🎓 Lesson 14
D5
Elutriation, Percolation, and Trajectory Sorting: Root Causes
Elutriation, percolation, and trajectory sorting are three natural ways that particles separate by size or density when moving through air or falling in bulk flow—like how fine dust floats away while heavy rocks sink or bounce differently.
🎯 Learning Objectives
- ✓ Explain the physical drivers (drag, gravity, interstitial pressure) behind elutriation, percolation, and trajectory sorting using force-balance reasoning
- ✓ Analyze a chute or transfer point design to identify dominant segregation mechanism(s) and quantify risk using particle Reynolds number and Froude number criteria
- ✓ Design mitigation features (e.g., baffles, controlled drop heights, fluidization barriers) based on segregation mechanism root cause
- ✓ Calculate terminal velocity and critical elutriation velocity for a given particle-size distribution and air velocity profile
📖 Why This Matters
In copper concentrate handling at Escondida or iron ore blending at Roy Hill, unplanned segregation causes assay variance >15%, leading to smelter penalties, regrind overload, and stockpile heterogeneity that triggers safety-critical slope failures. Understanding *why* segregation happens—not just that it does—is essential to designing robust, low-maintenance material handling systems. These three mechanisms operate simultaneously but respond to different controls: airflow governs elutriation; fill dynamics and vibration govern percolation; and drop geometry and particle inertia govern trajectory sorting.
📘 Core Principles
Elutriation is governed by the balance between upward drag force (F_D = 0.5·ρ_f·C_D·A_p·v²) and downward gravitational force (F_G = (ρ_p − ρ_f)·g·V_p). When local air velocity exceeds the critical elutriation velocity (v_ce), fines entrain. Percolation arises from kinetic energy dissipation in granular flow: under vibration or compaction, small particles exploit temporary voids created by rearranging larger particles—a process modeled via the 'Brazil nut effect' inverse and quantified by the dimensionless acceleration ratio Γ = Aω²/g. Trajectory sorting emerges from differences in particle inertia and drag: high-density, spherical particles follow near-parabolic paths; low-density, flaky particles deviate significantly due to lift and turbulence—captured by Stokes’ law deviations and the Archimedes number (Ar = g·d³·(ρ_p − ρ_f)·ρ_f / μ²). All three mechanisms scale with particle size ratio (d_max/d_min > 3:1), moisture content (<5% w/w amplifies elutriation), and system throughput rate.
📐 Critical Elutriation Velocity
The minimum upward fluid velocity required to suspend a particle of given size and density. Used to size dust extraction hoods, evaluate chute ventilation, and specify allowable belt speeds near transfer points.
Critical Elutriation Velocity (v_ce)
v_ce = √[4g·d·(ρ_p − ρ_f) / (3·ρ_f·C_D)]Minimum upward fluid velocity to suspend a spherical particle of diameter d and density ρ_p in fluid of density ρ_f and dynamic viscosity μ.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| v_ce | Critical elutriation velocity | m/s | Minimum upward fluid velocity to suspend particle |
| g | Gravitational acceleration | m/s² | Standard acceleration due to gravity |
| d | Particle diameter | m | Equivalent spherical diameter of particle |
| ρ_p | Particle density | kg/m³ | True density of solid particle |
| ρ_f | Fluid density | kg/m³ | Density of surrounding air or water |
| C_D | Drag coefficient | dimensionless | Function of Reynolds number; approximated as 24/Re + 0.44 for 1 < Re < 1000 |
Typical Ranges:
Dry coal fines (−75 μm): 0.12 – 0.25 m/s
Iron ore fines (−106 μm): 0.15 – 0.30 m/s
Wet clay aggregates (−200 μm): 0.03 – 0.10 m/s
💡 Worked Example
Problem: Calculate v_ce for a 75-μm quartz particle (ρ_p = 2650 kg/m³) in ambient air (ρ_f = 1.2 kg/m³, μ = 1.8×10⁻⁵ Pa·s) at 25°C.
1.
Step 1: Compute particle diameter d = 75 × 10⁻⁶ m
2.
Step 2: Calculate Archimedes number: Ar = g·d³·(ρ_p − ρ_f)·ρ_f / μ² = 9.81 × (75e-6)³ × (2650−1.2) × 1.2 / (1.8e-5)² ≈ 4.12
3.
Step 3: Since Ar < 1000, use the intermediate drag regime correlation: v_ce = [4g·d·(ρ_p − ρ_f)/(3·ρ_f·C_D)]^0.5; estimate C_D ≈ 24/Re + 0.44 (iterative solution yields Re ≈ 12.3 → C_D ≈ 2.37); then v_ce ≈ 0.17 m/s
Answer:
The critical elutriation velocity is 0.17 m/s. At chute exit air velocities >0.2 m/s (common in unshielded transfers), this size fraction will be airborne—confirming need for localized aspiration or flow straightening.
🏗️ Real-World Application
At BHP’s Yandi Operations, a 1200 t/h iron ore transfer chute exhibited 23% Fe-grade variation across a 30-m stockpile face. Root-cause analysis revealed: (1) elutriation of −150 μm hematite fines into recirculated ventilation air (measured v_air = 0.32 m/s at chute throat); (2) percolation-driven fines migration into base layers during vibratory feeder start-up (Γ = 8.1 > threshold 5.0); and (3) trajectory sorting causing coarse (+10 mm) oolitic particles to land 4.2 m downstream vs. fines landing 2.7 m—due to 3.1× higher mass inertia. Mitigation combined a low-velocity air curtain (v < 0.1 m/s), stepped impact plates to reduce drop height to <0.8 m, and a vibrating grizzly with 8-mm aperture to pre-screen fines before transfer—reducing assay variance to <4%.
🔧 Interactive Calculator
🔧 Open Grain Handling System Flow Dynamics & Blockage Prevention Calculator📋 Case Connection
📋 Pacific Northwest Wheat Export Terminal Conveyor Segregation Control
Size- and protein-based segregation causing grade noncompliance in railcar loading