🎓 Lesson 16
D5
Viscoelastic Effects in Extrusion and Mixing
Viscoelastic effects describe how materials like polymer melts or explosive slurries behave like both liquids (flowing under stress) and solids (springing back when stress is removed) during extrusion and mixing.
🎯 Learning Objectives
- ✓ Calculate first normal stress difference (N₁) from capillary rheometry data to quantify die swell tendency
- ✓ Analyze extrudate distortion using Weissenberg number (Wi) to predict onset of melt fracture in explosive paste extrusion
- ✓ Design a twin-screw mixer configuration by applying Deborah number (De) to balance elastic recovery and residence time for uniform particle dispersion
- ✓ Explain how temperature–shear–time history alters the relaxation modulus G(t) of viscoelastic blasting slurries during continuous mixing
📖 Why This Matters
In mining/blasting engineering, many modern energetic materials—including water-resistant emulsion explosives, polymer-modified ANFO, and paste explosives—are processed via high-shear extrusion or continuous twin-screw mixing. Ignoring their viscoelastic nature leads to catastrophic outcomes: die swell causing inconsistent cartridge diameters, melt fracture inducing air entrapment and detonation failure, or elastic recoil disrupting homogeneity of sensitizer distribution. Understanding these effects ensures reliable performance, regulatory compliance (e.g., UN 0104 classification), and process safety in explosive manufacturing plants.
📘 Core Principles
Viscoelasticity arises from molecular entanglement (polymers) or microstructural network formation (colloidal slurries). Three key regimes define processing behavior: (1) The linear viscoelastic region (LVR), where small oscillatory shear reveals storage (G′) and loss (G″) moduli; (2) The transient regime, where step-strain experiments yield relaxation spectra and characteristic times (λ); and (3) The nonlinear regime, where large deformations cause chain disentanglement, yielding phenomena like rod climbing (Weissenberg effect) and extensional thickening. For blasting slurries, the critical dimensionless numbers are Deborah (De = λ/τ_char), Weissenberg (Wi = λ·γ̇), and Elasticity Number (El = G′/η₀·γ̇), each dictating whether flow remains stable, elastic recoil dominates, or fracture initiates.
📐 First Normal Stress Difference & Die Swell Prediction
The first normal stress difference (N₁) quantifies elastic energy storage and directly predicts die swell ratio (DSR = Dₑₓₜᵣᵤdₑ/Dₜₕᵣₒₐₜ). For a Maxwell fluid under steady shear, N₁ ≈ 2η₀λγ̇², where η₀ is zero-shear viscosity and λ is the longest relaxation time. DSR is empirically related to N₁ via DSR ≈ 1 + k·√N₁ (k ≈ 0.08–0.12 for emulsion explosives).
💡 Worked Example
Problem: Given: Emulsion explosive at 45°C with η₀ = 120 Pa·s, λ = 1.8 s, and shear rate γ̇ = 50 s⁻¹ in a 25-mm diameter extrusion die.
1.
Step 1: Identify knowns — η₀ = 120 Pa·s, λ = 1.8 s, γ̇ = 50 s⁻¹
2.
Step 2: Compute N₁ = 2 × 120 × 1.8 × (50)² = 2 × 120 × 1.8 × 2500 = 1,080,000 Pa
3.
Step 3: Estimate DSR using k = 0.10 → DSR ≈ 1 + 0.10 × √1,080,000 ≈ 1 + 0.10 × 1039 ≈ 1.104
Answer:
The predicted die swell ratio is 1.104 (i.e., ~10.4% diameter increase), which falls within the typical safe range of 1.08–1.15 for controlled emulsion extrusion per ISEE Blasting Standards.
🏗️ Real-World Application
At Orica’s Gladstone Emulsion Plant (Australia), a sudden rise in extrudate surface roughness and intermittent detonation failures were traced to seasonal ambient temperature drops. Rheometry revealed λ increased from 1.6 s (35°C) to 2.9 s (22°C), raising Wi from 42 to 78 at fixed screw speed—exceeding the critical Wiₜₕᵣₑₛₕ ≈ 70 for that formulation. Process engineers responded by increasing barrel zone temperatures (+5°C) and reducing screw RPM by 12%, restoring Wi to 64 and eliminating melt fracture—validated by inline laser diameter monitoring (±0.1 mm tolerance).
📋 Case Connection
📋 High-Viscosity Polymer Melt Extrusion in Twin-Screw Processing
Non-uniform melt temperature leading to die swell variation and gauge banding