How Does the Shape Factor of Protein and Starch Particles Influence Air Classification Efficiency

In pulse dry‑fractionation air separation, performance is governed not only by particle size and true density, but also by particle shape factor. Shape factor describes how much a real particle deviates from an ideal smooth sphere. Irregular, flaky, angular or porous particles behave differently in air flow compared with spherical particles of identical mass and true density.

Milled pulse flour produces two main particle populations:

1. Starch‑rich particles: Native starch granules are roughly spherical / oval. After gentle milling, many remain near‑spherical; over‑grinding creates fragmented angular starch pieces.
2. Protein‑rich particles: Liberated protein‑body aggregates are typically irregular, angular, rough, and often porous, non‑spherical. Protein matrices tend to form jagged, plate‑like or clumpy morphologies after impact grinding.

Shape changes a particle’s aerodynamic drag coefficient, altering its effective aerodynamic diameter. This distorts both size‑based classification inside the air‑classifier mill and downstream density‑based protein‑starch separation. Even with perfect PSD and correct true‑density differences, poor particle shape can reduce separation purity and recovery.

Definition of Shape Factor in Pulse Powder Processing

Shape factor quantifies departure from spherical geometry:

• Spherical particle: shape factor ≈ 1.0, low drag coefficient.
• Irregular / angular / porous / flaky particle: shape factor << 1.0, higher drag coefficient.

Aerodynamic diameter is the diameter of a theoretical sphere that has identical settling behaviour in air as the real particle.
An irregular non‑spherical particle will have a larger aerodynamic diameter than its geometric size, due to higher air‑drag.

Shape‑Factor Effects on Size‑Based Classification (Air‑Classifier Mill)

Inside the integrated air‑classifier mill, the dynamic classifier wheel separates particles by aerodynamic behaviour. Shape directly shifts the effective cut‑point.

1. Irregular protein‑rich aggregates (high drag)
   For the same geometric size and true density, irregular protein particles experience higher air drag. They are more easily carried along by the air stream through the classifier wheel.

• Outcome: Some coarser‑geometric‑size protein aggregates pass through to finished flour, even though their physical dimension would suggest they should be rejected as oversize.

2. Near‑spherical starch granules (low drag)
   Spherical starch has lower drag. For equal geometric size, spherical starch particles are less easily lifted by air flow.

• Outcome: Finer‑geometric‑size starch granules may be rejected back to grinding zone, even though their actual physical size should allow them to pass.

Net consequence in the mill:

The actual PSD of output flour deviates from laser‑diffraction geometric‑size expectations. Laser diffraction measures geometric particle size; the classifier reacts to aerodynamic size modified by shape. Highly irregular particle populations broaden the PSD span, even with stable classifier‑wheel speed and feed rate.

Shape‑Factor Effects on Downstream Density‑Based Air Separation (Protein‑starch fractionation)

Density‑based separation relies on balancing centrifugal/inertial forces versus aerodynamic drag. Shape‑driven drag changes can override true‑density differences — the primary separation driver.

Scenario 1: Well‑liberated particles (ideal case)

• Spherical starch granules: low drag, lower true density (~1.25‑1.30 g/cm³). Tend to follow air flow toward starch‑rich fraction.
• Irregular protein aggregates: higher drag, higher true density (~1.35‑1.45 g/cm³). Inertia dominates, move toward protein‑rich fraction.
  Separation works reliably.

Scenario 2: Negative shape‑factor interference (real‑world milling)

1. Flat / flaky protein fragments
   Thin plate‑shaped protein particles have extremely high drag. Even with high true density, air drag dominates inertial force. Instead of reporting to protein concentrate, these protein fragments get carried by air into the starch stream → protein recovery drops.
2. Compact dense starch agglomerates
   Starch can form compact near‑spherical composite clumps. Low drag behaviour, combined with higher aggregate bulk density. These starch‑rich particles behave aerodynamically like high‑density protein particles and wrongly migrate into the protein concentrate → protein concentrate purity drops.
3. Un‑liberated composite particles (protein‑starch glued together)
   These composites take irregular angular shapes. Their bulk density is intermediate, and shape is variable. They split randomly into both product streams, creating cross‑contamination regardless of tuning parameters.

Milling‑Process Conditions That Modify Particle Shape Factor

Milling parameters directly change resulting particle morphology for pulse flour:

1. Excessive over‑grinding (too‑low feed rate, too‑high classifier speed)
   Produces many sharp‑fragmented, highly irregular protein and starch pieces. Shape‑factor distribution broadens; drag variability increases, separation efficiency degrades.
2. Overheating and plastic smearing (high‑moisture feed, over‑feeding)
   Heat‑sticky material does not fracture brittle‑style. Instead, particles smear, deform and form rounded‑lumpy composite agglomerates. This creates mixed‑shape composite particles which defeat density separation.
3. Optimum milling window (D90 10‑65 μm, correct moisture 8‑11 %)
   Brittle fracture dominates. Protein bodies break into moderately irregular aggregates; starch largely retains near‑spherical granular shape. Shape‑factor difference between protein‑rich and starch‑rich particles remains distinct, supporting good downstream separation.

Cryogenic grinding promotes brittle fracture, produces sharper‑fractured particle morphology; ambient over‑heating produces smeared, deformed agglomerated shapes.

Practical Quality Implications & Troubleshooting

1. You can achieve target D90 10‑65 μm by laser‑diffraction measurement, yet still get poor dry‑fractionation performance. One common root‑cause is unfavourable particle‑shape distribution. Laser diffraction reports geometric size, it does not measure shape factor.
2. Symptoms linked to poor shape‑factor distribution:
   • Protein concentrate purity cannot rise despite ideal PSD.
   • Significant protein loss into starch fraction.
   • Changing separator air‑speed / rotor‑speed gives limited improvement; cross‑contamination persists.
3. Process‑adjustment guidelines for shape‑related issues:
   • Operate within correct feed‑moisture window (8‑11 %) to avoid smearing‑type particle deformation.
   • Avoid over‑grinding; prevent excessive sharp fragmented ultrafine particles.
   • Ensure sufficient liberation: minimise un‑broken protein‑starch composite agglomerates.
   • Optimise feed‑rate; avoid chamber over‑loading which causes plastic deformation instead of brittle fracture.

Particle shape factor modifies aerodynamic drag and effective aerodynamic diameter, independent of geometric size and true density. Irregular protein‑rich aggregates have higher drag, while native starch granules are more spherical with lower drag.

In size‑based classification inside the air‑classifier mill, shape shifts the effective cut‑point and can broaden PSD span. In downstream density‑based separation, unfavourable particle shapes may override true‑density differences, causing protein loss in starch stream or starch contamination in protein concentrate.

Maintaining brittle fracture conditions (correct moisture, well‑tuned milling parameters, avoiding over‑grinding and thermal smearing) preserves the natural shape differences between liberated protein‑rich and starch‑rich particles, which is essential to maximise dry‑fractionation efficiency.