Reference ID: MET-1D2B | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Segregation‑tendency assessment is a rapid, empirical screening tool that quantifies how likely a free‑flowing, dry granular mixture is to demix during handling, conveying, or storage. In Process Engineering it is the first filter that formulators, packaging engineers, and QA/QC teams apply when designing breakfast cereals, snack mixes, pharmaceutical granules, cement blends or any multi‑particulate consumer product where visible layer separation is considered a quality failure. The method is intentionally pragmatic: by combining only the difference in mean particle size and the difference in bulk density it produces a dimensionless Segregation Number that can be compared to industry benchmarks without detailed powder‑rheology rigs or DEM simulations. When extra rigour is required, the Hausner ratio calculation for bulk density is simultaneously evaluated to capture flowability as an additional segregation driver.
Methodology & Formulas
All variables are in practical units: millimetres for diameter and kg m⁻³ for density. The following sequence mirrors the source code and must be executed in order.
Size Ratio
\(R = d_{large}\;/\;{\rm max}(d_{small},\;1\times10^{-9})\)
Density Difference
\(\Delta\rho = |\,ρ_{large,\ loose} - ρ_{small,\ loose}\,|\)
Segregation Number
\(N_{seg} = R \cdot \frac{\Delta\rho}{100 \, \text{kg m}^{-3}}\)
Risk Category
Dimensionless criterion
Risk
\(N_{seg}\;<\;0.4\)
low
\(0.4\le N_{seg}\le 0.8\)
medium
\(N_{seg}\;>\;0.8\)
high
Flowability Flag
Hausner value
Interpretation for segregation propensity
H < 1.15
free-flowing (segregates easily)
1.15 ≤ H ≤ 1.25
moderate flowability (segregation propensity depends on other factors)
H > 1.25
cohesive (self-masking, segregation suppressed)
Before using the correlation, abort if any operating variable lies outside the validated ranges below:
Quantity
Unit
Empirically validated span
particle size
mm
0.1 ≤ d ≤ 10
density difference
kg m⁻³
0 ≤ Δρ ≤ 600
Hausner ratio
-
1.0 ≤ H ≤ 1.5
All calculations are algebraic; no numerical values are permitted in the final equations.
Key drivers are particle size distribution, particle density, shape, and surface moisture. Use sieving, laser diffraction, and tap density tests to quantify these properties. Combine the results in a Jenike segregation tester or rotating drum to generate a segregation index under simulated process conditions.
Scale-up using dimensionless numbers (Froude, Stokes) to match shear rates between lab rig and silo/transfer chute.
Calibrate Discrete Element Method (DEM) models with lab segregation indices; validate against plant sampling at transfer points.
Set acceptable segregation limit as ±5% variation in critical component assay across batch composite samples.
If predicted variation exceeds limit, modify chute angles, add static mixers, or install mass-flow hoppers to re-blend.
Install NIR or LIBS probes at conveyor transfer points; combine signals via multivariate SPC to detect component drift >2σ. Tie alarms to automatic diverter gates to quarantine off-spec streams while continuing production of in-spec material.
Run a shortened three-level segregation test (low, mid, high shear) within 48 h of any supplier or spec change. If the new segregation index deviates >10% from baseline, repeat full Jenike test and update DEM parameters before releasing the batch to production.
Worked Example: Segregation Tendency Assessment for a Breakfast Cereal Mix
A process engineer is evaluating the segregation tendency of a dry, free-flowing breakfast cereal blend consisting of puffed rice and dried raisins under ambient, steady-state conditions. The particles are near-spherical, and the system operates below the fluidization velocity.
Known Input Parameters:
Particle size of puffed rice (small component), \( d_{\text{small}} \): 5.000 mm
Particle size of dried raisins (large component), \( d_{\text{large}} \): 10.000 mm
Loose bulk density of puffed rice, \( \rho_{\text{small, loose}} \): 120.000 kg m⁻³
Tapped bulk density of puffed rice, \( \rho_{\text{small, tapped}} \): 132.000 kg m⁻³
Loose bulk density of dried raisins, \( \rho_{\text{large, loose}} \): 640.000 kg m⁻³
Tapped bulk density of dried raisins, \( \rho_{\text{large, tapped}} \): 720.000 kg m⁻³
Step-by-Step Calculation:
Validate that input parameters are within the empirical correlation range:
Both ratios are within the valid range (1.000–1.500).
Compute size ratio (\( R \)):
\( R = \frac{d_{\text{large}}}{d_{\text{small}}} = \frac{10.000}{5.000} = 2.000 \)
Compute absolute density difference (\( \Delta\rho \)):
\( \Delta\rho = |\rho_{\text{large, loose}} - \rho_{\text{small, loose}}| = |640.000 - 120.000| = 520.000 \, \text{kg m}^{-3} \)
This is below the 600.000 kg m⁻³ limit, so the correlation is valid.
Compute the segregation number (\( N_{\text{seg}} \)) for quick ranking:
\( N_{\text{seg}} = R \times \frac{\Delta\rho}{100 \, \text{kg m}^{-3}} = 2.000 \times \frac{520.000 \, \text{kg m}^{-3}}{100 \, \text{kg m}^{-3}} = 10.400 \)
Determine segregation risk using empirical thresholds for free-flowing, dry food powders:
If \( N_{\text{seg}} < 0.400 \): low risk.
If \( 0.400 \leq N_{\text{seg}} \leq 0.800 \): medium risk.
If \( N_{\text{seg}} > 0.800 \): high risk.
Since \( N_{\text{seg}} = 10.400 > 0.800 \), the risk is high.
Final Answer: The segregation number \( N_{\text{seg}} \) is 10.400, indicating a high risk of segregation for this breakfast cereal mixture under the given conditions.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
