ISO 13318-1:2024

Determination of particle size distribution by centrifugal liquid sedimentation methods - Part 1: General principles, requirements and guidance

This document specifies the principles of particle size analysis by centrifugal liquid sedimentation (CLS). It also: - defines the relevant terms; - describes the various measurement techniques; - gives guidance for sample preparation, conducting measurements as well as data analysis; - establishes rules for method validation, determination of the uncertainty budget as well as representation of results. An important part of this document deals with the derivation of particle size distributions from CLS data, including discussions on: - the impact of Brownian motion; - the parallel determination of particle concentrations; - the working range with respect to size and concentration; -the handling of non-spherical and porous particles. This document applies to samples composed of dispersions of low particle concentration, so that the particles’ motion can be considered as that of fully isolated particles. This document does not cover particle migration by gravity, electric or magnetic forces. It also does not cover deriving particle properties other than size, sedimentation velocity and sedimentation coefficient. NOTE This document can involve hazardous materials, operations and equipment. It does not purport to address all the safety problems associated with its use. Regulations regarding explosion-proof analysers can apply when examining volatile liquids with a low flash point. It is the responsibility of the user of this document to establish appropriate safety and health practices and to determine the applicability of the regulatory limitations prior to its use.

Détermination de la distribution granulométrique par les méthodes de sédimentation centrifuge dans un liquide — Partie 1: Principes généraux, exigences et orientation

General Information

• Status: Published
• Publication Date: 30-Sep-2024
• ICS: 19.120 - Particle size analysis. Sieving
• Technical Committee: ISO/TC 24/SC 4 - Particle characterization
• Drafting Committee: ISO/TC 24/SC 4/WG 2 - Sedimentation, classification
• Current Stage: 6060 - International Standard published
• Start Date: 01-Oct-2024
• Due Date: 18-Jan-2024
• Completion Date: 01-Oct-2024

Relations

• Revises: ISO 13318-1:2001 - Determination of particle size distribution by centrifugal liquid sedimentation methods - Part 1: General principles and guidelines
• Effective Date: 23-Apr-2020

Overview

ISO 13318-1:2024 - "Determination of particle size distribution by centrifugal liquid sedimentation methods - Part 1: General principles, requirements and guidance" defines the fundamental principles and practical guidance for particle sizing using centrifugal liquid sedimentation (CLS). It describes measurands (sedimentation velocity, sedimentation coefficient, Stokes diameter), measurement techniques, sample and instrument preparation, data evaluation, validation and uncertainty estimation. The standard applies to low-concentration liquid dispersions where particles behave as fully isolated entities and does not cover migration driven by gravity, electric or magnetic forces.

Key technical topics and requirements

• Measurement principles and technical realizations: Theory of centrifugal sedimentation and practical instrument implementations (analytical centrifuges).
• Primary and derived measurands: Terminal sedimentation velocity and sedimentation coefficient as primary quantities; derivation of particle size distributions (Stokes diameter) under Stokes’ law assumptions.
• Data evaluation and distribution analysis: Methods for incremental and integral measurement modes, handling conversion between measurand types, and correction for diffusion (Brownian motion).
• Limits and applicability: Typical measurable size range (from a few nanometres up to 100 µm for aqueous systems) and migration velocities (10 nm/s to 1 mm/s); concentration guidance (generally ≤ 0.5 vol% without corrections).
• Non-ideal particles: Guidance on porous, heterogeneous or non‑spherical particles and limitations when Stokes’ law is not strictly valid.
• Quality, validation and uncertainty: Rules for method validation, system qualification, use of reference materials, and construction of an uncertainty budget for velocity and size results.
• Practical procedures: Sampling, primary and secondary sample preparation, instrument setup, measurement protocols (homogeneous‑start and line‑start methods), data analysis and reporting.
• Safety note: The document cautions about hazardous materials and explosion-proof requirements when volatile low‑flash‑point liquids are used.

Practical applications and users

ISO 13318-1 is intended for laboratories and organizations performing particle characterization by CLS, including:

• Analytical and metrology laboratories
• Pharmaceutical and biotechnology R&D and QC (e.g., protein aggregates, nanoparticles)
• Materials science and nanotechnology research
• Environmental testing and colloid science
• Manufacturers of dispersions (paints, inks, cosmetics, food)
• Instrument manufacturers and method developers

Benefits include high resolution particle size distributions, first‑principle measurands from directed particle motion, and potential multi‑parameter characterization when diffusion and multiwavelength detection are used.

Related standards

• ISO 13318 series (other parts covering specific CLS techniques)
• ISO 13317-1 (gravitational liquid sedimentation - related principles)

Keywords: ISO 13318-1, centrifugal liquid sedimentation, CLS, particle size distribution, sedimentation velocity, Stokes diameter, analytical centrifuge, particle characterization, method validation, measurement uncertainty.

Standards Content (Sample)

International
Standard
ISO 13318-1
Second edition
Determination of particle size
2024-10
distribution by centrifugal liquid
sedimentation methods —
Part 1:
General principles, requirements
and guidance
Détermination de la distribution granulométrique par les
méthodes de sédimentation centrifuge dans un liquide —
Partie 1: Principes généraux, exigences et orientation
Reference number
© ISO 2024
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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Published in Switzerland
ii
Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms. 7
5 Measurement principle and technical realisations . 10
5.1 General measurement principle .10
5.2 Technical realisation of sedimentation-based centrifugal measurement techniques . 13
6 Measurement data and basic rules of data evaluation.15
6.1 Primary and derived measurands in centrifugal liquid sedimentation . 15
6.2 Spatial distribution of particles in centrifugal fields .17
6.3 Determination of distribution functions .18
6.3.1 General remarks .18
6.3.2 Distribution analysis for incremental techniques —homogeneous-start method
(HSM) .19
6.3.3 Distribution analysis for incremental techniques — line-start method (LSM) . 20
6.3.4 Distribution analysis for integral techniques .21
6.3.5 Conversion with respect to the type of quantity .21
6.3.6 Total quantity of dispersed phase and non-normalised particle size distributions . 22
6.3.7 Measurement analysis with respect to sedimentation and diffusion . 23
6.4 Deviations from Stokes-based analysis . 25
6.4.1 General . 25
6.4.2 Upper limit for sedimentation velocity and particle size . 25
6.4.3 Lower limits for particle size . 26
6.4.4 Limits for particle concentration .27
6.4.5 Handling of porous and heterogeneous particles .27
6.4.6 Handling of non-spherical particles and particle agglomerates .27
7 Performing size analyses .28
7.1 General . 28
7.2 Sampling . 28
7.3 Continuous phase and primary sample preparation . 28
7.4 Secondary sample preparation (sample conditioning) . 29
7.5 Instrument preparation . 30
7.6 Measurement . 30
7.6.1 General procedures for CLS . 30
7.6.2 Procedures for homogeneous-start method (HSM) .31
7.6.3 Procedures for line-start method (LSM) .31
7.6.4 Criteria for adjusting the rotational speed .32
7.7 Data analysis .32
7.8 Reporting . 33
8 System qualification and quality control .34
8.1 General remarks . 34
8.2 Reference materials . 35
8.3 Installation, operational and performance qualifications . 36
8.4 Sources of measurement uncertainty . 36
8.5 Accuracy and measurement of uncertainty of particle velocity and particle size . 38
8.6 Combined and expanded uncertainty of particle velocity and particle size measurement
(Stokes diameter) . 38
Annex A (informative) Particle sizing techniques based on centrifugal liquid sedimentation
(CLS) . 41

iii
Annex B (informative) Remarks on particle density .44
Annex C (informative) Sedimentation beyond the validity of Stokes’ law .50
Annex D (informative) Trueness, reproducibility and uncertainty determination for velocity
and particle size .57
Annex E (informative) Multiwavelength approach .62
Annex F (informative) Spatial distribution of particles in centrifugal fields .64
Annex G (informative) Additional particle and dispersion characteristics based on centrifugal
sedimentation velocity and sedimentation coefficient .73
Bibliography . 74

iv
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
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The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO document should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
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Any trade name used in this document is information given for the convenience of users and does not
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Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 24, Particle characterization including sieving,
Subcommittee SC 4, Particle characterization.
This second edition cancels and replaces the first edition (ISO 13318-1:2001), which has been technically
revised.
The main changes are as follows:
— revision of core terms (3.3, 3.5, 3.10, 3.11, 3.16, 3.14) and inclusion of further terms;
— revised and expanded explanation of measurement principle and techniques (Clauses 5 and 6);
— inclusion of the terminal sedimentation velocity as a measurand;
— introduction of informative annexes that provide:
— an overview of particle sizing techniques based on centrifugal liquid sedimentation (Annex A);
— remarks on particle density (Annex B);
— information regarding sedimentation beyond the validity of Stokes' law (Annex C);
— trueness, reproducibility and uncertainty determination for velocity and particle size (Annex D);
— an explanation on the multiwavelength approach (Annex E);
— a description of the spatial distribution of particles in centrifugal fields (Annex F);
— the use of CLS for particle characterization beyond the particle size and sedimentation velocity
(Annex G).
A list of all parts in the ISO 13318 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

v
Introduction
Particle size analysis by centrifugal liquid sedimentation (CLS) methods has been performed for several
decades, and there are numerous national and international standards employed in various academic and
industrial applications. Along with the development of manifold new measurement techniques during the
last two decades, sedimentation methods are currently enjoying a renaissance due to technical progress (e.g.
multiwavelength features) and the fact that most sedimentation techniques are based on the first-principle
measurement of the directed motion (migration) of particles in gravitational or centrifugal fields. The rate
of this motion is the particle sedimentation velocity, its acceleration-specific value is called "sedimentation
coefficient". Both are individual particle properties, which are related to the particles’ external dimensions,
and can be considered as primary measurands of liquid sedimentation methods.
Analytical centrifuges determine distributions of these primary measurands from the variation of
concentration-dependent signals over time and/or along the radial coordinate of the centrifugal field. This
step does not require any pre-knowledge of the dispersed or liquid phase. Further, data processing allows
for particle size distributions to be derived from sedimentation velocity and sedimentation coefficient. For
this purpose, spherical particles and the applicability of Stokes’ law are assumed; the equivalent particle
diameter is called the Stokes diameter. The conversion requires knowledge of the relevant properties of
the particles and liquids (e.g. particle shape, density or refractive index). In this regard, CLS resembles
gravitational liquid sedimentation (see ISO 13317-1 for further information).
The ISO 13318 series covers methods for characterizing dispersed materials in liquids by centrifugation
with respect to the particle size distribution and the related distributions of sedimentation velocity and
sedimentation coefficient. Their common principle is allocating a particle quantity to the rate of migratory
motion in the centrifugal field. They differ with respect to particle quantification, mode of operation and
data analysis.
The measurement techniques described in the ISO 13318 series are applicable to liquid dispersions, like
suspensions and emulsions, with the continuous phase being a Newtonian liquid. Particles and liquid should
not undergo any interactions, which cause significant changes of the dispersed phase in the course of the
measurement, such as swelling, shrinking, and dissolution. For some instrumentation, the density difference
(also called density contrast) between the dispersed and continuous phase should be limited to positive values.
The measurable particle size range depends on the properties of the materials and typically reaches from
a few nm to 100 μm for aqueous samples, whereas the migration velocity can be quantified for the range of
10 nm/s to 1 mm/s. Sedimentation analysis is conducted for low particle concentrations. The permissible
range of concentration depends on the measurement technique and theory of analysis; with no correction, it
is typically no higher than 0,5 vol%.
As a fractionating technique, sedimentation analysis allows for distinguishing between particle fractions of
close sedimentation velocity and the corresponding equivalent Stokes diameter. Accordingly, particle size
distributions can be finely resolved, which is an advantage compared to spectroscopic ensemble techniques.
Finally, CLS techniques principally offer the chance to characterize liquid dispersions beyond sedimentational
particle properties (see Annex G). For instance, some CLS techniques facilitate the quantification of the total
and fractional particle concentration. Moreover, if particles are very fine, i.e. in the case of nanoparticles
such as protein aggregates or quantum dots, the diffusional flux of particles can be in the order of the
sedimentation flux. Such a situation allows a multidimensional characterization of particle systems, i.e. the
simultaneous determination of more than one distributed quantity (e.g. particle size and density or shape
factor).
vi
International Standard ISO 13318-1:2024(en)
Determination of particle size distribution by centrifugal
liquid sedimentation methods —
Part 1:
General principles, requirements and guidance
1 Scope
This document specifies the principles of particle size analysis by centrifugal liquid sedimentation (CLS). It also:
— defines the relevant terms;
— describes the various measurement techniques;
— gives guidance for sample preparation, conducting measurements as well as data analysis;
— establishes rules for method validation, determination of the uncertainty budget as well as representation
of results.
An important part of this document deals with the derivation of particle size distributions from CLS data,
including discussions on:
— the impact of Brownian motion;
— the parallel determination of particle concentrations;
— the working range with respect to size and concentration;
—the handling of non-spherical and porous particles.
This document applies to samples composed of dispersions of low particle concentration, so that the
particles’ motion can be considered as that of fully isolated particles. This document does not cover particle
migration by gravity, electric or magnetic forces. It also does not cover deriving particle properties other
than size, sedimentation velocity and sedimentation coefficient.
NOTE This document can involve hazardous materials, operations and equipment. It does not purport to address
all the safety problems associated with its use. Regulations regarding explosion-proof analysers can apply when
examining volatile liquids with a low flash point. It is the responsibility of the user of this document to establish
appropriate safety and health practices and to determine the applicability of the regulatory limitations prior to its use.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 9276-1, Representation of results of particle size analysis — Part 1: Graphical representation
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
sedimentation
directional motion of particles (3.7) in a viscous liquid under the action of gravity or centrifugal fields
Note 1 to entry: For a positive density contrast (3.18), sedimentation occurs in the direction of centrifugal acceleration;
it is counter directed to this acceleration for a negative density contrast.
Note 2 to entry: An outward motion due to centrifugal force is also called "settling" or "falling".
Note 3 to entry: An inward motion due to centrifugal force is also called "creaming" (e.g. droplets) or, more generally,
"rising" and "floating".
[SOURCE: ISO 13317-1:2024, 3.1, modified — notes are adapted for centrifugal liquid sedimentation]
3.2
migration
directional motion of particles in a viscous liquid under the action of a force field
Note 1 to entry: Migration in gravitational or centrifugal fields is called sedimentation (3.1).
[SOURCE: ISO 13317-1:2024, 3.2]
3.3
terminal sedimentation velocity
sedimentation velocity in the case that gravity or the centrifugal force is completely balanced by buoyancy
and the drag force
[SOURCE: ISO 13317-1:2024, 3.3]
3.4
sedimentation coefficient
velocity of sedimentation divided by the acceleration of the force field (gravitation or centrifugation)
[1]
[SOURCE: IUPAC Gold book ]
3.5
Stokes diameter
equivalent diameter of a sphere that has the same buoyant density (3.17) and terminal sedimentation velocity
(3.3) as the real particle in the same liquid under creeping flow (3.20) conditions
Note 1 to entry: The general rule that the buoyant density is used for calculating the Stokes diameter also applies to
coated particles or multiconstituent particles (such as droplets in multiple emulsions). The buoyant density can be
approximated with the skeleton density (3.15) for monoconstituent particles.
Note 2 to entry: For porous particles, it is common use to compute particle size based on the apparent particle density
(3.16). This approach considers the stagnant liquid in the open pores (3.10) as intrinsic constituent of the dispersed
phase. Thus, the obtained size values are hydrodynamic equivalent diameters.
Note 3 to entry: For close-packed agglomerates or aggregates, the buoyant density can be replaced by the apparent
particle density, with "particle" referring to the agglomerate or aggregate, in order to get the hydrodynamic equivalent
diameter.
[SOURCE: ISO 13317-1:2024, 3.4]

3.6
shape correction factor
ratio of the sedimentation velocity of a non-spherical particle to the one of a spherical particle of the same
volume and apparent particle density (3.16)
[SOURCE: ISO 13317-1:2024, 3.5]
3.7
hindrance function
ratio of the terminal sedimentation velocity (3.3) of a particle placed in well-mixed dispersion to its
sedimentation velocity in an infinite vessel in the absence of other particles
[SOURCE: ISO 13317-1:2024, 3.6, modified "divided by" changed to "to" and "for" changed to "in".]
3.8
particle
minute piece of matter with defined physical boundaries
[SOURCE: ISO 26824:2022, 3.1.1, modified — Notes 1, 2 and 3 to entry have been deleted.]
3.9
agglomerate
collection of weakly or medium-strongly bound particles (3.8) where the resulting external surface area is
similar to the sum of the surface areas of the individual components
Note 1 to entry: The forces holding an agglomerate together are weak forces such as, for example, van der Waals forces
or simple physical entanglement.
Note 2 to entry: Agglomerates are also termed secondary particles and the original source particles are termed
primary particles.
[SOURCE: ISO 26824:2022, 3.1.2]
3.10
open pore
pore that is not totally enclosed by its walls and is open to the particle surface, either directly or by
interconnecting with other pores, and is therefore accessible to liquid
[SOURCE: ISO 15901-1:2016, 3.11, modified — the word "fluid" is replaced by "liquid" and "surface" is
changed to "particle surface".]
3.11
closed pore
pore that is totally enclosed by its walls and, hence not interconnecting with other pores and not accessible
by liquids
[SOURCE: ISO 15901-1:2016, 3.10, modified— the word "fluids" is replaced by "by liquids".]
3.12
dynamic viscosity
measure of flow resistance for Newtonian liquids, calculated as the ratio of the shear stress to the rate of
shear for laminar flow exposed to a pre-set shear stress or strain
[SOURCE: ISO 13317-1:2024, 3.11]
3.13
apparent viscosity
measure of flow resistance for non-Newtonian liquids at a defined shear stress or strain, calculated as the
ratio of the shear stress to the shear rate
[SOURCE: ISO 13317-1:2024, 3.12]

3.14
true density of the dispersed phase
ratio of mass to volume for a body solely consisting of the dispersed phase without pores, voids, inclusions
or surface fissures
[SOURCE: ISO 13317-1:2024, 3.13]
3.15
skeleton density
ratio of the sample mass to the volume of the sample, including the volume of closed pores (3.11) (if present)
but excluding the volume of open pores (3.10)
Note 1 to entry: The skeleton density refers to solid particles and is determined for samples of dry powder.
[SOURCE: ISO 12154:2014, 3.3, modified — reference to the volume of void spaces between particles within
the bulk sample is removed and Note 1 is added]
3.16
apparent particle density
effective particle density
ratio of mass to volume for a particle including particulate inclusions, entrapped stagnant liquid and gas in
pores, voids and surface fissures as well as surface layers and coatings
Note 1 to entry: The apparent particle density is the density of a migrating entity and is calculated as the weighted
average of its constituents.
Note 2 to entry: The apparent particle density depends on the wettability of open pores (3.10) and the kinetics of
wetting or the replacement of pore liquid. Therefore, it is affected by sample preparation.
Note 3 to entry: The apparent particle density is not identical with the buoyant density (3.17). They deviate from each
other for porous particles and particle agglomerates (3.8) in particular.
[SOURCE: ISO 13317-1:2024, 3.15]
3.17
buoyant density
ratio of mass to volume for a particle (3.7) including particulate inclusions, liquid and gas in closed pores
(3.11) and voids, as well as surface layers and coatings, but excluding the liquid continuous phase that
penetrates open pores (3.10)
Note 1 to entry: The buoyant density equals the (hypothetical) density of the continuous phase for which the
gravitational force acting on the immersed particle is counterbalanced by buoyancy.
Note 2 to entry: The buoyant density of a particle can be experimentally determined. See ISO 18747-1 and ISO 18747-2
for further information.
Note 3 to entry: The buoyant density of monoconstituent particles can be approximated with their skeleton density (3.15).
Note 4 to entry: The buoyant density of multiconstituent particles (e.g. coated pigments and droplets of multiple
emulsions) can be approximated with the averaged densities of the single constituents.
Note 5 to entry: The buoyant density is affected by the adsorption of dissolved species at the particle surface and,
therefore, depends on the solvent and its composition.
Note 6 to entry: The buoyant density is not identical with the apparent particle density (3.16), particularly for porous
particles and particle agglomerates.
[SOURCE: ISO 13317-1:2024, 3.16]

3.18
density contrast
difference between the particle density and the density of the continuous phase
Note 1 to entry: For quantifying the density contrast, the buoyant (particle) density (3.17) is used, but for porous
particles the apparent particle density (3.16) is more appropriate.
[SOURCE: ISO 13317-1:2024, 3.17]
3.19
particle Reynolds number
dimensionless parameter expressing the ratio of inertial to viscous forces within a fluid flowing past a
particle
Note 1 to entry: The particle Reynolds number is based on the volume equivalent diameter.
Note 2 to entry: In other contexts, the definition of the particle Reynolds number can refer to different equivalent
diameters or to the equivalent radii.
Note 3 to entry: The particle Reynolds number is a characteristic of the flow field and mobility of the particle.
[SOURCE: ISO 13317-1:2024, 3.18]
3.20
creeping flow
type of flow solely governed by viscous forces and not affected by inertial forces
Note 1 to entry: For moving particles or for the flow past a particle, the creeping flow condition applies if the particle
Reynolds number (3.19) is well below 0,25.
[SOURCE: ISO 13317-1:2024, 3.19]
3.21
Brownian motion
random motion of particles caused by collisions with the molecules or atoms of the surrounding
continuous phase
Note 1 to entry: The trajectory of Brownian motion is not differentiable.
Note 2 to entry: Brownian motion results on a macroscopic level in mass transport of the dispersed phase, e. g., in case
of diffusion, thermophoresis or photophoresis.
[SOURCE: ISO 13317-1:2024, 3.20]
3.22
lower size limit
size of the smallest particles that are detectable and with a diffusional particle flux that is negligible
compared to the sedimentational one
Note 1 to entry: The ratio of sedimentational flux to diffusional flux (also called Péclet number, Pe) should be > 1.
[SOURCE: ISO 13317-1:2024, 3.21]
3.23
upper size limit
size of the largest particle that satisfies the condition of creeping flow (3.20) and of which the terminal
sedimentation velocity (3.3) is detectable
[SOURCE: ISO 13317-1:2024, 3.22]

3.24
type of quantity
specification of the physical property employed to quantify the individual particle fractions
Note 1 to entry: The type of quantity is a cumulable property of single particles or disperse systems, such as number,
mass, intensity of scattered light (within the single scattering limit), light extinction (within the Lambert-Beer-limit),
refractive index increment or X-ray attenuation.
Note 2 to entry: The type of quantity is indicated by a numerical or character subscript when symbolising the density
and cumulative function of a size distribution. Moreover, the subscript also specifies distribution parameters such as
median, mean and modal values or any quantiles.
Note 3 to entry: The following conventions apply for the subscript of geometric or gravimetric properties:
number: subscript r = 0
length: subscript r = 1
area: subscript r = 2
volume or mass: subscript r = 3
Note 4 to entry: The following conventions apply for the subscript of physical properties:
light extinction: subscript toq = “ext”
light intensity: subscript toq = “int”
[SOURCE: ISO 9276-1:1998, 4.3, modified — the definition and notes are expanded to include frequently
used, non-geometrical quantities.]
3.25
sensitivity
change of instrument response with respect to changes in concentration or absolute quantity of particles in
a specified size class
Note 1 to entry: Concentration or quantity can be given in relative or absolute values depending on the detection aim.
Note 2 to entry: Sensitivity depends on the type of quantity (3.24).
Note 3 to entry: Sensitivity is a function of size.
[SOURCE: ISO 13317-1:2024. 3.24]
3.26
limit of quantity detection
smallest quantity of specified particle size class for which the instrument response can be distinguished
from the background
Note 1 to entry: The limit of quantity detection depends on factors such as the size range, precision, noise level,
smoothing algorithms, etc.
Note 2 to entry: The limit of quantity detection affects the lower (3.22) and upper size limit (3.23).
[SOURCE: ISO 13317-1:2024, 3.25]
3.27
measurement uncertainty
uncertainty of measurement
parameter associated with the result of a measurement that characterizes the dispersion of the values that
can reasonably be attributed to the measurand
[SOURCE: ISO/IEC Guide 98-3:2008, 2.2.3, modified — the term "measurement uncertainty" has been added]

3.28
homogeneous-start method
HSM
method characterized by measurement cell(s) filled with a homogeneously mixed dispersion
3.29
line-start method
LSM
method characterized by measurement cell(s) filled with a thin layer of the sample either on top or below a
particle free (spin) liquid depending on the density contrast of the dispersed and continuous phase
4 Symbols and abbreviated terms
For the purposes of this document, the following symbols apply. In some cases, an alternative SI unit is given
in parentheses in the right column.
Ar Archimedes number 1
-2 -2
a centrifugal acceleration m·s (cm·s )
c
b systematic deviation of measured value from true value varying
C drag coefficient 1
D
C relative centrifugal acceleration 1
rel
C concentration density of particle size being indicated by the index "toq" varying
toq

C concentration density of the sedimentation coefficient with respect to the type varying
toq
of quantity being indicated by an index
2 -1 2 -1
D particle diffusion coefficient m ·s (µm ·s )
p
c particle concentration with respect to a specified index "toq" varying
toq
F drag force (also known as "hydrodynamic resistance") N
D
-2 -2
g gravitational acceleration m·s (cm·s )
H hindrance function 1
-2 -1
K auxiliary coefficient of centrifugation m ·s
c
-23 -1 -1
k Boltzmann’s constant, k = 1,380 649×10 J·K J·K
B B
k shape correction factor 1
shape
Lj Ljaščenko number 1
M is the amount of dispersed phase quantified by a specified property varying
disp
Pe Péclet number 1
Q cumulative function of distributed quantity, index “toq” indicates which of the 1
toq
fractions are weighted
-1
q density function of particle size, index “toq” indicates which of the fractions m
toq
are weighted
-1

q density function of sedimentation coefficient, index “toq” indicates which of s
toq
the fractions are weighted
Re particle Reynolds number 1
p
r radial distance from rotor axis, radial coordinate m
S signal of CLS measurement, being proportional to particle concentration varying
T absolute temperature K
t time
t sedimentation time s
sed
U expanded uncertainty of a measurand varying
u uncertainty of a measurand varying
-1 -1
v terminal sedimentation velocity m·s (µm·s )
sed
-1 -1
v terminal sedimentation velocity for creeping flow (Stokes regime) m·s (µm·s )
Stokes
x particle size m (µm, nm)
x Stokes diameter m (µm, nm)
Stokes
Δr radial sedimentation distance m
Δρ density contrast between the dispersed and continuous phase
ε porosity 1
η viscosity of the continuous phase N·s/m (Pa·s)
c
θ volume fraction of open pores that is filled with liquid 1

κ ,κ
kernel functions of Formulae (22) and (23), respectively 1
-3 -3
ρ density of the continuous phase kg·m (g·cm )
c
-3 -3
ρ particle density kg·m (g·cm )
p
τ sedimentation coefficient s
sed
φ volume fraction of the dispersed phase 1
V
Ψ sphericity 1
-1
ω angular frequency rad·s
For the purposes of this document, the following subscripts apply.

0 initial state, start position
aggl agglomerate, aggregate
app apparent
bias bias, deviation from true value
bouy bouyancy
c continuous phase
cr critical
d dispersed phase
incl inclusions
max maximum
meas measurement position
min minimum
occl occluded voids
ref reference
rel relative
rep repeatability
RMS root mean square, quadratic mean
Rw reproducibility
sed sedimentation
sk skeleton
toq type of quantity
tot total
For the purposes of this document, the following abbreviated terms apply.
CLS centrifugal liquid sedimentation
CRM certified reference material
DBM direct boundary method
HSM homogeneous-start method
LSM line-start method
QCM quality control material
RCA relative centrifugal acceleration
RM reference material
5 Measurement principle and technical realisations
5.1 General measurement principle
1)
Centrifugal liquid sedimentation (CLS) techniques quantify the separation of particles (dispersed phase)
from a liquid (continuous phase) under the presence of a centrifugal force. This phase separation relies on
the directional, migratory motion of each particle, which this document refers to as "sedimentation". Its
rate is called the "sedimentation velocity", while the acceleration-specific rate is named the "sedimentation
coefficient". Both depend on the particle size and, thus, offer a chance for the granulometric characterization
of particle systems. Additional factors are particle shape and the particle density.
NOTE 1 CLS techniques are generally called “sedimentation techniques” in this document, irrespective of whether
the particles move along or against a centrifugal force.
CLS occurs for any particle dispersed in a quiescent viscous liquid and exposed to a centrifugal field, as
long as a density contrast exists. It is driven by centrifugal forces that act on the particle (weight) and the
displaced liquid (buoyancy). The resulting net force (excess force) causes a migratory directed particle
motion, which is retarded by a frictional force (also called the drag force). The drag force increases linearly
with the migration velocity. If the excess force is positive (i.e. weight > buoyancy), the particle motion is called
falling or settling. In the opposite case, it is called rising, creaming or floating. In contrast to gravitational
sedimentation (see ISO 13317-1), particle motion never reaches a true steady state as the centrifugal force
depends on the radial position (in relation to the centre of rotation) and thus changes in the course of
sedimentation (see 6.1). Particles settling outwards are steadily accelerated whereas creaming, i.e. inwards
moving, particles experience a gradual deceleration. Nevertheless, the time scale of this alteration is much
larger than the time scale of viscous relaxation. Hence, the particles are considered to be in a quasi-steady
state, which means that at each radial position, they move with the terminal sedimentation velocity [see
Formula (4)] they would achieve if the local force field prevailed at all radial positions.
The main advantage of centrifugal versus gravitational liquid sedimentation is in the considerably higher
and more variable driving force, which allows the characterization of nanosized particles and facilitates a
broadening of the measurement range. Particle size analysis for CLS is typically conducted at centrifugal
accelerations of 10 × g to about 25 000 × g. Yet some instruments (analytical ultracentrifugation) can even
realise rotation speeds of up to 60 000 rpm corresponding to centrifugal accelerations considerably above
100 000 × g, which facilitates an expanded characterization to very fine objects, such as macromolecules
[2]
or quantum dots, and may include shape and material analyses. It is common to calculate the relative
centrifugal acceleration (RCA) as a ratio of the centrifugal to gravitational acceleration. This dimensionless
parameter relates the time scales of sedimentation phenomena under gravity to those in centrifugal fields.
Sedimentation results in a size-dependent separation of dispersed particles from the liquid, which coincides
with classification in the case of polydisperse materials. These effects can be employed to measure the
particle size distribution. In CLS there are two principal approaches (see Figure 1).
— One approach is a gradual demixing of a homogenously mixed dispersion [i.e. the homogeneous-start
method (HSM)], which consists of the following:
— an initially homogenous sample undergoes a gradual depletion of the dispersed phase which leads to
the formation of a particle layer at the outermost or innermost cell position for settling and creaming,
respectively;
— in HSM, depletion occurs as successive separation of the respective largest particles at a given
position and time;
1) CLS techniques are also referred to as analytical centrifugation. Instruments are called analytical centrifuges.

— within the dispersed phase, a concentration gradient is observed, which is directed to the
aforementioned particle layer.
— The other approach is a chromatography-like separation in a particle-free medium (i.e LSM), which
consists of the following:
— a thin layer of the particle sample is placed on the top of a particle-free liquid (supernatant or spin
liquid);
— particles move through this “stationary phase” according to their size and density;
— polydisperse materials are split into separate bands, which contain all particles of a certain size and
density fraction;
— this kind of separation requires density gradients within the supernatant or spin liquid in order to
avoid instabilities and attain a high size resolution.
Particle motion in centrifugal fields occurs along radial trajectories at a steadily increasing or decreasing
velocity resulting in a change of the particle concentration, which is independent from the separation
between fine and coarse particles. A radial dilution is observed for settling particles (i.e. for positive
density contrast), which is due to the divergence of the trajectories and to the acceleration along the
sedimentation path. The effect is particularly comprehensible for the LSM. Radial acceleration broadens the
chromatographic band, while radial divergence widens its perimeter. As the total amount of particles within
the band remains constant, their concentration becomes reduced.
Key
r radial coordinate, starting at the axis of rotation
t sedimentation time
t two successive time points
1/2
A1 particle-free supernatant
A2 depleted dispersion phase (due to loss of coars
...