ISO 18747-2:2019

© ISO 2019 – All rights reserved
INTERNATIONAL STANDARD
Deleted: /FDIS
2019-06
ISO TC 24/SC 4
Secretariat: BSI
Determination of particle density by sedimentation methods — Part 2: Multi-
velocity approach
Détermination de la densité de particules par méthodes de sédimentation — Partie 2:
Approche à multi vitesses
© ISO 2019, Published in Switzerland
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ii © ISO 2019 – All rights reserved

Contents
Foreword . 5
Introduction. 6
1  Scope . 1
2  Normative references . 1
3  Terms and definitions . 1
4  Symbols . 2
5  Basic principle of the method . 2
Figure 1 — Schematic structures of particles (cross section) with regard to the measurand
particle density . 3
6  Measuring techniques to determine sedimentation and creaming/flotation velocity
of dispersed particles . 4
7  Preparation of samples . 5
7.1  Continuous phase liquids . 5
7.2  Dispersing procedure . 5
8  Measurements and data analysis . 6
Table 1 — Stock emulsion diluted with mixtures of H O and D O of different fractions,
2 2
density and dynamic viscosity of continuous phase (tuned by normal and heavy
water mixtures) and harmonic mean separation velocity of dispersed oil droplets
calculated from velocity distributions (see Figure B.1) . 6
Figure 2 — Experimental determined droplet density of polydimethylsiloxane emulsion . 7
9  Reference materials and measurement uncertainty . 7
9.1  Reference materials . 7
9.2  Measurement uncertainty . 8
Annex A (informative) Isopycnic density gradient (buoyant density) centrifugation . 9
Annex B (informative) Examples of measurements and data analysis to determine particle
density by multi-velocity approach . 10
B.1  Density determination of liquid particles (droplets) of polydimethylsiloxane
emulsion . 10
Figure B.1 — Creaming of dispersed phase (oil droplets) during centrifugation . 10
B.2  Density determination of spherical monodisperse polystyrene (PS) particles . 11
Figure B.2 — Cumulative velocity distributions and densities of monodisperse polystyrene
particles (x = 1,1 µm) dispersed in water and in five different concentrated sucrose
solutions . 12
B.3  Density determination of non-spherical reference particles produced from pine
pollen . 12
Figure B.3 — Cumulative velocity distributions of solid non-spherical microparticles
produced from pine pollen and pairwise calculated particle density according to
Formula (3) for three different percentiles . 13
© ISO 2019 – All rights reserved iii

Annex C (informative) Uncertainty derivation of particle density based on uncertainty
propagation rules . 14
Bibliography . 17

iv © ISO 2019 – All rights reserved

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national
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see www.iso.org/iso/foreword.html. Deleted: www.iso.org/iso/foreword.ht
ml
This document was prepared by Technical Committee ISO/TC 24, Particle characterization including
sieving, Subcommittee SC 4, Particle characterization.
A list of all parts in the ISO 18747 series can be found on the ISO website.
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© ISO 2019 – All rights reserved v

Introduction
Dispersions are widely used in industry and everyday life. There is a need to understand the density of
dispersed particles or droplets, e.g. for physico‐chemical calculations such as kinematic viscosity of
[1] [2][3] [4]
dispersions , determination of particle size distribution by sedimentation or acoustic techniques ,
[5]
particle characterization by field‐flow approaches , optimization of dispersion long‐term stability by
[6]
density matching as well as, more generally, characterization of particles (e.g. composition, internal
phase content of double emulsions or homogeneity of hollow capsules) in manifold academic and
industrial areas. Nowadays there is an increasing interest in using particle density to estimate the mass
transfer of nanoparticles atop cell layers by sedimentation (dosage calculation for in vitro nanotoxicity
[7][8][9]
assessment ).
The density of a body is defined as its mass divided by its volume. This calculation is straightforward for
a large uniform body or particle. However, determination of the volume of a macroscopic body is
difficult. The geometrical volume (defined by length, width and thickness) and the volume relevant for
the determination of density may differ due to surface irregularities, fractures, fissures and pores or the
measuring techniques employed.
Density determination of micro‐particles, especially nanoparticles dispersed in a liquid, is difficult not
only due to the determination of mass and volume for small particles, but also due to the fuzzy
[10]
boundary between the liquid and the particle, which is often described in terms of a corona . Liquid
and solute molecules in the continuous phase are partially immobilized at the surface. Physico‐chemical
properties (e.g. viscosity, ion composition, solute concentration) in the fuzzy coat differ from the bulk.
This effect is especially important for small microparticles and nanoparticles that are dispersed in a
[11]
polymer or biological media . The so‐called corona may be interpreted as an integral part of the
particle and increases the effective/apparent volume compared to the space occupied by the dry
particle. The thickness of this layer ranges between a few to tens of nanometres. The effective/apparent
volume deviates increasingly from the “geometrical” volume of dry particles as the particles become
smaller. Correspondingly, density determination by traditional methods is affected. These concerns
hold also for particle size, which may refer to different geometrical and physical properties. In the
context of this document, the Stokes diameter and diameter of the enveloping sphere/hull are
particularly relevant.
vi © ISO 2019 – All rights reserved

Determination of particle density by sedimentation methods —
Part 2: Multi-velocity approach
1 Scope
This document specifies an in situ method for the determination of the density of solid particles or
liquid droplets (herein referred to as “particle”) dispersed in liquid continuous phase. The method is
based on direct experimental determination of particle velocity in these liquids or media in
gravitational or centrifugal fields based on Stokes law. The particle density is calculated from
experimentally determined particle velocities in different liquids or media, taking into account their
dynamic viscosities and densities, respectively. The approach does not require the knowledge of
particle size distribution but assumes that sedimentation relevant characteristics (e.g. volume, shape,
agglomeration state) do not change. This document does not consider polydispersity with regard to
particle density, i.e. all particles are assumed to be of the same material composition.
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 14887, Sample preparation — Dispersing procedures for powders in liquids
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/ Deleted: http://www.electropedia.or
g/
— ISO Online browsing platform: available at https://www.iso.org/obp Deleted: https://www.iso.org/obp
3.1
buoyant density
ratio of particle mass to particle volume including filled or closed pores as well as adjacent layers of
liquid or other coating materials
3.2
dynamic viscosity
measure of the resistance of a fluid which is being deformed by shear stress
Note 1 to entry: Dynamic viscosity is calculated by shear stress divided by shear rate and determines the
dynamics of an incompressible Newtonian fluid.
3.3
migration
directed particle movement (sedimentation or creaming/flotation) due to acting gravitational or
centrifugal fields
Note 1 to entry: Sedimentation occurs when the density of droplets/particles is larger than that of the liquid.
Creaming/flotation occurs when the density of droplets/particles is smaller than that of the liquid. In these two
processes, particles move in opposite directions.
© ISO 2019 – All rights reserved 1

3.4
migration velocity
absolute value of sedimentation or creaming/flotation terminal velocity
Note 1 to entry: Velocity of creaming/flotation is indicated by a negative sign.
3.5
shape factor
ratio of the sedimentation velocity of a non‐spherical particle to the one of a spherical particle of the
same volume and density
4 Symbols
Quantity Symbol Unit Derivative unit
Acceleration a m/s
Angular velocity ω rad/s
Coverage factor k —
Dynamic viscosity η Pa·s mPa·s
Expanded uncertainty for density U kg/m
Liquid density ρ kg/m
L
Maximum density ρ kg/m
max
Minimum density ρmin kg/m
Particle density ρ kg/m
P
Radius r m mm
Relative centrifugal acceleration RCA —
Standard acceleration due to
g m/s
gravity
Temperature ϑ °C
Time t s
Velocity v m/s
Wavelength λ m nm
5 Basic principle of the method
Density is the mass of a body divided by its volume. In case of fine particles, microscopic surface and
internal structure have to be taken into account to define the true particle volume of a dry particle. The
true volume can be defined as the volume of the particle envelope minus the volume of external and
internal voids as depicted in Figure 1 a) and Figure 1 b). Voids may also be pores [see Figure 1 d)]. The
measured “volume” depends on the applied determination technique (ideally 3D) and conditions of
measurement. When determining the envelope volume, adequate resolution is crucial for detecting
external voids due to surface irregularities, small fractures, fissures etc. Often the only information
[13][14]
available is from image analysis , and the volume is extrapolated based on geometric assumptions.
True particle density according to Reference [15] is defined as the ratio of particle mass to its volume,
excluding open and closed pores.
[9]
If a particle is dispersed into a liquid continuous phase, additional uncertainties emerge , due to the
creation of a heterogeneous system. Liquid molecules, solutes etc. interact with the particle surface, and
an “unstirred” or adsorption layer forms, becoming an integral part of the particle and consequently of
its volume [see Figure 1 c)], similar to a soft core‐shell particle. The thickness of such a layer is fuzzy
2 © ISO 2019 – All rights reserved

and the term corona was introduced to emphasize that fact. In general, the density and physico‐
chemical parameters in the corona are not constant, and gradients with respect to the distance from the
“real” dry particle surface exist. The “soft” structure of this layer may be influenced by ions, surface
active molecules, macromolecules or polymers of the continuous phase as well as by particle
kinematics. This peculiarity is especially distinct in the case of surface‐functionalized particles, such as
polymer brush‐grafted particles (brushed particles). The influence on “apparent particle volume”
increases with decreasing particle size. Finally, filled or incompletely filled pores affect the values of
these quantities [see Figure 1 d)]. Especially for dead end pores, wettability is crucial. In the case of
Figure 1 d), the widely‐used term “skeletal density” is defined as the ratio of the mass of the discrete
particle of solid material to the sum of the volumes of the solid material in the particle and closed (or
[16]
blind) pores within the solid particle .

a) Macroscopic solid b) Particle with c) Particle with an d) Particle with open
particle closed pores adjacent/immobilised pores
layer to its surface
NOTE Bold lines indicate obtained solid volume relevant envelope by applied measurement technique (reproduced with
permission from Reference [17]).
Figure 1 — Schematic structures of particles (cross section) with regard to the measurand
particle density
Sedimentation techniques allow, principally, in situ density determination, ρ, of particles dispersed in
P
liquid continuous phases. In any case, density of the liquid ρ has to be known and in most cases also
L
liquid viscosity η. Four experimental approaches have been used for decades.
— Density calculation from experimentally determined velocity based on Stokes law [see
Formula (1)], if shape and particle size are known.
— Measurement of migration direction of particles dispersed in a series of continuous liquid phases
with different densities. Liquids densities are required to be lower and higher than that of particles
to be analysed (ρ < ρ < ρ ). Particle density is obtained interpolating quantitative data
L,i P L,(i+1)
reflecting the reversal of migration direction to isopycnic liquid density (zero velocity). Shape does
not matter, but the particles should not shrink or swell in used liquids. For details refer to
ISO 18747‐1.
— Buoyant density centrifugation or isopycnic gradient centrifugation. This approach is
predominantly employed for preparative particle separation but was adopted for particle density
determination. Density gradient centrifugation separates particles solely based on their density in
contrast to migration velocity (see Annex A).
— Density determination based on precise measurement of migration velocity of particles dispersed
into at least two continuous phases exhibiting different densities, driven by gravitational or
centrifugal fields.
© ISO 2019 – All rights reserved 3

This document deals with the latter approach. It was first applied by the analytical ultracentrifugation
[18][19]
(AUC) community and is based on Stokes law [see Formulae (1) and (2)]. Migration velocity v for a
given particle of size x and shape factor w depends on the density contrast between liquid ρ and
L
particle ρ and on the liquid viscosity η, respectively. If sedimentation or creaming velocity of the same
p
particle in at least two different liquids is experimentally determined, the two velocities v and v are
1 2
connected with particle density via Stokes law as given in Formula (1) and Formula (2).
wxa

PL,1
v 
(1)
18
wxa

PL,2
v  (2)
18
where
a corresponds to the standard acceleration due to gravity g or centrifugal acceleration
a = ω∙r;
v is the migration velocity;
w is the shape factor;
x is the apparent spherical particle size;
ρL is the density of the liquid;
ρ is the density of the particle;
P
η is the liquid viscosity;
1 and 2 are indices corresponding to the two liquids.
This approach does not require the knowledge of particle size distribution. It assumes that
sedimentation related particle characteristics do not change being dispersed into the different liquids
or during the measurement, i.e. the shape‐size value w∙x does not alter. With that assumption,
Formulae (1) and (2) can be rearranged with regard to (w∙x) and equated. The result in Formula (3)
calculates particle density based on velocity determination of particles dispersed in liquid 1 and
liquid 2.
vv  
11 L,2 22 L,1
  (3)
P
vv
11 22
To calculate particle density ρ, the viscosities η and η as well as the fluid densities ρ and ρ need to
p 1 2 L,1 L,2
be known at the measurement temperature. Uncertainty is reduced if i samples (i > 2) are used and is
calculated for all possible pairs ρ (multivelocity approach).
P
Size and shape are not included in Formula (3) but equalization of Formulae (1) and (2) presupposes
that migrating particles shall not be altered by the chosen liquids.
6 Measuring techniques to determine sedimentation and creaming/flotation
velocity of dispersed particles
Determination of the particle density according to Formula (3) requires an accurate measurement of
the particle velocity in chosen liquids. Any method is appropriate that allows quantitative measurement
[2][3]
of particle migration velocity (e.g. sedimentation or creaming/flotation ). Particle migration may be
driven by gravity or, especially for nanoparticles, by enhanced gravity (centrifugal field). Basic
measurement principles of standard techniques which each generates information about an aspect of
the sample are described in detail in References [20] and [21]. In recent years, space‐resolving
[22][23][24]
techniques with high resolution have become available .
4 © ISO 2019 – All rights reserved

Velocity determination should be in accordance with the Stokes law. It is obtained from direct
observation of distance of particle travel over a period of time. The uncertainty of velocity
measurement depends mainly on the time resolution of the measuring system and the resolution of
position. A precise determination of the starting (reference) point, typically the meniscus, is important.
Care shall be taken to meet the required conditions for the Stokes equation to be valid. These conditions
include Reynolds number, particle concentration, wall interaction, particle‐particle interaction and
[25]
rheological behaviour of the continuous phase .
Gravitational migration velocity may be very slow in the case of particles of low density contrast or
submicron particles. In such cases, analytical centrifugation is advantageous to accelerate the
[26] [27]
evaluation of particle migration (see ISO/TR 13097 and ISO 13318‐2 ). Multichannel instruments
increase the throughput and allow for increased similarity in measurement conditions.
Care should be taken to maintain temperature stability, since liquid density and viscosity are sensitive
to temperature. Therefore, instruments shall provide temperature control. Measurements for different
samples shall be performed at the same temperature. Multichannel instruments are advantageous since
they increase the sample throughput, and samples are measured under similar experimental conditions.
Analytical cuvette centrifugation is especially appropriate for nanoparticles and continuous phases of
high viscosity.
7 Preparation of samples
7.1 Continuous phase liquids
Very often water of different hydrogen isotope composition are used as liquids: normal (HO) and
heavy (DO) water. Viscosity and density values with small uncertainties are tabulated for these waters
in Reference [28] Both liquids interact with the particles in the same way chemically; therefore, the
shape and size of the particles are expected to be the same in both liquids, and the values w∙x in
Formulae (1) and (2) are identical.
It may also be appropriate to prepare solutions which differ in density due to different solute
concentration. It is convenient to start with a concentrated solution ρ and dilute with the pure solvent
L,1
to obtain density difference for the second one, ρ . In contrast to ISO 18747‐1, densities of both liquids
L,2
can be below or over particle density ρp.
Another approach consists of mixing two liquids of different density. Typical examples may be water‐
[29][30]
ethanol‐mixtures or water‐glycerol mixtures. Both of them are well characterized . Densities of
3 3 3 3
these mixtures range from 789,7 kg/m to 998,2 kg/m and 998,2 kg/m to 1 263,9 kg/m at ϑ = 20 °C,
respectively.
Numerical values of density as well as dynamic viscosity are functions of temperature. If the density and
viscosity values are not known for a specific temperature, they shall be determined experimentally (see
[1] [31]
ISO 3105 for viscosity and ISO 2811‐3 for density) and meet corresponding uncertainty
requirements for particle density [see Formula (4), 9.2].
CAUTION — Liquids shall be chosen so that the particles, especially of organic or hydrocolloid matter,
do not alter in shape nor swell or shrink due to, e.g. effects of solvation, osmotic pressure or ionic
strength. In the case of particles with open pores, the pores shall be fully filled with the liquid; therefore,
liquids with contact angle > 90° shall be avoided. Furthermore, the selected liquid should not allow
gelation or particle network formation.
7.2 Dispersing procedure
Powders shall be dispersed in test liquids in accordance with the procedures specified in ISO 14887 or
appropriate for particles to be analysed. Any agglomerates or flocs shall be avoided since such
suspensions exhibit a wider size distribution, and the state of agglomeration or flocculation may alter
during the experiment and affect the velocity distribution. All particles shall be wetted thoroughly to
© ISO 2019 – All rights reserved 5

avoid density underestimation due to adhering gas bubbles to the particle surface. The continuous
phase should be free of gas bubbles to avoid interference with particle migration.
The volume concentration of all samples should be the same and in accordance with the requirements
of the measuring technique. In general, the volume fraction of particles shall be below 0,005, to avoid
corrections for hindered settling that may differ due to different hydrodynamic particle interactions in
[32][33]
the two continuous phases .
If the original samples are provided as dispersions, a high volume concentration is desirable. The
concentrated samples should be centrifuged; the supernatant discharged and replaced by the
corresponding test liquid. This procedure should be repeated until the continuous phase of original
dispersion is ultimately exchanged. Any alteration of particle size distribution or shape shall be avoided.
If the density and mass of original continuous phase of test sample are known, the liquid density can
also be adjusted by adding defined amo
...