ISO 9276-2:2014
Representation of results of particle size analysis — Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions
ISO 9276-2:2014 provides relevant equations and coherent nomenclatures for the calculation of moments, mean particle sizes and standard deviations from a given particle size distribution. Two notation systems in common use are described. One is the method of moments while the second describes the moment-ratio method. The size distribution may be available as a histogram or as an analytical function.
The equivalent diameter of a particle of any shape is taken as the size of that particle. Particle shape factors are not taken into account. Samples of particles measured are intended to be representative of the population of particles.
For both notation systems, numerical examples of the calculation of mean particle sizes and standard deviation from histogram data are presented in an annex.
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Section sec_1
Section sec_2
Section sec_3
Section sec_4
Section sec_4.1
Section sec_4.2
Section sec_4.2.1
Table tab_1
Section sec_4.2.2
Section sec_4.2.3
Section sec_4.2.4
Section sec_4.2.5
Section sec_4.3
Section sec_4.3.1
Section sec_4.3.2
Section sec_4.4
Section sec_4.5
Section sec_4.6
Section sec_5
Section sec_5.1
Section sec_5.2
Section sec_5.2.1
Table tab_2
Section sec_5.2.2
Section sec_5.2.3
Section sec_5.3
Section sec_5.4
Section sec_5.5
Section sec_5.6
Section sec_6
Table tab_3
Section sec_7
Annex sec_A
Table tab_A.1
Table tab_A.2
Table tab_A.3
Annex sec_B
Table tab_B.1
Table tab_B.2
Table tab_B.3
Annex sec_C
Table tab_e
Figure fig_C.1
Reference ref_1
Reference ref_2
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Reference ref_5
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Foreword
Introduction
1 Scope
2 Normative references
3 Definitions, symbols and abbreviated terms
4 The moment-notation
4.1 Definition of moments according to the moment-notation
4.2 Definition of mean particle sizes according to the moment-notation
4.3 Calculation of moments and mean particle sizes from a given size distribution
4.4 Variance and standard deviation of a particle size distribution
4.5 Calculation of moments and mean particle sizes from a lognormal distribution
4.6 Calculation of volume specific surface area and the Sauter mean diameter
5 The moment-ratio-notation
5.1 Definition of moments according to the moment-ratio-notation
5.2 Definition of mean particle sizes according to the moment-ratio-notation
5.3 Calculation of mean particle sizes from a given size distribution
5.4 Variance and standard deviation of a particle size distribution
5.5 Relationships between mean particle sizes
5.6 Calculation of volume specific surface area and the Sauter mean diameter
6 Relationship between moment-notation and moment-ratio-notation
7 Accuracy of calculated particle size distribution parameters
Annex A (informative) Numerical example for calculation of mean particle sizes and standard deviation from a histogram of a volume based size distribution
Annex B (informative) Numerical example for calculation of mean particle sizes and standard deviation from a histogram of a volume based size distribution
Annex C (informative) Accuracy of calculated particle size distribution parameters
Bibliography
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Section sec_1
Section sec_2
Section sec_3
Section sec_4
Section sec_4.1
Section sec_4.2
Section sec_4.2.1
Table tab_1
Section sec_4.2.2
Section sec_4.2.3
Section sec_4.2.4
Section sec_4.2.5
Section sec_4.3
Section sec_4.3.1
Section sec_4.3.2
Section sec_4.4
Section sec_4.5
Section sec_4.6
Section sec_5
Section sec_5.1
Section sec_5.2
Section sec_5.2.1
Table tab_2
Section sec_5.2.2
Section sec_5.2.3
Section sec_5.3
Section sec_5.4
Section sec_5.5
Section sec_5.6
Section sec_6
Table tab_3
Section sec_7
Annex sec_A
Table tab_A.1
Table tab_A.2
Table tab_A.3
Annex sec_B
Table tab_B.1
Table tab_B.2
Table tab_B.3
Annex sec_C
Table tab_e
Figure fig_C.1
Reference ref_1
Reference ref_2
Reference ref_3
Reference ref_4
Reference ref_5
Reference ref_6
Reference ref_7
Reference ref_8
Reference ref_9
Reference ref_10
Reference ref_11
Reference ref_12
Reference ref_13
Reference ref_14
Reference ref_15
Foreword
Introduction
1 Scope
2 Normative references
3 Definitions, symbols and abbreviated terms
4 The moment-notation
4.1 Definition of moments according to the moment-notation
4.2 Definition of mean particle sizes according to the moment-notation
4.3 Calculation of moments and mean particle sizes from a given size distribution
4.4 Variance and standard deviation of a particle size distribution
4.5 Calculation of moments and mean particle sizes from a lognormal distribution
4.6 Calculation of volume specific surface area and the Sauter mean diameter
5 The moment-ratio-notation
5.1 Definition of moments according to the moment-ratio-notation
5.2 Definition of mean particle sizes according to the moment-ratio-notation
5.3 Calculation of mean particle sizes from a given size distribution
5.4 Variance and standard deviation of a particle size distribution
5.5 Relationships between mean particle sizes
5.6 Calculation of volume specific surface area and the Sauter mean diameter
6 Relationship between moment-notation and moment-ratio-notation
7 Accuracy of calculated particle size distribution parameters
Annex A (informative) Numerical example for calculation of mean particle sizes and standard deviation from a histogram of a volume based size distribution
Annex B (informative) Numerical example for calculation of mean particle sizes and standard deviation from a histogram of a volume based size distribution
Annex C (informative) Accuracy of calculated particle size distribution parameters
Bibliography