🎓 Lesson 3
D2
Cohesion and Wall Friction: Laboratory Testing and Field Correlation
Cohesion is how strongly grain particles stick together, and wall friction is how much resistance grains feel when sliding against a surface like a silo wall.
🎯 Learning Objectives
- ✓ Calculate wall friction angle (δ) from shear cell test data using graphical or regression methods
- ✓ Analyze cohesion values to classify flowability (e.g., cohesive, easy-flowing) per ASTM D6773 and Jenike standards
- ✓ Explain how cohesion and wall friction jointly determine minimum hopper outlet size using the ‘flow factor’ and ‘critical outlet diameter’ equations
- ✓ Apply laboratory-measured c and δ to design mass-flow hoppers per ASME B20.1 and CEMA guidelines
📖 Why This Matters
Over 65% of grain handling blockages—especially in wheat, barley, and soybean systems—are caused by unanticipated cohesive arching or ratholing due to underestimated cohesion or wall friction. In one 2022 Midwest elevator incident, a 4.2 m diameter silo experienced 72-hour flow stoppage after rain increased moisture content by just 1.8%, raising cohesion from 1.2 kPa to 4.7 kPa—beyond the design margin. Understanding and measuring these properties isn’t academic: it directly determines whether your system flows reliably—or shuts down production.
📘 Core Principles
Cohesion arises from van der Waals forces, liquid bridges (capillary), electrostatic attraction, and interlocking in fine particles (<100 µm). It diminishes with drying, aeration, or vibration—but increases sharply near the critical moisture content (CMC). Wall friction depends on surface roughness, particle shape, moisture, and wall material: stainless steel yields δ ≈ 12–18° for dry wheat; rubber-lined walls reduce δ to 8–12° but may increase cohesion via static charge. The Jenike shear cell model treats bulk solids as Coulomb materials: shear stress τ = c + σ tan φ, where φ is the effective internal friction angle. For wall interfaces, τ_wall = σ_n tan δ, where σ_n is normal stress. Flowability classification (e.g., 'free-flowing' vs. 'cohesive') integrates both c and φ via the flow function FF = σ_1 / σ_c, where σ_c is the unconfined yield strength derived from c and φ.
📐 Critical Outlet Diameter for Mass Flow
The minimum hopper outlet diameter (D_min) ensures mass flow (no ratholing) and is calculated using the flow factor (ff), unconfined yield strength (σ_c), and bulk density (ρ_b). It relies on cohesion (c) and wall friction angle (δ) through empirical hopper geometry relationships defined in Jenike’s method.
💡 Worked Example
Problem: Given: wheat flour (moisture 13.2%), measured cohesion c = 3.1 kPa, internal friction angle φ = 42°, wall friction angle δ = 16.5° on mild steel, bulk density ρ_b = 820 kg/m³, gravitational acceleration g = 9.81 m/s². Determine D_min for a conical hopper with semi-included angle θ = 30°.
1.
Step 1: From Jenike charts (or interpolation), δ = 16.5° and θ = 30° give flow factor ff ≈ 1.52.
2.
Step 2: Calculate unconfined yield strength: σ_c = c × (1 + sin φ)/(1 − sin φ) = 3.1 × (1 + sin42°)/(1 − sin42°) ≈ 3.1 × 3.74 ≈ 11.6 kPa.
3.
Step 3: Apply D_min = (σ_c × ff) / (ρ_b × g) = (11,600 × 1.52) / (820 × 9.81) ≈ 17,632 / 8044 ≈ 2.19 m.
Answer:
The minimum outlet diameter is 2.19 m, which exceeds the typical safe lower limit of 1.8 m for wheat-based powders—confirming mass flow is achievable with this geometry.
🏗️ Real-World Application
At the Port of Vancouver Grain Terminal (2021), engineers redesigned a 12,000-tonne capacity leg silo handling malted barley after repeated bridging at the transition hopper. Laboratory shear testing revealed c = 4.8 kPa (vs. assumed 1.5 kPa) and δ = 19.2° on galvanized steel—attributed to diastatic enzyme activity increasing surface tackiness. Using Jenike analysis, they increased the hopper angle from 25° to 40°, lined walls with UHMW-PE (reducing δ to 11.5°), and installed air-assisted fluidization pads. Post-modification, zero flow interruptions occurred over 18 months of continuous operation—validating field correlation of lab-derived c and δ.