ISO 19430:2024

International
Standard
ISO 19430
Second edition
Determination of particle
2024-08
size distribution and number
concentration by particle tracking
analysis (PTA)
Détermination de la distribution granulométrique et de la
concentration en nombre par l’analyse de suivi de particule (PTA)
Reference number
© ISO 2024
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ii
Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms. 6
5 Principles . 7
5.1 General .7
5.2 Measurement types .7
5.2.1 General .7
5.2.2 Particle detection.8
5.2.3 Brownian motion tracking .9
5.2.4 Gravitational motion tracking . .9
5.3 Key physical parameters .10
5.4 Limits of detection .10
5.4.1 General .10
5.4.2 Lower size limit of detection .11
5.4.3 Upper size limit of detection .11
5.4.4 Particle number concentration measurement limits . 12
5.4.5 Sample and sampling volume . 13
5.5 Measurement precision and uncertainties . 13
5.5.1 Size measurement uncertainty . 13
5.5.2 Counting efficiency .14
5.5.3 Size resolution . 15
5.5.4 Polydispersity . 15
5.5.5 Sensing volume . 15
6 Apparatus . 17
6.1 General .17
6.2 Sample cell (with sample in dispersion) .17
6.3 Illumination .17
6.4 Optical image capturing .18
6.5 Image analysis, tracking and data processing computer. . .18
7 Measurement procedure .20
7.1 General . 20
7.2 Sample preparation . 20
7.3 Instrument set-up and initialisation .21
7.4 Sample delivery . .21
7.5 Sample illumination . 22
7.6 Particle imaging and video capture . 22
7.7 Track analysis . 22
7.8 Measurements . . 23
7.8.1 Particle sizing and number-based size distribution . 23
7.8.2 Total particle number measurement .24
7.8.3 Particle background count .24
7.8.4 Volume concentration .24
7.9 Results evaluation .24
7.9.1 General .24
7.9.2 Particle size evaluation .24
7.9.3 Particle count results interpretation .24
7.9.4 Distribution analysis . 25
7.9.5 Data analysis and results display . 25
8 System qualification and quality control .25

iii
8.1 General . 25
8.2 System installation requirements . 25
8.3 System maintenance . 25
8.4 System operation . 26
8.5 Instrument qualification (for sizing) . 26
8.6 Instrument qualification (for number concentration) .27
9 Data recording .27
10 Test report .28
Annex A (informative) Theory .30
Annex B (informative) Comparative study of number concentration evaluation of gold
nanoparticles in suspension .33
Annex C (informative) Using sedimentation data with PTA .35
Annex D (informative) Serial dilution experiment .37
Bibliography .40

iv
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
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The procedures used to develop this document and those intended for its further maintenance are described
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of ISO document should be noted. This document was drafted in accordance with the editorial rules of the
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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 19430:2016), which has been technically
revised.
The main changes are as follows:
— Inclusion of particle counting and number concentration measurements.
— Inclusion of information on gravitational motion tracking.
— Inclusion of information on simultaneous multispectral detection.
— Inclusion of particle number concentration comparison to other methods.
— Inclusion of information on serial dilution for PTA.
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
Regulatory, scientific and commercial requirements for nanomaterial characterization or characterization
of particulate suspensions where particle sizing and counting is used provide a strong case for further
development of techniques such as particle tracking analysis (PTA), also known as nanoparticle tracking
[1] 1)
analysis (NTA). Due to the fact that the term PTA covers a larger size range and is more generic, the term
PTA is used throughout this document to refer to NTA and PTA.
PTA is based on measuring the diffusion movement of objects (particles, droplets or bubbles) in a dispersion,
but can also be used to undertake gravitational migration tracking by means of laser illumination, imaging
2)
of scattered light, particle identification and localization, and individual particle tracking. This document
covers two tracking regimes.
— Brownian motion tracking for smaller particles.
— Gravitational fall tracking for larger particles.
In both cases, the suspension is an even dispersion of particles, gas bubbles or other liquid droplets. The
hydrodynamic diameter of the individual particles, droplets or bubbles is related to Brownian motion
parameters via the Einstein equation and via Stokes law for gravitational migration dynamics.
In recent years, the academic community working in fields such as liposomes and other drug delivery
vehicles, nanotoxicology, viruses, exosomes, protein aggregation, inkjet inks, pigment particles, cosmetics,
foodstuffs, fuel additives and ultrafine bubbles began using the PTA technology for characterization. ASTM
E2834-12 was developed to give guidance to the measurement of particle size distribution by means of
NTA. This document aims to broaden the scope of the specification and to introduce system tests for PTA
operation as well as to extend the particle size range from nanoscale to microscale sizes. One way to do this
is to combine Brownian motion tracking with gravitational migration tracking in the same device on the
same sample.
For a number of years, the stakeholders working with nanomaterials safety, regulation, compliance and
fundamental research into applications such as biomedicine, catalysis, fuel additives and others were looking
for a method (or a combination of methods) for counting and sizing particles in a wide size range (larger
than 1 nm to 100 nm). Particle size distributions are often used to evaluate nanomaterials for regulatory
purposes (see Reference [41] on the definition of nanomaterial) or for material specification compliance. A
number of techniques are available for such characterization, but samples need to be monodisperse. A bigger
challenge is to provide an accurate particle count. Techniques such as PTA, electron microscopy, spICP-MS or
electrical sensing zone (see ISO 13319-1) allow particle count but have method-specific issues.
One of the key aspects of PTA is the interpretation of data. The key measurand obtained from PTA
measurement is the number-based particle size distribution where the size is taken to mean the
hydrodynamic diameter of the particles in the sample. The hydrodynamic particle diameters measured
[3]
with PTA can be different from equivalent particle diameters obtained with different techniques such as
dynamic light scattering (DLS) (see ISO 22412:2017) or electron microscopy (see ISO 21363 and ISO 19749).
1) NTA is the most recognised abbreviation for the technique described in this document. However, PTA includes NTA
in its size range of measurements.
2) For the purpose of this document, “tracking” is intended to mean “following in terms of particle’s x and y position”;
“track” is defined in 3.32.
vi
International Standard ISO 19430:2024(en)
Determination of particle size distribution and number
concentration by particle tracking analysis (PTA)
1 Scope
This document specifies the particle tracking analysis (PTA) method under static (no flow) conditions for
the determination of the number–based particle size distribution and the number concentration in liquid
dispersions (solid particles, liquid droplets or bubbles suspended in liquids).
This document covers two tracking regimes.
— Brownian motion tracking for smaller particles.
— Gravitational fall tracking for larger particles.
This document outlines the theory and basic principles of the PTA method along with its limitations and
advantages for both size evaluation and number concentration measurements. It also describes commonly
used instrument configurations and measurement procedures as well as system qualifications and data
reporting.
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 13322-1:2014, Particle size analysis — Image analysis methods — Part 1: Static image analysis methods
ISO/IEC 17025, General requirements for the competence of testing and calibration laboratories
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
nanoscale
length range approximately from 1 nm to 100 nm
[SOURCE: ISO 80004-1:2023, 2.1]
3.2
nanoparticle
discrete piece of material with all external dimensions in the nanoscale (3.1)
Note 1 to entry: If the dimensions differ significantly (typically by more than three times), terms such as "nanofibre"
or "nanoplate" are preferred to the term nanoparticle.
[SOURCE: ISO 80004-1:2023, 3.3.4]

3.3
particle
minute piece of matter with defined physical boundaries
Note 1 to entry: A physical boundary can also be described as an interface.
Note 2 to entry: This general particle definition applies to nano-objects.
[SOURCE: ISO 80004-1:2023, 3.2.1]
3.4
particle size
linear dimension of a particle (3.3) determined by a specified measurement method and under specified
measurement conditions
Note 1 to entry: Different methods of analysis are based on the measurement of different physical properties.
Independent of the particle property actually measured, the particle size can be reported as a linear dimension, e.g. as
an equivalent spherical diameter.
[SOURCE: ISO/TS 80004-6:2021, 3.1.1]
3.5
particle size distribution
distribution of the quantity of particles (3.3) as a function of particle size (3.4)
Note 1 to entry: Particle size distribution may be expressed as cumulative distribution or a distribution density
(distribution of the fraction of material in a size class, divided by the width of that class).
Note 2 to entry: The quantity can be, for example, number, mass or volume based.
[SOURCE: ISO/TS 80004-6:2021, 4.1.2]
3.6
equivalent diameter
diameter of a sphere that produces a response by a given particle size (3.4) measurement method that is
equivalent to the response produced by the particle (3.3) being measured
Note 1 to entry: The physical property to which the equivalent diameter refers is indicated using a suitable subscript
(see ISO 9276-1:1998).
Note 2 to entry: For discrete-particle-counting, light-scattering instruments, an equivalent optical diameter is used.
Note 3 to entry: Other material constants like density of the particle are used for the calculation of the equivalent
diameter like Stokes diameter (3.22) or sedimentation equivalent diameter. The material constants, used for the
calculation, should be reported additionally.
Note 4 to entry: For inertial instruments, the aerodynamic diameter is used. Aerodynamic diameter is the diameter of
−3
a sphere of density 1 000 kg m that has the same settling velocity as the irregular particle.
[SOURCE: ISO/TS 80004-6:2021, 4.1.5, modified — Note 1 to entry and Note 3 to entry changed.]
3.7
light scattering
change in propagation of light at the interface of two media having different optical properties
[SOURCE: ISO/TS 80004-6:2021, 4.2.5]
3.8
hydrodynamic diameter
equivalent diameter (3.6) of a particle (3.3) in a liquid having the same diffusion coefficient as a spherical
particle with no boundary layer in that liquid
Note 1 to entry: In practice, nanoparticles (3.2) in solution can be non-spherical, dynamic and solvated.

Note 2 to entry: A particle in a liquid will have a boundary layer. This is a thin layer of fluid or adsorbates close to
the solid surface, within which shear stresses significantly influence the fluid velocity distribution. The fluid velocity
varies from zero at the solid surface to the velocity of free stream flow at a certain distance away from the solid
surface.
[SOURCE: ISO/TS 80004-6:2021, 4.2.6]
3.9
particle tracking analysis
PTA
method where particles (3.3) undergoing Brownian and/or gravitational motion in a liquid suspension
(3.14) are illuminated by a laser and the change in position of individual particles is used to determine their
equivalent diameters (3.6)
Note 1 to entry: Analysis of the time-dependent particle position yields the translational diffusion coefficient and
hence the hydrodynamic diameter (3.8) using the Einstein relationship.
Note 2 to entry: Nanoparticle tracking analysis (NTA) is often used to describe PTA. NTA is a subset of PTA, since PTA
covers a length range that exceeds the nanoscale (3.1).
3.10
nanomaterial
material with any external dimension in the nanoscale (3.1) or having internal structure or surface structure
in the nanoscale
Note 1 to entry: See “engineered nanomaterial”, “manufactured nanomaterial” and “incidental nanomaterial” in
ISO 80004-1 for definitions of certain types of nanomaterial.
Note 2 to entry: The nanoform of a material is a nanomaterial.
[SOURCE: ISO 80004-1:2023, 3.1.4, modified — Reference to ISO 80004-1 added to Note 1 to entry.]
3.11
diluent
non-volatile homogeneous liquid which is used to decrease the concentration of particles (3.3) in a suspension
(3.14) without any deleterious effects such as changing particle total number, state of aggregation, particle
size (3.4) or surface chemistry
3.12
viscosity
η
ratio between the applied shear stress and rate of shear of a liquid
Note 1 to entry: It is a measure of the resistance to flow or deformation of a liquid.
Note 2 to entry: The term "dynamic viscosity" is also used in a different context to denote a frequency-dependent
quantity in which shear stress and shear rate have a sinusoidal time dependence.
[SOURCE: ISO 3104:2020, 3.2, modified — Preferred terms and Note 3 to entry have been deleted.]
3.13
dispersion
multi-phase system in which discontinuities of any state (solid, liquid or gas: discontinuous phase) are
distributed in a continuous phase of a different composition or state
Note 1 to entry: This term also refers to the act or process of producing a dispersion; in this context, the term
“dispersion process” should be used.
Note 2 to entry: If solid particles (3.3) are distributed in a liquid, the dispersion is referred to as a suspension (3.14). If
the dispersion consists of two or more immiscible liquid phases, it is termed an “emulsion”. A suspoemulsion consists
of both solid and liquid phases distributed in a continuous liquid phase.
[SOURCE: ISO/TS 80004-6:2021, 3.14]

3.14
suspension
heterogeneous mixture of materials comprising a liquid and a finely dispersed solid material
[SOURCE: ISO/TS 80004-6:2021, 3.13]
3.15
simultaneous multispectral detection
SMD
method where optically scattering objects [such as particles (3.3) or bubbles] are detected, counted and tracked
by means of particle tracking analysis (3.9), using light sources of different wavelengths and different powers.
Note 1 to entry: Detection, counting and tracking of objects is performed independently in each spectral regime.
3.16
total particle count method
particle (3.3) counting method in which the total number of particles in a certain sample volume is
determined without classification according to size
[SOURCE: ISO 29463-4:2011, 3.2]
3.17
particle counting and sizing method
particle (3.4) counting method which allows both the determination of the number of particles and also the
classification of the particles according to size
[SOURCE: ISO 29463-4:2011, 3.3]
3.18
particle number concentration
number of particles (3.3) per unit of volume of suspension (3.14)
3.19
number concentration distribution density
distribution density (frequency) of the particle number concentration (3.18) represented as a function of the
particle size (3.4)
[SOURCE: ISO 26824:2022, 3.9.5]
3.20
limit of quantification
quantification limit
LOQ
lowest amount of an analyte that is quantifiable with a given confidence level
Note 1 to entry: The confidence level can be calculated as ten times the standard deviation of blank measurement
results. This concept applies to concentration measurements only.
Note 2 to entry: The value LOQ can be used as a threshold value to assure quantitative measurement of an analyte
accurately.
[SOURCE: EN 1540:2021, 5.3.5, modified — Note 2 to entry has been modified and Note 3 to entry has been
deleted.]
3.21
limit of detection
LOD
lowest amount of an analyte that is detectable with a given confidence level
Note 1 to entry: The limit of detection can be calculated as three times the standard deviation of blank measurement
results. This represents a probability of 50 % that the analyte will not be detected when it is present at the
concentration of the LOD.
Note 2 to entry: The LOD can be used as a threshold value to assert the presence of a substance with a known
confidence.
Note 3 to entry: The LOD only refers to concentration measurements and not to particle sizing.
[SOURCE: EN 1540:2021, 5.3.4, modified — Note 3 added]
3.22
Stokes diameter
equivalent diameter (3.6) of a sphere that has the same buoyant density and terminal sedimentation velocity
as the real particle (3.3) in the same liquid under creeping flow conditions
[SOURCE: ISO 26824:2022, 3.4.4]
3.23
migration velocity
absolute value of sedimentation or creaming and flotation terminal velocity
Note 1 to entry: Velocity of creaming and flotation is indicated by a negative sign.
[SOURCE: ISO 18747-1:2018, 3.3]
3.24
migration
directed particle (3.3) movement (sedimentation or creaming and flotation) due to acting gravitational or
centrifugal fields
Note 1 to entry: Sedimentation occurs when the density of droplets or particles is larger than that of the liquid.
Creaming and flotation occur when the density of droplets or particles is smaller than that of the liquid. In these two
processes, particles move in opposite directions.
[SOURCE: ISO 18747-2:2019, 3.3]
3.25
analyte
element or constituent to be determined
[SOURCE: ISO 10136-2:1993, 3.3]
3.26
track
path of an object through space
3.27
frame
single static image obtained by a camera in a video recording process
Note 1 to entry: For the purpose of this document, the term "frame" does not include the edge of the field of view (3.31).
3.28
transparent medium
medium which has a high transmittance of light in a given spectral range
3.29
aspect ratio
ratio of length of a particle (3.3) to its width
[SOURCE: ISO 14966:2019, 3.7]
3.30
tracking
process of obtaining a track (3.26) in x and y coordinates

3.31
field of view
area viewed by the imaging probing system
[SOURCE: ISO 10360-7:2011, 3.3]
4 Symbols and abbreviated terms
For the purposes of this document, the following symbols and abbreviated terms apply.
CCD charge coupled device
CMOS complementary metal oxide semiconductor
CRMs certified reference materials
DLS dynamic light scattering
MSD mean square distance
d hydrodynamic diameter m
h
d Stokes diameter m
s
−1
v
terminal velocity m∙s
g −2
gravitational acceleration ~9,8 m∙s
−3
ρ
apparent density of the particle kg∙m
−3
ρ
density of the liquid kg∙m
2 -1
D
translational diffusion coefficient in 1 dimension m s
x
2 -1
D
translational diffusion coefficient in 2 dimensions m s
xy
2 -1
D
translational diffusion coefficient in 3 dimensions m s
xyz
-2
η viscosity of the suspension medium N∙s∙m
−1
k Boltzmann’s constant N∙m∙K
B
T absolute temperature K
t time s
2 mean square displacement in 1 dimension m
x
()
2 mean square displacement in 2 dimensions m
()xy,
2 mean square displacement in 3 dimensions m
()xy,,z
−3
C
total particle number concentration m
N
total particle number in a sampling volume
V
sensing volume m
s
N
array of values containing original total number of particles in
o
size-bins before sample dilution

−3
c
array of values containing PTA results as number of particles per  m
s
unit volume in size-bins
V
volume of diluent used m
d
V
original volume of the dispersion before dilution m
o
−3
c
array of values containing diluent number of particles per unit  m
d
volume in size-bins
−3
c
array of values containing original number of particles per unit  m
o
volume in size-bins before sample dilution
Re Reynolds number
5 Principles
5.1 General
In general, PTA can be used to detect, size and count individual particles, droplets or bubbles through
Brownian motion or gravitational fall particle dynamics. Historically, only Brownian motion was used for
particle size determination and construction of number-based particle size distribution. However, this
document covers all known particle tracking methods, thus including gravitational fall. This document is
focused on particle sizing, particle counting, particle number concentration and constructing number-based
particle size distribution.
NOTE This document is applicable to particles, droplets and bubbles in liquid dispersions which are referred to in
the text as particles.
5.2 Measurement types
5.2.1 General
Determination of particle size distribution by PTA commonly makes use of:
— Brownian motion of particles, or
— the gravitational fall or floating of particles, or
— both of the above
combined with the light scattering properties of particles suspended in liquids.
Irradiation of the sample (typically by means of one or several laser beam(s) of wavelength(s) in the
visible region) leads to light scattering by objects with a refractive index that is different from that of the
surrounding medium. Light scattered from each particle is collected by magnifying optics and visualized
by way of a suitable camera, equipped with a charge coupled device (CCD) or complementary metal oxide
semiconductor (CMOS) sensor. By recording a series of sequential images, the instrument’s software tracks
positions of particles as a function of time, allowing analysis of their movement.
[3],[4]
By tracking individual particles undergoing Brownian motion or gravitational migration (see
ISO 13317-1) from frame to frame, the average spatial displacement of the particles per unit time can be
calculated. This displacement can be related to the hydrodynamic diameter of the particles through the
[5]
Einstein equation or through Stokes law for gravitational migration of particles.
NOTE In practice, the particles are either tracked in Brownian motion regime or in gravitational migration regime.

PTA instruments use a dark field imaging configuration, with the optical capture axis (Figure 1) commonly
oriented vertically (a) or horizontally (b).
A broad range of particle sizes in a dispersion must be detected, sized and counted for the context of
this document. Different methods are used to effectively extend the size range of the PTA method. The
size working range of the method is often determined by the geometry of the instrument as well as data
processing steps, properties of the optical system, the size and optical properties of the particles. There are
a number of publications outlining optimum data processing methods used for track analysis (see ASTM
E2834-12 and Reference [6]) but their use varies from one manufacturer to another.
a) Vertical b) Horizontal
Key
1 direction of gravity
2 is optical capture
3 illumination
4 sample volume
Figure 1 — PTA configurations
The illumination may be provided by a single wavelength laser or a number of lasers with different
wavelengths and power settings, allowing for wider particle size distribution and polydispersity in the
sample. Detailed requirements for PTA instruments are outlined in Clause 6. Table 1 summarises the
availability of measurements in various instrument geometries.
Table 1 — Summary of instrument configurations and capabilities
Vertical [Figure 1 a)] Horizontal [Figure 1 b)]
Single laser Available Available
Multiple laser (SMD) Not known to exist Available
Gravitational tracking Not possible Available
Both horizontal and vertical system geometries are available with a single laser, while no vertically
orientated instruments are known to exist for multiple laser illumination. Gravitational fall tracking can
only be implemented in horizontal geometries [Figure 1 b)].
5.2.2 Particle detection
The scattering from particles in a dispersion are detected by imaging them in a dark-field mode under a
microscope which provides a quantifiable magnification. Once a microscope is combined with a camera, this
magnification shall be calibrated. This is important for evaluation of several length measurements such as

the track steps lengths used to calculate the diffusion coefficient as well as the effective field of view for the
device as this affects the effective sensing volume used for particle number concentration evaluation.
5.2.3 Brownian motion tracking
When a particle is detected on microscope images, its position is recorded as a function of time in a series
[5]
of steps making up tracks of individual particles. The underlying physics were described by Einstein. The
Navier-Stokes equation with small Reynolds number limit is solved in Formula (1), giving Formula (2):
dν
m =−3πηdFν + ()t (1)
h
dt
νρd
h 2
For Re= 1 , and because mkν = T and xF()tx= Ft() = 0 , the solution is:
B
η
4kT
2 B
r = Δt (2)
3πηd
h
where the averaging is over the assembly of particles observed. Analysis of the track is done by evaluating
the mean square distance (MSD) that single particle has travelled in 2–dimensions (2D) over N frames (with
rd
the 3 dimension parallel to the microscope axis). It has been shown that in order to replace time average
[7]
with assembly average (the so-called ergodicity), a delay (lag) of n frames should be introduced :
1 Nn−
MSDn()= ()xx− +−()yy (3)
∑ i+ni i+ni
i=1
Nn−
The diffusion coefficient D obtained by the optimised least-square fit of MSD(n) as a function of n is given by
4ΔtD n (see Annex A). Hence the resulting PTA hydrodynamic diameter d is given by:
()
h
kT
B
d = (4)
h
3ππηηD
Due to the fact that the unrestricted diffusion process in 3-dimensions (3D) is separable (see Annex A) into
x , y and z independent components, measuring x in the x direction is sufficient for particle
()
hydrodynamic diameter (d ) evaluation.
h
5.2.4 Gravitational motion tracking
Brownian motion PTA has a limit in terms of the largest particle size it can measure due to slow movement
of large particles. This limit is reached for particles of approximately a few micrometres in diameter, which
are relatively immobile. The large particles require better image processing to find particle centres and long
tracking times for appropriate measurement statistics. Particles of such a size also scatter a lot of light and
can prevent the detection and tracking of much smaller particles in the same dispersion.
In addition to the Brownian motion tracking method, it is possible to use the particle tracking data to
calculate the gravitational fall or floating dynamics of larger particles in the dispersion. This method can
only be applied in the instrument configuration in Figure 1 b), i.e. the horizontal configuration. This method
extends the range of sizes of particles that can be sized and counted by PTA to large particle fractions.
For particles exhibiting gravity-induced motion, equivalent diameters are determined from the Stokes
constant-speed falling sphere approximation (migration velocity); Stokes diameter (d ) of a tracked particle
s
is then:
18vη
d = (5)
s
g||()ρρ−
The sensitivity of gravitational motion tracking is limited to particles with densities that are different
from the dispersion medium. The sizing process is also very sensitive to the changes in liquid viscosity and

temperature. However, these parameters affect size measurements but do not directly affect the ability to
count particles in the number concentration measurement.
PTA instruments offering a gravitational sedimentation option for large particle sizing operate in a
“homogeneous mode” where the sample is homogenised at the start of the measurement. The terminal
velocity (ν) of the particle in Formula (5) is obtained by measuring the distance that a tracked particle has
travelled in vertical direction in a given time. Such vertical motion can be virtually zero for particles with
either equivalent diameters below 1 micrometre or apparent densities close to the density of the continuous
phase, or both. For larger particle sizes (typically over 1 μm diameter), the Brownian motion is negligible
compared to the gravitational migration, so they display gravitational fall with terminal velocity (ν).
The terminal velocity is often reached very quickly compared to the video acquisition time. For particles
between the purely Brownian and purely gravitational regimes, there exists a range of sizes where neither
effect dominates and neither effect can be neglected, leading to a very high uncertainty in sizing.
NOTE The particle gravitational sizing process also shows a large uncertainty for samples where continuous medium
and particles have similar densities. The effect is a very slow sedimentation because of the near-zero value of ||()ρρ− .
PTA sedimentation tracking offers an individual particle sizing method rather than the ensemble
sedimentation methods that are described in the ISO 13317 series. An example of such data sets is given in
A
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