Rosin-Rammler Distribution
Rosin-Rammler-Sperling Distribution · Also known as: Rosin-Rammler Model, RRS Distribution, Weibull Distribution (particle size)
The Rosin-Rammler Distribution, introduced by Paul Rosin and Erich Rammler in 1933, is an empirical probability distribution that describes the particle size distribution of ground or crushed materials. It characterizes fineness by two parameters: the characteristic size (d-prime) and the uniformity index (n). This distribution is remarkably accurate for mineral processing streams and is ubiquitous in comminution engineering.
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When to use it
Use Rosin-Rammler fitting when analyzing particle size distributions in comminution processes, flotation circuits, and downstream sizing operations. It is most accurate for distributions spanning 2-3 orders of magnitude in particle size (e.g., 1 mm to 10 micrometers). Assume the material is homogeneous and that sieving errors are small. For multi-modal distributions (e.g., primary crushed material with distinct coarse and fine modes), use mixture models or alternative approaches.
Strengths & limitations
- Simple two-parameter model provides compact description of complex particle size distributions
- Empirically accurate across most mineral and ore types in industrial range
- Easy to compare distributions: two numbers (d', n) replace full sieve curves
- Enables prediction of size fractions below measured sieve sizes through extrapolation
- Computationally lightweight; readily implemented in spreadsheets or simple software
- Not accurate for bimodal or multimodal distributions (e.g., primary crushed material with distinct size peaks)
- Poor fit for very fine material (<10 micrometers) where agglomeration or electrostatic forces dominate
- Assumes continuous distribution; does not capture discrete size classes from mechanical screening
- Fitting parameters are sensitive to extremes in the sieve data; outliers can distort fitted d' and n
- Does not account for particle shape; spheres and needles with the same size have different mass-size relationships
Frequently asked
What do typical values of d-prime and n mean in industrial practice?
Characteristic sizes (d') in comminution typically range from 10 micrometers (fine grinding) to 1 mm (coarse crushing). Uniformity indices (n) range from 1 (very broad, lots of fines) to 4 (sharp, nearly mono-dispersed). n=1.5-2.5 is common for grinding; n>3 indicates very uniform product.
How do I fit the Rosin-Rammler distribution to my sieve data?
Plot cumulative % passing versus sieve size on log-log paper. The data should form a straight line. Use linear regression on the log-transformed data to extract slope (related to n) and intercept (related to d'). Spreadsheet software (Excel) can fit this with built-in regression functions. Specialized software can also fit using maximum likelihood estimation.
Can I use Rosin-Rammler for very fine material (submicron)?
The distribution loses accuracy for material much finer than 1 micrometer. Below this range, particle cohesion, electrostatic forces, and agglomeration dominate, violating the independence assumptions underlying the distribution. Use laser diffraction or specialized PSD methods for submicron material.
What does a high uniformity index (high n) tell me about grinding efficiency?
High n (sharper distribution) generally indicates efficient, controlled grinding where most material is near the target size with few large or small particles. Low n (broad distribution) suggests some material is over-ground (fines) while other material is under-ground (coarse), indicating either mixed feed quality or uncontrolled milling.
How do I compare particle size distributions from different mills?
Calculate d' and n for each distribution. Distributions with identical d' but different n have the same median size but different spreads. Use iso-plotted lines on Rosin-Rammler plots to visualize families of distributions and highlight differences in milling performance.
Sources
- Rosin, P., & Rammler, E. (1933). The laws governing the fineness of powdered coal. Journal of the Institute of Fuel, 7, 29-36. link ↗
- Austin, L. G., Klimpel, R. R., & Luckie, P. T. (2006). Process engineering of size reduction: Ball grinding mills. Society for Mining, Metallurgy & Exploration. link ↗
How to cite this page
ScholarGate. (2026, June 3). Rosin-Rammler-Sperling Distribution. ScholarGate. https://scholargate.app/en/mining-engineering/rosin-rammler-distribution
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