Determination of particle density by sedimentation methods

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.

Détermination de la densité de particules par méthodes de sédimentation

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Status
Published
Publication Date
02-Jul-2019
Current Stage
6060 - International Standard published
Start Date
07-May-2019
Completion Date
03-Jul-2019
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INTERNATIONAL ISO
STANDARD 18747-2
First edition
2019-06
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
Reference number
ISO 18747-2:2019(E)
ISO 2019
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ISO 18747-2:2019(E)
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© ISO 2019

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Published in Switzerland
ii © ISO 2019 – All rights reserved
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ISO 18747-2:2019(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Symbols .......................................................................................................................................................................................................................... 2

5 Basic principle of the method ................................................................................................................................................................. 2

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 ........................................................................................................................................................................ 6

8 Measurements and data analysis ........................................................................................................................................................ 6

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 ...................................10

Annex B (informative) Examples of measurements and data analysis to determine particle

density by multi-velocity approach ...............................................................................................................................................11

Annex C (informative) Uncertainty derivation of particle density based on uncertainty

propagation rules .............................................................................................................................................................................................15

Bibliography .............................................................................................................................................................................................................................18

© ISO 2019 – All rights reserved iii
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ISO 18747-2:2019(E)
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 ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

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 documents 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).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/patents).

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constitute an endorsement.

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expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade 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.
A list of all parts in the ISO 18747 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.
iv © ISO 2019 – All rights reserved
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ISO 18747-2:2019(E)
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

[1] [2][3]

of dispersions , determination of particle size distribution by sedimentation or acoustic

[4] [5]

techniques , particle characterization by field-flow approaches , optimization of dispersion long-

[6]

term stability by 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

[7][8][9]
vitro nanotoxicity 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 boundary

[10]

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 polymer or

[11]

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.

© ISO 2019 – All rights reserved v
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INTERNATIONAL STANDARD ISO 18747-2:2019(E)
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/
— ISO Online browsing platform: available at 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.
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ISO 18747-2:2019(E)
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.
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
Maximum density ρ kg/m
max
Minimum density ρ kg/m
min
Particle density ρ kg/m
Radius r m mm
Relative centrifugal acceleration RCA —
Standard acceleration due to gravity g m/s
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.
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ISO 18747-2:2019(E)
[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 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

liquid continuous phases. In any case, density of the liquid ρ has to be known and in most cases also

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).
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ISO 18747-2:2019(E)

— 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.

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

particle ρ and on the liquid viscosity η, respectively. If sedimentation or creaming velocity of the same

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).

ρρ− ⋅⋅wx ⋅a
PL,1
v = (1)
18⋅η
ρρ− ⋅⋅wx ⋅a
PL,2
v = (2)
18⋅η
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;
ρ is the density of the liquid;
ρ is the density of the particle;
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⋅⋅ηρ −⋅ηρ⋅
11 L,2L22 ,1
ρ = (3)
vv⋅−ηη⋅
11 22

To calculate particle density ρ , the viscosities η and η as well as the fluid densities ρ and ρ need

p 1 2 L,1 L,2

to 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).

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

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ISO 18747-2:2019(E)
[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 .

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 rheological

[25]
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 (H O) and

heavy (D O) 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 ρ .

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

[1] [31]

(see 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.
© ISO 2019 – All rights reserved 5
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ISO 18747-2:2019(E)
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 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 amounts of liquids with different density or soluble substances.

One should avoid creating bubbles in the sample. Attached to particles, bubbles can give false low-

density values, and in test liquids, they can interfere with particle migration.

The particle density measured for a batch of material is valid only if the test sample taken is

representative for that batch.
8 Measurements and data analysis

The sedimentation velocities of particles dispersed into at least two liquids differing in density shall

be determined according to Clause 6. It is recommended to use in addition 2 or 3 mixtures of these

two liquids and to perform duplicate measurements for each liquid pair. Table 1 shows example

data obtained for an emulsion. The continuous phase density was tuned by mixtures of H O/D O

2 2

(first column of Table 1). Density and viscosity data of the corresponding continuous phases are

summarized in Table 1. The mean velocities were calculated according to Reference [33] and are given

in Table 1 (fourth column). Based on the five experimentally obtained velocities, 10 pairwise velocity

combinations were sorted and for each pair the droplet density was calculated according to Formula (3)

and was displayed in Figure 2. The mean particle density and its standard uncertainty are calculated

from each pair result. For details refer to B.1. The use of additional dispersions based on the mixtures

of the two different liquids improves the standard uncertainty of the density result. It allows also to

check, whether the chosen different continuous phases have an influence on density relevant particle

properties. For details refer to B.1.

Table 1 — Stock emulsion diluted with mixtures of H O and D O of different fractions, density

2 2

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)
Liquid density Viscosity Mean velocity
Fraction H O : D O ρ η v
2 2 L
kg/m mPa∙s µm/s
1:0 997 0,891 4,96
1:3 1 021 0,941 8,67
1:1 1 047 0,991 12,44
3:1 1 072 1,038 15,62
0:1 1 104 1,094 19,26
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ISO 18747-2:2019(E)
Key
X density difference Δρ 1 standard uncertainty
Y particle density ρ in kg/m 2 mean value
3 standard uncertainty

NOTE Density of continuous phase was tuned by mixtures of different fractions of H O and D O.

2 2

Figure 2 — Experimental determined droplet density of polydimethylsiloxane emulsion

Particle density determination can also be carried out utilizing liquids with densities lower and higher

[12]

than the particle density, similar to the isopycnic interpolation approach (see ISO 18747-1 ). Examples

are described in B.2.

Above, the mean particle velocity was employed. If the measurement technique provides particle

[33]

velocity distributions , percentiles of the velocity may also be used. This allows getting infor

...

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