Rosin–Rammler equation and Numerical Example 1

 

1. Definition

The Rosin–Rammler equation is a mathematical formula used by engineers to describe the size distribution of crushed or ground particles.

Instead of listing all particle sizes, the equation creates a smooth curve using just two parameters:

  1. D63.2 (Size Modulus): The particle size at which 63.2% of the material is smaller. It shows how coarse the overall material is.
  2. λ (Lambda – Distribution Modulus): Indicates the spread of particle sizes.
      • High λ → particles mostly similar in size
      • Low λ → wide mix of very fine and coarse particles

The Formula:

P(D) = 1 – exp [ – ( D / D63.2 )λ ]

Where:
D = particle size being evaluated
P(D) = fraction (or %) passing size D

2. Numerical Example

Scenario:
A ball mill product is analyzed and found to have Rosin–Rammler parameters:

  • D63.2 = 100 µm
  • λ = 1.5

Question:
What percentage of the material is smaller than 50 µm?

Step-by-Step Calculation

1. Insert into the equation:
   P(50) = 1 – exp [ – ( 50 / 100 )1.5 ]

2. Simplify the fraction:
   50 / 100 = 0.5

3. Apply exponent 1.5:
   0.51.5 ≈ 0.354

4. Compute exponential term:
   exp(–0.354) ≈ 0.702

5. Final step:
   1 – 0.702 = 0.298

Final Answer:
Approximately 29.8% of the material is smaller than 50 µm.


Cumulative particle size distribution curve

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