploration, Geophysics & Core Logging

6.1 Geochemical & Remote Sensing Exploration Techniques 6.2 Geophysical Exploration Methods in Mining Geology 6.3 Diamond Drilling, Core Logging & QA/QC Protocols

7 Chapter 7: Geostatistics, Resource Estimation & PMRC Code

7.1 Ore Body Block Modeling & Spatial Variography 7.2 Inverse Distance & Ordinary Kriging Grade Estimation 7.3 Philippine Mineral Reporting Code (PMRC 2020) & Resource Classification

8 Chapter 8: Comminution, Sizing & Physical Mineral Separation

8.1 Crushing, Grinding & Bond Work Index Calculations 8.2 Particle Screening, Hydrocyclone Classification & Sizing 8.3 Gravity Concentration & Magnetic/Electrostatic Separation

9 Chapter 9: Froth Flotation & Extractive Hydrometallurgy

9.1 Froth Flotation Chemistry, Reagents & Cell Kinetics 9.2 Leaching Technologies (Heap, Agitation & Tank) 9.3 Precious Metal Recovery: CIP, CIL, Merrill-Crowe & Electrowinning

10 Chapter 10: Process Plant Flowsheets & Environmental Tailings Management

10.1 Metallurgical Plant Flowsheets & Pulp Mass Balances 10.2 Tailings Storage Facility (TSF) Design & Dam Safety 10.3 Acid Mine Drainage (AMD) Mitigation & Environmental Protection (EPEP/FMR/DP)

11 Chapter 11: 2025 PRC Blueprint, Prospecting Tools & Exploration Decisions

11.1 Official 2025 TOS, Three-Paper Structure & Exam Strategy 11.2 Prospecting Instruments, Base Maps & Surface Geological Mapping 11.3 Integrating Direct and Indirect Evidence for Exploration Decisions

12 Chapter 12: Mine Infrastructure, Sustainable Development & Climate

12.1 Power, Water, Drainage & Support-Facility Selection 12.2 Sustainable Development, Progressive Rehabilitation & Community Impact 12.3 Mining, Climate, Reforestation, Coal & Energy-Transition Minerals

13 Chapter 13: Mine Valuation, Financial Analysis & Due Diligence

13.1 Time Value of Money, Future Value & Present Value 13.2 Financial Statements, Mine Economics & External Price Drivers 13.3 Exploration Provenance, Technical Review & Legal Due Diligence

14 Chapter 14: Mine Organization, Communication & Accountable Leadership

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15 Chapter 15: Philippine Mining Law, Indigenous Rights & Professional Ethics

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16 Chapter 16: Applied Mathematics & Mine Surveying

16.1 Engineering Mathematics for Safe, Efficient Mine Decisions 16.2 Survey Control, Instruments, Traverses & Error Adjustment 16.3 Topographic Maps, Underground Set-Out & Survey Timeliness

17 Chapter 17: Feasibility Studies, Data Quality & Project Decisions

17.1 Scoping, Pre-Feasibility & Final Feasibility Study Maturity 17.2 Data Accuracy, Assumption Control & Go/No-Go Decisions 17.3 Multidisciplinary Integration, Interfaces & Independent Review

18 Chapter 18: Mining Computer Applications, Digital Control & Global Developments

18.1 Computer Functions, Office Applications & Data Governance 18.2 Geological Modeling, Mine Planning, Scheduling & Valuation Software 18.3 Real-Time Control, Critical Minerals & Regional Mining Developments

19 Chapter 19: Earth Systems, Geologic Time & Philippine Hazards

19.1 Solar-System Origin, Earth Interior & Atmospheric Layers 19.2 Rock Cycle, Landforms & the Geologic Time Scale 19.3 Philippine Tectonics, Geologic Hazards & Mitigation

20 Chapter 20: Metallurgy, Foundry Practice & Assaying

20.1 Extractive, Physical & Adaptive Metallurgy Principles 20.2 Foundry Materials, Casting, Solidification & Defects 20.3 Sampling, Fire Assay, Cupellation, Parting & Assay Calculations

21 Chapter 21: Solid–Liquid Separation, Environmental Law & Mine Ecology

21.1 Thickening, Filtration & Solid–Liquid Separation 21.2 Philippine Air, Water, Waste & Hazardous-Substance Controls 21.3 Mine Ecology, Closure, Tailings, Waste & Community Livelihood

8.2 Particle Screening, Hydrocyclone Classification & Sizing

Key Takeaways Explain This Topic AI

Industrial screens classify mainly by passage probability relative to aperture; particle size, shape, orientation, moisture, near-size fraction, bed depth, presentation, and blinding all affect the separation.

Screen overall efficiency (E) incorporates both undersize recovery (Eu) and oversize recovery (Eo), expressed as E = Eu * Eo = [u(f - o) / f(u - o)] * [(1-o)(u-f) / (1-f)(u-o)], where f, u, and o are mass fractions of undersize in feed, undersize product, and oversize product.

Hydraulic classification separates particles based on relative settling velocity in a fluid medium; fine particles follow Stokes' Law (vt directly proportional to d^2 under laminar flow), while coarse particles obey Newton's Law (vt directly proportional to sqrt(d) under turbulent flow).

Hydrocyclone classification utilizes centrifugal force to achieve fine size separation, governed by the d50 cut size; the anomaly known as the 'fish-hook effect' causes fine particle entrainment into the underflow due to boundary layer short-circuiting.

Closed-circuit grinding loops pair ball mills with hydrocyclones to return coarse underflow back to the mill inlet, ensuring tight product size control and optimizing energy utilization.

Last updated: August 2026

Particle Screening, Hydrocyclone Classification & Sizing

Particle sizing separates a bulk mixture of broken ore into uniform size fractions. Accurate size control is essential to prevent overgrinding, avoid misplacement of coarse material into downstream flotation or leaching circuits, and optimize separation efficiency. Sizing operations in mineral processing are divided into physical screening (mechanically sizing particles on apertures) and classification (sorting particles based on settling rates in fluids).

Industrial Screening Principles & Equipment

Screening presents a bed of particles to a surface containing uniform apertures. Separation depends on particle size, bed depth, screen inclination, moisture content, and vibration amplitude.

Industrial Screen Machinery

Stationary Grizzlies : Heavy parallel steel bars sloped at 35 ∘ – 45 ∘ 35^\circ\text{--}45^\circ 3 5 ∘ – 4 5 ∘ positioned ahead of primary crushers to bypass undersize ROM ore ( < 100 mm <100\ \text{mm} < 100 mm ), preventing crusher overload.

Vibrating Screens : The standard machine for sizing between 0.5 mm 0.5\ \text{mm} 0.5 mm and 100 mm 100\ \text{mm} 100 mm . Inclined vibrating screens ( 15 ∘ – 25 ∘ 15^\circ\text{--}25^\circ 1 5 ∘ – 2 5 ∘ ) utilize eccentric shafts rotating at 800 – 1200 rpm 800\text{--}1200\ \text{rpm} 800 – 1200 rpm to stratify the material bed, bringing fine particles into contact with the mesh.

Trommel Screens : Revolving cylindrical screens inclined at a shallow angle ( 4 ∘ – 8 ∘ 4^\circ\text{--}8^\circ 4 ∘ – 8 ∘ ), widely deployed in alluvial gold and aggregate washing plants.

Screen Efficiency Mathematics

Screen performance is quantified by evaluating undersize material recovery and oversize rejection. Consider a screen receiving Mass Feed F F F with undersize fraction f f f , producing Undersize Product U U U with undersize fraction u u u , and Oversize Product O O O with undersize fraction o o o .

From overall and component mass balances: F = U + O F = U + O F = U + O F f = U u + O o F f = U u + O o F f = Uu + O o

Solving for product mass splits: U F = f − o u − o and O F = u − f u − o \frac{U}{F} = \frac{f - o}{u - o} \quad \text{and} \quad \frac{O}{F} = \frac{u - f}{u - o} F U ​ = u − o f − o ​ and F O ​ = u − o u − f ​

The Undersize Recovery ( E u E_u E u ​ ) and Oversize Recovery ( E o E_o E o ​ ) are: E u = U u F f = u ( f − o ) f ( u − o ) E_u = \frac{U u}{F f} = \frac{u(f - o)}{f(u - o)} E u ​ = F f Uu ​ = f ( u − o ) u ( f − o ) ​ E o = O ( 1 − o ) F ( 1 − f ) = ( 1 − o ) ( u − f ) ( 1 − f ) ( u − o ) E_o = \frac{O(1 - o)}{F(1 - f)} = \frac{(1 - o)(u - f)}{(1 - f)(u - o)} E o ​ = F ( 1 − f ) O ( 1 − o ) ​ = ( 1 − f ) ( u − o ) ( 1 − o ) ( u − f ) ​

The Overall Screen Efficiency ( E E E ) is the product of both efficiencies: E = E u × E o = [ u ( f − o ) f ( u − o ) ] × [ ( 1 − o ) ( u − f ) ( 1 − f ) ( u − o ) ] E = E_u \times E_o = \left[ \frac{u(f - o)}{f(u - o)} \right] \times \left[ \frac{(1 - o)(u - f)}{(1 - f)(u - o)} \right] E = E u ​ × E o ​ = [ f ( u − o ) u ( f − o ) ​ ] × [ ( 1 − f ) ( u − o ) ( 1 − o ) ( u − f ) ​ ]

Hydraulic Classification Fundamentals & Settling Laws

Classification sorts particles in a fluid medium based on terminal settling velocity ( v t v_t v t ​ ), which is governed by particle size, density, and fluid drag forces.

Terminal Settling Velocity Dynamics

When a particle falls in a fluid, gravitational force ( F g F_g F g ​ ) is balanced by buoyant force ( F b F_b F b ​ ) and drag force ( F d F_d F d ​ ). At terminal velocity, net acceleration is zero.

1. Stokes' Law (Laminar Flow, R e < 0.2 Re < 0.2 R e < 0.2 )

For fine particles ( d < 50 μ m d < 50\ \mu\text{m} d < 50 μ m ) settling slowly in viscous fluids: v t = g d 2 ( ρ s − ρ f ) 18 μ v_t = \frac{g d^2 (\rho_s - \rho_f)}{18 \mu} v t ​ = 18 μ g d 2 ( ρ s ​ − ρ f ​ ) ​

Where:

• v t v_t v t ​ = Terminal settling velocity ( m/s \text{m/s} m/s )
• g g g = Gravitational acceleration ( 9.81 m/s 2 9.81\ \text{m/s}^2 9.81 m/s 2 )
• d d d = Equivalent spherical particle diameter ( m \text{m} m )
• ρ s \rho_s ρ s ​ = Particle density ( kg/m 3 \text{kg/m}^3 kg/m 3 )
• ρ f \rho_f ρ f ​ = Fluid density ( kg/m 3 \text{kg/m}^3 kg/m 3 )
• μ \mu μ = Fluid dynamic viscosity ( Pa ⋅ s \text{Pa}\cdot\text{s} Pa ⋅ s )

Under Stokes' regime, settling velocity is directly proportional to the square of particle diameter ( d 2 d^2 d 2 ) .

2. Newton's Law (Turbulent Flow, R e > 1000 Re > 1000 R e > 1000 )

For coarse particles ( d > 2 mm d > 2\ \text{mm} d > 2 mm ) creating turbulent wakes: v t = 1.74 g d ( ρ s − ρ f ) ρ f v_t = 1.74 \sqrt{\frac{g d (\rho_s - \rho_f)}{\rho_f}} v t ​ = 1.74 ρ f ​ g d ( ρ s ​ − ρ f ​ ) ​ ​

Under Newton's regime, terminal velocity varies directly with the square root of particle diameter ( d \sqrt{d} d ​ ) .

Free vs. Hindered Settling

Free Settling : Occurs in dilute suspensions ( < 10 % <10\% < 10% solids by volume) where particles settle independently without interparticle collisions.

Hindered Settling : Occurs in dense pulp suspensions ( > 15 % >15\% > 15% solids by volume) where mutual fluid displacement creates upward interstitial velocities, reducing settling rates. Hindered settling velocity ( v h v_h v h ​ ) is calculated using the Richardson-Zaki equation: v h = v t ϵ n v_h = v_t \epsilon^n v h ​ = v t ​ ϵ n , where ϵ \epsilon ϵ is pulp voidage and n n n is an empirical exponent ( 4.65 4.65 4.65 in laminar flow).

Hydrocyclone Classification Geometry & Dynamics

A hydrocyclone is a static cylindrical-conical vessel utilizing centrifugal acceleration ( 100 G – 1000 G 100G\text{--}1000G 100 G – 1000 G ) to achieve rapid size separation in wet slurry streams.

Construction & Internal Flow Regime

Tangential Feed Inlet : Slurry is pumped under pressure ( 50 – 200 kPa 50\text{--}200\ \text{kPa} 50 – 200 kPa ) into the cylindrical chamber, generating a high-velocity outer helical downward swirl along the outer wall.

Underflow Apex / Spigot : Coarse, dense particles experiencing high centrifugal force are flung outward to the conical wall and discharge at the bottom apex as a thick underflow slurry.

Vortex Finder & Overflow : Fluid drag overcomes centrifugal force for fine, low-density particles, drawing them into an inner upward vortex that exits through the central vortex finder tube as overflow.

Cut Size ( d 50 d_{50} d 50 ​ ) & The Fish-Hook Effect

d 50 d_{50} d 50 ​ Cut Size : The specific particle size at which 50% of particles report to the underflow and 50% report to the overflow.

The Fish-Hook Effect : An anomaly in hydrocyclone partition curves where the recovery of ultra-fine particles ( − 10 μ m -10\ \mu\text{m} − 10 μ m ) to the underflow increases rather than decreasing monotonically. This can reflect water bypass and entrainment of fine particles in the underflow, including boundary-layer short-circuiting toward the apex, as well as measurement and material effects. Diagnose it with corrected partition data, water split, sampling QA/QC, and repeat tests.

Closed-Circuit Grinding-Classification Loops

Hydrocyclones operate in closed-circuit with ball mills to maximize grinding energy efficiency. +------------------------+

• | Primary Crusher |
• +-----------+------------+
• |
• v
• +----------------------+
• | SAG / Ball Mill |
• +----------+-----------+
• |
• v
• +----------------------+
• | Sump Pump |
• +----------+-----------+
• |
• v
• +----------------------+
• +------------------->| Hydrocyclone |
• | +----+------------+----+
• | | |
• | Coarse Underflow | | Fine Overflow
• +-------------------------+ v
• +------------------+
• | Flotation Plant |
• +------------------+

Mill discharge slurry is diluted in a sump pump and delivered to the hydrocyclone bank. The coarse underflow streams return to the mill inlet, while the fine overflow ( 80 % < 74 μ m 80\% < 74\ \mu\text{m} 80% < 74 μ m ) feeds flotation. Controlling feed pulp density (typically 40% to 55% solids) ensures maximum classification sharpness.

Comparison of Sizing & Classification Methods

• Feature Industrial Screening Hydrocyclone Classification
• Governing Property Geometrical particle dimensions Settling velocity (size + density)
• Effective Size Range 0.5 mm to 150 mm 0.005 mm to 0.25 mm
• Pulp Density Limit High density / dry operation 20% to 55% solids by weight
• Footprint & Capacity Large floor area requirement Very compact, high volume capacity
• Capital / Maintenance Higher wear parts cost (mesh) Low capital cost, ceramic liners

Reading Separation Performance

A screen or cyclone must be evaluated from a reconciled partition curve, not one nominal aperture or d50. For each size class, partition is the fraction reporting to a stated product. Correct for water bypass where the convention requires it, show sampling uncertainty, and confirm that feed equals products by dry mass and size distribution. The curve's d50 describes the midpoint, while its slope or probable error describes sharpness; neither alone describes misplaced mass when the feed contains many near-size particles.

For screens, near-aperture particles require repeated presentation and are sensitive to bed depth, moisture, shape, pegging and blinding. For cyclones, pressure, geometry, feed solids, viscosity, particle density and shape, apex condition, vortex finder, roping, air core and water split all affect classification. Diagnose a coarse overflow by checking feed change, pressure, wear, overload and sampling before changing one dimension. Diagnose a fine underflow upturn only after verifying size analysis and water entrainment. Equipment control should connect the measured partition to downstream circulating load, mill power, flotation liberation, dewatering, and recovery.