Determination of particle density by sedimentation methods

ISO 18747-1:2018 specifies a method for the determination of the density of solid particles or liquid droplets (below referred to generically as "particles") dispersed in a liquid. The method is based on the fact that a particle wholly immersed in fluid experiences buoyancy equal to the weight of the fluid displaced by this particle (Archimedean principle), and if its mass force matches the buoyant force, it stops gravitational or centrifugal settling/creaming and the particle remains suspended. This implies that the density of the particle equals the density of the liquid. In this document, particle density determination is conducted by analysing the direction of the migration movement of particles dispersed in liquids with densities that are lower and higher than particle density. All particles are of the same material composition.

Détermination de la densité de particules par méthodes de sédimentation

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Status
Published
Publication Date
21-Mar-2018
Current Stage
6060 - International Standard published
Start Date
18-Feb-2018
Completion Date
22-Mar-2018
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INTERNATIONAL ISO
STANDARD 18747-1
First edition
2018-03
Determination of particle density by
sedimentation methods —
Part 1:
Isopycnic interpolation approach
Détermination de la densité de particules par méthodes de
sédimentation —
Partie 1: Approche par interpolation isopycnique
Reference number
ISO 18747-1:2018(E)
ISO 2018
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ISO 18747-1:2018(E)
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© ISO 2018

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Published in Switzerland
ii © ISO 2018 – All rights reserved
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ISO 18747-1:2018(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 method ........................................................................................................................................................................... 2

6 Measuring techniques to determine the direction of gravitational and centrifugal

migration of dispersed particles.......................................................................................................................................................... 4

7 Preparation of samples.................................................................................................................................................................................. 5

7.1 Solutions ....................................................................................................................................................................................................... 5

7.2 Dispersing procedure ........................................................................................................................................................................ 6

8 Measurements ......................................................................................................................................................................................................... 7

9 Data analysis ............................................................................................................................................................................................................. 7

9.1 General ........................................................................................................................................................................................................... 7

9.2 Graphical interpolation .................................................................................................................................................................... 8

9.3 Two point interpolation .................................................................................................................................................................. 8

9.4 Linear or non-linear fit..................................................................................................................................................................... 9

10 Reference materials and measurement uncertainty ...................................................................................................10

10.1 Reference materials .........................................................................................................................................................................10

10.2 Measurement uncertainty ..........................................................................................................................................................10

Annex A (informative) Discrimination between sedimentation or creaming/flotation by

bottom focused backscattering intensity ................................................................................................................................12

Annex B (informative) Determination based on measurement of direct migration velocity.................15

Annex C (informative) Linearization of migration velocity versus density plots ...............................................22

Annex D (informative) Buoyant density centrifugation ................................................................................................................24

Annex E (informative) Propagation of uncertainty for isopycnic velocity in the case of

linear interpolation according to Formula (4) ...................................................................................................................25

Bibliography .............................................................................................................................................................................................................................27

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ISO 18747-1:2018(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

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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).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and

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 the following

URL: 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.
iv © ISO 2018 – All rights reserved
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ISO 18747-1:2018(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 like kinematic viscosity of

[4][5][7]

dispersions (ISO 3105), determination of particle size distribution by separation techniques ,

[10]

characterization of core/shell or capsule-like particles, determination of particle compressibility or

[11]
optimization of dispersion stability by density matching .

The density of a body is its mass divided by its volume. This is straightforward for the mass of a larger

body or particle. However, experimental determination of the volume of a macroscopic body is difficult.

The geometrical volume (length, width and thickness) and the volume relevant for the determination

of density can differ due to surface irregularities, fractures, fissures and open and closed pores or the

measuring techniques employed.

Density determination of micro-particles, in particular nanoparticles dispersed in a liquid, raises issues,

not only for the determination of mass and volume due to the small size but also, and mainly, because of

the boundary between the liquid and the particle, which is fuzzy. Molecules in the continuous phase are

partially immobilized at the surface. Physico-chemical properties (e.g. viscosity, ion concentration) in

the fuzzy coat differ from bulk. This is especially important for small microparticles and nanoparticles

[12]

which are dispersed in a polymer or biological fluid . The so-called corona can be interpreted as

an integral part of the particle and increases the effective/apparent volume compared to the space

occupied by the dry material. The thickness of this layer ranges between a few to tens of nanometres

and the effective/apparent volume deviates increasingly from the “geometrical” volume, if the particles

become smaller. As a consequence, density determination by traditional methods is affected.

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INTERNATIONAL STANDARD ISO 18747-1:2018(E)
Determination of particle density by sedimentation
methods —
Part 1:
Isopycnic interpolation approach
1 Scope

This document specifies a method for the determination of the density of solid particles or liquid

droplets (below referred to generically as “particles”) dispersed in a liquid. The method is based on

the fact that a particle wholly immersed in fluid experiences buoyancy equal to the weight of the fluid

displaced by this particle (Archimedean principle), and if its mass force matches the buoyant force, it

stops gravitational or centrifugal settling/creaming and the particle remains suspended. This implies

that the density of the particle equals the density of the liquid. In this document, particle density

determination is conducted by analysing the direction of the migration movement of particles dispersed

in liquids with densities that are lower and higher than particle density. All particles are 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 14887:2000, 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
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.
3.2
migration

directed particle movement (sedimentation or creaming/flotation) due to acting gravitational or

centrifugal fields

Note 1 to entry: Sedimentation occurs when density of particles is larger than that of liquid density.

Creaming/flotation occurs when density of particles is smaller than that of liquid density. In these two processes,

particles move in opposite directions.
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ISO 18747-1:2018(E)
3.3
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.
3.4
true particle density

ratio of particle mass to particle volume excluding all pores, closed or open, and surface fissures

3.5
skeletal density

ratio of the mass of discrete pieces of solid material to the sum of the volumes of the solid material in

the pieces and closed (or blind) pores within the pieces
[SOURCE: ASTM D3766]
3.6
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
4 Symbols
For the purposes of this document, the following symbols apply.
Quantity Symbol Unit Derivative unit
Acceleration a m/s
Angular velocity ω rad/s
Dynamic viscosity η Pa·s mPa·s
Force due to buoyancy F N
Force due to gravity F N
Liquid density ρ kg/m
Particle density ρ kg/m
Radius r m mm
-1 -1
Rotational frequency n s min
Standard acceleration due to gravity g m/s
Temperature ϑ °C
Time t s
Velocity v m/s
Velocity measurand y
Volume V m
Wavelength λ m nm
5 Basic principle of method

The Archimedean principle states that a particle wholly immersed in liquid experiences buoyancy equal

to the weight of the fluid displaced by this particle. The balance of the weight forces of a particle due

to gravity, F , and of buoyancy force, F , determines whether its net gravitational motion is upward,

G B
downward, or neither [Formula (1)].
F = ρ · V · g = F = ρ · V · g (1)
G P B L
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ISO 18747-1:2018(E)
where
ρ is the density of the particle;
V is the particle volume;
g is the gravitational acceleration;
ρ is the density of the liquid.

A particle stops migration if forces F and F are equal, and therefore the density of the particle shall

G B

equal the density of the liquid (ρ − ρ = 0). These considerations are applicable, independent of size or

P L

shape of the particle, as well as independent on dynamic viscosity of continuous phase. In the case of

multicomponent dispersions, all particle species stay suspended only when the density of all particles

is the same as the liquid density.

Formula (1) and the above considerations also hold for dispersed particles in a centrifugal field, where

g shall be replaced by a centrifugal acceleration a [Formula (2)].
2 2
a = ω · r = (2 · π · n) · r (2)
where
ω is the angular velocity of the rotor;

r is the distance of the particle under consideration from the centre of revolution;

n is the number of rotations per seconds of the rotor.

a) Macroscopic solid b) Particle with closed c) Particle with an adja- d) Particle with open

particle pores cent/immobilised layer pores
to its surface
[ ]
Figure 1 — General structures of particles regarding density determination 21

According to Formula (1), density corresponds to the volume of displaced liquid. This equals the

geometrical volume of a macroscopic solid particle [Figure 1 a)]. It follows that determined density

equals true solid particle density, which corresponds to the true material density. If the particle is made

of different materials, true density reflects the (material) density and volume/mass fraction of each

material.

In case of a particle with closed pores [Figure 1 b)] or pores not filled with liquid of continuous phase,

as well as with a surface layer [Figure 1 c)], Formula (1) determines the buoyant density, ρ (also called

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ISO 18747-1:2018(E)

effective, average, or apparent density), of the particle of total volume, V , which can be calculated

tot
according to Formula (3):
ρρ⋅+VV⋅
11 22
ρ = (3)
tot
where
ρ is the skeletal density;
V is the volume of the skeleton;
ρ is the density of the material of closed and open not filled pores;
V is the volume of the pores;
V is the total volume.
tot

Figure 1 b) shows particles with closed pores. The same applies to particles coated with a layer of a

different material of a volume of V [Figure 1 c)]. The term “coated” is used in a generic way. It can

refer to a shell of different materials (e.g. silica coated magnetic nanoparticles), a particle brushed by

polymers or macromolecules or even an immobilised (unstirred) layer of liquid molecules. The layer

itself can be porous or exhibit material gradients. Formula (3) is based on the assumption that the

composition of volume V does not change when dispersing the particles into different test liquids

(see Clause 6). Volume V is not mixed or exchanged with the continuous phase or at least only with a

time constant larger than the experimental measuring time. The term “unstirred” also reflects the fact

that, in case the particle exhibits any movement (e.g. due to electrical or gravity fields), then volume V

shall be treated as an “integral part” of the particle, which moves together with the main particle. It is

obvious that the density determined according to Formula (3) deviates more and more from the true

particle density if particles become smaller (e.g. nanoparticles).

Figure 1d) shows a particle that has open pores whose content can be freely exchanged with the

continuous phase. In other words, density determination applies to particles whose pores are filled

with the continuous phase. In this case, skeletal density is determined.

This document focuses on buoyant density, which coincides with the true (material) density

[Figure 1 a)], with apparent density [Figure 1 b) and Figure 1 c)] and with skeletal density [Figure 1 d)].

The above four cases are separately discussed for clarity, but particles which belong to several cases

exist, e.g. particles with closed pores and open pores filled with the liquid of continuous phase.

6 Measuring techniques to determine the direction of gravitational and
centrifugal migration of dispersed particles

The determination of particle density, according to Formula (1) or (2), is based on the detection

(measurement) of the migration direction of particles dispersed in continuous liquid phases with

different densities, which are lower or higher than the expected particle density.

Any method which allows detection of the direction of particle migration (sedimentation or

creaming/flotation) is appropriate. Particle migration may be driven by earth gravity or centrifugal

field. Basic principles available include:

a) monitoring the concentration change near an appropriate interface, e.g. below the meniscus

(dispersion/air interphase), or above the bottom of the measuring cell, either directly or by a

concentration related signal, e.g. voltage, current, light intensity, X-ray absorption, conductivity, or

electro-acoustic;

b) measuring the value of migration velocity or a directly correlating measurand of dispersed

particles in the bulk of the dispersion;
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ISO 18747-1:2018(E)
c) sedimentation or creaming/flotation in a density gradient .

Attention should be paid to temperature changes. Instruments which allow for temperature setting and

control are preferable. Alternatively, measurements can be conducted within a short time. Multichannel

instruments are advantageous as 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.

The volume fraction of dispersed phase does not enter into the calculations in Formulae (1) and (2).

Choose the final volume concentration in accordance with the specification of the analytical technique

employed. High volume fraction of particles (greater than 5 %) should be avoided in that, because

migration velocity decreases with increasing volume concentration due to hydrodynamic interaction

[13][14][20]

(hindrance) , experimental determination of the migration direction can be more difficult and

time-consuming.
7 Preparation of samples
7.1 Solutions

Solutions which differ in density but cover the expected particle density range should be prepared. It is

convenient to start with a concentrated solution and dilute with a solvent until the liquid density ρ , is

smaller than the buoyant particle density, ρ . Prepare two solutions as a minimum, but for more precise

results, a series of five to eight test liquids where the median density corresponds to the approximate

particle density is recommended. If possible, density spacing should be about equidistant. A number of

suitable solutions are tabulated in the literature (e.g. References [15] and [16]). Typical examples are

shown in Figure 2.

1) The buoyant density centrifugation method is not part of this document. Nevertheless, a short description is

given in Annex D.
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ISO 18747-1:2018(E)
a) Sucrose b) Sodium polytungstate
Key
X mass fraction in %
Y1 density ρ in kg/m
Y2 dynamic viscosity η in mPa·s
1 density dependence
2 viscosity dependence
NOTE See References [15] and [16] for more information.

Figure 2 — Density and dynamic viscosity dependence on sucrose and sodium polytungstate

mass fraction at ϑ = 25 °C

Another approach consists of mixing two liquids of different density. Typical examples include water-

[18][19]

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 from 998,2 kg/m to 1 263,9 kg/m at

ϑ = 20 °C, respectively.

NOTE 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 can be experimentally determined according

to International Standards (viscosity: ISO 3105, density: ISO 2811-3).

CAUTION — Particles, especially of organic or hydrocolloid matter, should not swell or shrink

in chosen liquids due to the effects of solvation or osmotic pressure. In case of particles with

open pores, liquids shall wet the pore material (contact angle > 90°) and the preparation time

of dispersion shall allow fully filled pores. Furthermore, the liquid selected should not allow

gelation or particle network formation.
7.2 Dispersing procedure

Disperse powders in the test liquids in accordance with the procedures specified in ISO 14887. A

mild dispersing procedure is sufficient because, in contrast to other methods, e.g. particle sizing,

any aggregates, agglomerates or flocks do not disturb the density measurement. Wet all particles

thoroughly to avoid density underestimation due to adhering gas bubbles remaining in the test liquid.

The volume concentration of all samples should be the same and in accordance with the requirements

of the measuring technique. In general, high concentrations should be avoided, as the sensitivity of

[20]
migration detection will be reduced due to particle hindrance .
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ISO 18747-1:2018(E)

If the original samples are provided as dispersion, a high volume concentration is desirable. These

samples should be centrifuged and the supernatant should be discharged and replaced by the

corresponding test liquid. This procedure should be repeated until the continuous phase of the original

dispersion is exchanged.

With particles of a fractured nature or dense flocks, care should be taken to ensure the removal of all

the included original liquid.

If the density and mass of the original continuous phase of the test sample are known, the liquid density

can also be adjusted by adding defined amounts of density changing fluids or soluble substances.

Avoid bubbles attached to particles, which can give false low-density values, or bubbles in test liquids,

which can interfere with particle migration.

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

representative of this batch.
8 Measurements

After dispersing particles into five to eight test liquids, fill and incubate corresponding measurement

cells, e.g. in a water bath, to obtain the temperature specified for density values of test liquids. Then

gently shake the cells (homogenization of dispersed phase; avoid air bubbles) and insert them into

the measuring instrument (preconditioned to the same temperature). Measurement is terminated

if migration direction is identified by monitoring concentration changes or if velocity is determined.

Measurement time will depend on the measurement principle and necessary test liquids. Repeat this

procedure for all five to eight dispersed samples.

In case the change of migration direction or change in velocity direction cannot be detected or takes

place only in the sample of the lowest or highest liquid density, further determinations in adequate test

fluids with broader density range shall be performed.

Gravitational migration velocity can be very slow in the case of submicron particles or even

nanoparticles. In these cases, analytical centrifugation is advantageous to accelerate the evaluation of

particle migration (ISO/TR 13097, ISO 13318-2). Multichannel instruments increase the throughput

and allow for increased similarity in measurement conditions.

If instruments do not have temperature control, room temperature variations shall be prevented

(< 1 K) and sample temperature should be measured precisely. Density data of test liquids employed

shall correspond to measurement temperature. Nevertheless, such an approach without adjustable

temperature control should be avoided, if possible, as the precision of density determination is

decreased.

Annex A describes the determination of migration direction. Annex B provides more information on

migration velocity determination for liquid and solid particles dispersed in solutions with different

densities.
9 Data analysis
9.1 General

Measurements according to Clause 8 yield quantitative data describing the change of a particle

migration velocity related measurand in arbitrary units v* or particle migration velocity v depending on

density ρ of a series of i different test liquids (continuous phases). As detailed in Annex C, experimental

data v* and v obtained for each test liquid shall be linearized by multiplying with the corresponding

liquid viscosity η at measurement temperature to increase the precision of interpolation, especially for

curves with low slopes.

NOTE In the following, the measurand in arbitrary units v* or particle migration velocity v is named y.

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ISO 18747-1:2018(E)

Examples of typical data are compiled in Table 1. The figures given have been obtained according to

migration direction approach [Clause 6 a)], with backscattering intensity measured just above cell

bottom for suspensions of polystyrene particles. The increase in backscattering intensity indicates an

increase in particle concentration, i.e. sedimentation, and vice versa, creaming.

Table 1 — Exemplary data for density determination by detection of migration direction of

particles dispersed in solutions of different sucrose mass fractions
Backscattering
Determined
Sucrose mass Liquid density Liquid viscosity intensity
backscattering
fraction multiplied by
intensity
viscosity
ρ η
% kg/m mPa·s a.u. a.u.∙mPa·s
0 998,2 1,018 12,08 12,30
5 1 017,8 1,250 4,97 6,21
10 1 038,1 1,481 0,74 1,10
15 1 059,1 1,713 −0,99 −1,70
20 1 081,0 1,945 −1,82 −3,54
30 1 127,0 3,187 −2,72 −8,67
NOTE For further information, see Annex A.

Particle density is determined by plotting changes in viscosity normalized backscattering (column 5

of Table 1) over the density of corresponding test liquids (column 2 of Table 1) as depicted in Figure 3

a). Particle density should be estimated based on this plot by interpolating data points nearest to the

value “zero” of backscattering intensity multiplied by liquid viscosity (in this case for sucrose mass

fractions of 10 % and 15 %). In general and mathematically speaking, inte
...

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