Why the Square Root of Two in Particle Size Distribution?

In metallurgical testing, particle size distribution plays a crucial role in understanding material behavior in grinding, flotation, and leaching processes. But why do we often see size fractions follow a √2 progression (e.g., 75 µm, 106 µm, 150 µm, 212 µm, etc.)?

📌 The Reason? Consistency & Comparability
The square root of two (~1.414) ensures each size class boundary increases by approximately 41%, maintaining a uniform logarithmic scale. This approach:
✔ Minimizes bias when analyzing distribution curves
✔ Ensures statistical significance in partitioning fines, mid-range, and coarse fractions
✔ Aligns with industry standards (ISO, Tyler series, ASTM, and others)

📊 When working with grind size targets, flotation efficiency, or leaching kinetics, maintaining a consistent particle size scaling is key to ensuring reproducibility across different test campaigns.