ISO 20998-3:2017

Measurement and characterization of particles by acoustic methods — Part 3: Guidelines for non-linear theory

ISO 20998-3:2017 gives guidelines for ultrasonic attenuation spectroscopy methods for determining the size distributions of one or more material phases dispersed in a liquid at high concentrations, where the ultrasonic attenuation spectrum is not a linear function of the particle volume fraction. In this regime, particle-particle interactions are not negligible. ISO 20998-3:2017 is applicable to colloids, dispersions, slurries, and emulsions. The typical particle size for such analysis ranges from 10 nm to 3 mm, although particles outside this range have also been successfully measured. Measurements can be made for concentrations of the dispersed phase ranging from about 5 % by volume to over 50 % by volume, depending on the density contrast between the continuous and the dispersed phases, the particle size, and the frequency range[9] [10]. These ultrasonic methods can be used to monitor dynamic changes in the size distribution, including agglomeration or flocculation.

Mesurage et caractérisation des particules par des méthodes acoustiques — Partie 3: Lignes directrices pour la théorie non linéaire

General Information

• Status: Published
• Publication Date: 20-Apr-2017
• ICS: 19.120 - Particle size analysis. Sieving
• Technical Committee: ISO/TC 24/SC 4 - Particle characterization
• Drafting Committee: ISO/TC 24/SC 4/WG 14 - Acoustic methods
• Current Stage: 9093 - International Standard confirmed
• Completion Date: 07-Sep-2022

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 20998-3
First edition
2017-04
Measurement and characterization of
particles by acoustic methods —
Part 3:
Guidelines for non-linear theory
Mesurage et caractérisation des particules par des méthodes
acoustiques —
Partie 3: Lignes directrices pour la théorie non linéaire
Reference number
ISO 20998-3:2017(E)
©
ISO 2017

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ISO 20998-3:2017(E)

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ISO 20998-3:2017(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 1
5 Limits of applicability of linear theory . 3
5.1 Multiple scattering . 3
5.2 Concentration considerations . 3
5.3 Steric repulsion . 6
6 Measurement issues in concentrated systems . 7
6.1 General . 7
6.2 Path length limitation. 7
6.3 High attenuation . 7
6.4 Increased viscosity . 7
6.5 Change in velocity . 7
6.6 Change in pulse shape . 8
6.7 Homogeneity . . 8
7 Nonlinear attenuation . 8
8 Determination of particle size. 8
8.1 Calculation . 8
8.2 Limits of application. 9
9 Instrument qualification . 9
9.1 Calibration . 9
9.2 Precision . 9
9.2.1 Reference materials . 9
9.2.2 Repeatability . 9
9.2.3 Reproducibility . 9
9.3 Accuracy . 9
9.3.1 Qualification procedure . 9
9.3.2 Reference materials .10
9.3.3 Instrument preparation .10
9.3.4 Accuracy test .10
9.3.5 Qualification acceptance criteria .10
10 Reporting of results .10
Annex A (informative) Theories of attenuation in concentrated systems .11
Annex B (informative) Practical example of PSD measurement (coupled phase model) .14
Bibliography .22
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ISO 20998-3:2017(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
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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
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For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and
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URL: w w w . i s o .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 the parts in the ISO 20998 series can be found on the ISO website
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ISO 20998-3:2017(E)

Introduction
Ultrasonic spectroscopy is widely used to measure particle size distribution (PSD) in colloids,
[1][2][3][4]
dispersions, and emulsions . The basic concept is to measure the frequency-dependent
attenuation and/or velocity of the ultrasound as it passes through the sample. This attenuation includes
contributions due to scattering or absorption by particles in the sample, and the size distribution and
[5][6][7]
concentration of dispersed material determines the attenuation spectrum . Once this connection
is established by empirical observation or by theoretical calculations, one can estimate the PSD from
the ultrasonic data.
Ultrasonic techniques are useful for dynamic online measurements in concentrated slurries and
emulsions. Traditionally, such measurements have been made offline in a quality control lab, and
constraints imposed by the instrumentation have required the use of diluted samples. By making in-
process ultrasonic measurements at full concentration, one does not risk altering the dispersion state
of the sample. In addition, dynamic processes (such as flocculation, dispersion, and comminution) can
[8]
be observed directly in real time . This data can be used in process control schemes to improve both
the manufacturing process and the product performance.
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INTERNATIONAL STANDARD ISO 20998-3:2017(E)
Measurement and characterization of particles by acoustic
methods —
Part 3:
Guidelines for non-linear theory
1 Scope
This document gives guidelines for ultrasonic attenuation spectroscopy methods for determining the
size distributions of one or more material phases dispersed in a liquid at high concentrations, where the
ultrasonic attenuation spectrum is not a linear function of the particle volume fraction. In this regime,
particle-particle interactions are not negligible.
This document is applicable to colloids, dispersions, slurries, and emulsions. The typical particle size
for such analysis ranges from 10 nm to 3 mm, although particles outside this range have also been
successfully measured. Measurements can be made for concentrations of the dispersed phase ranging
from about 5 % by volume to over 50 % by volume, depending on the density contrast between the
[9] [10]
continuous and the dispersed phases, the particle size, and the frequency range . These ultrasonic
methods can be used to monitor dynamic changes in the size distribution, including agglomeration or
flocculation.
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 14488:2007, Particulate materials — Sampling and sample splitting for the determination of
particulate properties
ISO 20998-1:2006, Measurement and characterization of particles by acoustic methods — Part 1: Concepts
and procedures in ultrasonic attenuation spectroscopy
ISO 20998-2:2013, Measurement and characterization of particles by acoustic methods — Part 2:
Guidelines for linear theory
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 20998-1 and ISO 20998-2 apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at http:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Symbols and abbreviated terms
For the purposes of this document, the following symbols and abbreviated terms apply.
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ISO 20998-3:2017(E)

a particle radius
c, c′ speed of sound in the liquid and particle, respectively
C specific heat at constant pressure
P
CV coefficient of variation (ratio of the standard deviation to the mean value)
d average distance between adjacent particles
dB decibel
e base of the natural logarithm
ECAH Epstein-Carhart-Allegra-Hawley (theory)
f frequency
G real part of the effective coupling parameter S
i the imaginary number
k complex wavenumber
M radius of shell in core-shell model
PSD particle size distribution
R imaginary part of the effective coupling parameter S
S complex number representing the effective coupling between fluid and particle
SNR ratio of signal level to noise level
x particle diameter
x the 10th percentile of the cumulative PSD
10
x median size (50th percentile)
50
x the 90th percentile of the cumulative PSD
90
α attenuation spectrum
β, β′ compressibility of the liquid and particle, respectively
mean compressibility of the slurry
β
δ thermal wave skin depth
T
δ viscous wave skin depth
V
η viscosity of the liquid
κ thermal conductivity
ρ, ρ′ density of the liquid and particle, respectively
mean density of the slurry
ρ
ρ* mean density at the complementary concentration (1-ϕ)
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ISO 20998-3:2017(E)

ϕ volume concentration of the dispersed phase
ϕ maximum volume concentration of the dispersed phase (maximum packing)
m
ϕ concentration at which the skin depth becomes equal to the interparticle distance
NL
ω angular frequency (i.e. 2π times the frequency)
5 Limits of applicability of linear theory
5.1 Multiple scattering
The interaction of a plane compressional sound wave with a particle generates three waves propagating
outward: 1) a compressional wave; 2) a thermal wave; and 3) a viscous (transverse) wave. The thermal
and viscous waves propagate only a short distance (of the order of 0,5 μm in water at 1 MHz) through
the liquid.
In the linear model (discussed in ISO 20998-2), attenuation is directly proportional to particle volume
concentration since only the forward compressional wave is considered as propagating beyond the
region of a single isolated particle, and the effect of multiple particles is determined by the average
superposition of their scattered fields.
However in the nonlinear model, the wave arriving at any particle is a combination of the incident wave
together with all waves scattered by other particles. The resulting total scattered wave field is therefore
a result of scattering of the incident wave by all particles and the rescattering (or multiple scattering)
of already-scattered waves. All three wave modes (produced by scattering at a particle) contribute to
the wave field at neighbouring particles, and can therefore be scattered by these neighbours, thereby
producing compressional scattered waves as well as other modes. This effect creates a nonlinear
concentration dependence of attenuation.
NOTE Multiple scattering depends on the configuration and aperture of the transducers as well as on the
[20]
type of excitation signal, e.g. pulse, tone-burst, quasi-continuous, or continuous .
Multiple scattering models have largely considered only the multiple scattering of the compressional
wave mode, neglecting the contribution of scattered thermal and shear waves to the wave field which is
[11][12][13][14]
incident at a particle . The second-order concentration effects obtained from these multiple
scattering models are significant only where there is a substantial density difference between the
phases. In many systems, the nonlinear effects due solely to compressional wave multiple scattering
are small, and they can be modelled using the multiple scattering models mentioned above. Substantial
nonlinear effects arise primarily because of the contributions of scattered thermal and shear waves to
the incident field at any particle.
5.2 Concentration considerations
The distances over which thermal and viscous waves decrease by a factor of (1/e) are known as the
thermal and viscous skin depths, respectively, which are calculated by Formulae (1) and (2). The skin
depths for water are shown as a function of frequency in Figure 1.
2κ
δ = (1)
T
ρωC
P
2η
δ = (2)
V
ρω
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ISO 20998-3:2017(E)

Key
δ skin depth (μm)
f frequency (MHz)
δ viscous wave skin depth
V
δ thermal wave skin depth
T
Figure 1 — Skin depth for viscous (dashed line) and thermal (solid line) waves
in water at 20 °C
At high concentrations, the interparticle spacing may become small enough that the particles can no
longer be considered to be completely isolated. This effect is compounded at low frequencies, where
the skin depths calculated in Formulae (1) and (2) are longer. The thermal and shear waves produced
by scattering at a particle contribute significantly to the wavefield at a neighbouring particle, being
rescattered to produce compressional waves (and other modes). For practical purposes, the breakdown
of linear theory (or nonlinear compressional models) occurs when the viscous or thermal waves
from adjacent particles overlap significantly. Quantifying the overlap in simple terms is difficult, but
a standard approach is to determine the concentration when the interparticle distance is less than
or equal to the skin depth. Since the viscous layer has greater thickness in most liquids, the onset of
multiple scattering occurs when the interparticle distance d equals the viscous skin depth.
For a suspension of monosized spheres, the interparticle distance d is given as a function of volume
[15]
concentration ϕ by
13/
 
 
φ
 
m
dx=   −1 (3)
 
 
φ
 
 
 
where
ϕ is the maximum volume concentration based on the packing arrangement;
m
x is the sphere diameter.
For random packing, ϕ typically has a value of approximately 0,6.
m
To determine conditions where consideration should be given to using a nonlinear model, Formulae (2)
and (3) are combined to determine the concentration ϕ at which the viscous skin depth becomes
NL
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ISO 20998-3:2017(E)

equal to the interparticle distance. The resulting Formula (4) is expressed in terms of xf to produce
a universal function:
−3
 
 
η 1
 
 
d =⋅φ +1 (4)
m
 
 ρπ 
xf
 
 
The results for aqueous slurries are shown in Figures 2 and 3; the calculations were done by assuming
that ϕ = 0,6 and by substituting the viscosity and density of water.
m
For comparison, the calculation for slurries in hexadecane (a common solvent) is included as a broken
line in Figure 2. The contour plot in Figure 3 repeats the calculation for water for explicit values of
frequency and particle diameter.
Key
ϕ volume concentration at which nonlinear effects may become evident
NL
½
product of particle size and square root of ultrasonic frequency (m·Hz )
xf
__________
water
___ ___
. . hexadecane
Figure 2 — Estimate of ϕ (approximate concentration at which nonlinear effects
NL
may become evident) calculated for water and for hexadecane
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Key
f frequency (MHz)
x particle diameter (mm)
Figure 3 — Contour plot of ϕ for water, as a function of frequency and particle diameter
NL
As a practical example, consider a hypothetical ultrasonic spectroscopy system operating at frequencies
in the range of 10 MHz to 100 MHz and measuring 0,1 μm diameter particles. The results shown in
Figure 3 suggest that nonlinear effects should be considered at concentrations greater than a few
volume percent. On the other hand, the same system could be used to measure particle size of 10 μm
particles at concentrations of 50 % or more.
NOTE 1 Formula (4) and Figures 2 and 3 are provided only as a guideline for estimating ϕ , the concentration
NL
limit beyond which the viscous wave interacts directly with neighbouring particles.
For concentrations in excess of ϕ , the linear theories described in ISO 20998-2 may not be adequate
NL
for estimating particle size from measurements of the ultrasonic attenuation spectrum. In that
situation, theories that predict a nonlinear relationship between attenuation and volume concentration
(such as those described below) may be needed.
NOTE 2 Deviation from linear theory generally becomes greater with increasing concentration, decreasing
frequency, or decreasing particle size.
5.3 Steric repulsion
Additional effects arise from the development of structure in the suspension due to steric exclusion
of the particles, possibly augmented by hydrodynamic interaction forces and interactions of the
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ISO 20998-3:2017(E)

electrostatic double layers, or flocculation. Structure affects ultrasonic attenuation, and these effects
[16][17][18][19]
have been studied extensively by Riebel et al. The collective interaction of particles
produces a “dependent scattering” contribution to the attenuation that is distinct from multiple
[20]
scattering.
6 Measurement issues in concentrated systems
6.1 General
The measurement of concentrated suspensions and emulsions may be complicated by difficulty in
obtaining representative attenuation spectra. Commonly encountered issues and possible remedies are
described below.
6.2 Path length limitation
In ultrasonic spectroscopy systems, the total attenuation (dB loss) in the received signal must be within
the dynamic range of the instrument. The maximum path length between transmitting and receiving
transducers is limited by the attenuation coefficient (dB/cm), which increases with concentration and
frequency. Therefore, measurement of concentrated particle systems may require a shorter acoustic
path length, which may not be practical depending on the application, or the use of a lower frequency
range (if possible).
6.3 High attenuation
As the total attenuation increases, the signal-to-noise ratio (SNR) drops, and without some form of
signal processing there will be a negative impact on data quality. A common signal processing technique
is to average the result of many measurements of the attenuation spectrum. Another approach is to
encode the transmitted ultrasound and to filter the received signals to reject those that do not correlate
[21]
with the transmission.
Bubble formation contributes to high signal attenuation and in some cases may block the ultrasonic
signal completely.
6.4 Increased viscosity
For a given PSD, increasing particle concentration generally increases the viscosity of the slurry.
Increased viscosity leads to several detrimental effects.
— First, bubbles become more prevalent and also more persistent once formed.
— Second, fluid flow is impeded in sensors with small transducer separation; two consequences are
increased back-pressure in the sensor and particle segregation or exclusion within the flow.
— The third issue is the increased potential for transducer fouling, which necessitates frequent
cleaning of the sensor.
In some applications, elevating the temperature might reduce the viscosity, but in general, it is
preferable to minimize bubble formation, use a sensor with no constriction in flow, and provide for
transducer cleaning if necessary.
6.5 Change in velocity
Sound velocity, which may change with particle concentration, affects ultrasonic propagation in
three ways:
— First, group velocity determines the transit time between transducers.
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— Second, changes to phase velocity can distort and broaden the waveform of an ultrasonic pulse.
Without a feedback mechanism to adjust the timing and width of the time-domain signal capture,
spectrometers that use a pulse technique might truncate the waveform. This feedback is generally
provided via software.
— Finally, changes in sound velocity alter the wavelength and hence the diffraction field, thereby
affecting the detected signal.
In order to measure concentrated suspensions, an ultrasonic spectrometer of any type shall be capable
of adapting to changes in group and phase velocity.
6.6 Change in pulse shape
As noted above for instruments that are based on pulse techniques, changes in phase velocity will
distort the shape of the received pulse. Additional distortion is caused by the frequency-dependent
attenuation, which suppresses some frequency components more than others. This effect can also be
seen in dilute suspensions.
6.7 Homogeneity
Agglomeration and flocculation become more prevalent at high concentration, which broadens the
apparent PSD in the sample. Stirring or pumping may help to improve homogeneity temporarily.
7 Nonlinear attenuation
The observed ultrasonic attenuation spectrum, α, is dependent on the particle size distribution and
on the particle concentration. In dilute suspensions and emulsions, the sound field interacts with each
particle independently and the linear theories described in ISO 20998-2 are adequate for determining
particle size. Some nonlinear dependence of attenuation on particle concentration results from
multiple scattering of compressional waves, but these contributions are often small. However linear
theories begin to fail in the case of emulsions when the thermal wavelength approaches or exceeds
[10]
the interparticle spacing . In cases dominated by visco-inertial effects, linear theories fail when the
evanescent shear waves generated by mode conversion at one particle overlap with shear waves coming
from another particle. In either case, the proximity of particles results in a nonlinear dependence of
attenuation on concentration, and different theories are needed to determine particle size. A few
examples are provided in Annex A; other theoretical models are reviewed in References [1], [2] and [10].
NOTE The term “scattering” is widely used to refer to the process by which all wave modes are produced at
a particle.
8 Determination of particle size
8.1 Calculation
The mathematical methods described in ISO 20998-2:2013, 6.2 are recommended in conjunction
with the nonlinear theories shown in Annex A to determine particle size distribution from observed
ultrasonic attenuation data in concentrated systems. It is permitted to use empirical or semi-empirical
calibration curves in place of these theories, provided the user qualifies the results as shown in Clause 9.
NOTE 1 Empirical and semi-empirical calibrations generally have a limited range of validity and can change
suddenly as a result of physical changes in the system.
NOTE 2 Annex B provides one example of how to estimate PSD from an attenuation spectrum using the
methods described in this document.
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