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Rosin Rammler

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Rosin-Rammler cumulative distribution

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Rosin CDF
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Rosin CDF

Rosin CDF Calculator

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doubleRosin_CDF(	double	`Dm`
	int	`n`
	double	`D`	)

The Rosin-Rammler distribution is frequently used to describe the particle size distribution of powers of various types and sizes. The function is particularyly suited to representing particles generated by grinding, milling and crushing operations. The conventional Rosin-Rammler function is described by

$R = exp \left [ - \left ( \frac{D}{D_m} \right )^n \right ]$

(1)

where R is the retained weight fraction of particles with a diameter greater than D, D is the particle size and

is the mean particle size, and n is a measure of the spread of particle sizes.

The Cumulative Distribution Function (CDF) is therefore

$R_{cdf} = 1- exp \left [ - \left ( \frac{D}{D_m} \right )^n \right ]$

(2)

As an additional note, the PDF is:

$R_{pdf} = -\frac{n}{D} \left ( \frac{D}{D_m} \right )^n exp \left [- \left( \frac{D}{D_m} \right )^n \right ]$

(3)

$\graph Dm=0.1e-3, n=2, D=0:0.3e-3$

If you have observed data, then a least square regression analysis can used to fit the data points.

References

K.M. Djamarani and I.M. Clark, 1997. Powder Technology, Elsevier Science. 93, No 2, pp. 101-108(8)

Parameters

Dm	mean particle diameter
n	measure of the spread of particle sizes
D	particle size

Authors

Will Bateman (2006)

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