Measurement and characterization of particles by acoustic methods

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

General Information

Status
Published
Publication Date
20-Apr-2017
Current Stage
6060 - International Standard published
Start Date
01-Mar-2017
Completion Date
21-Apr-2017
Ref Project

Buy Standard

Standard
ISO 20998-3:2017 - Measurement and characterization of particles by acoustic methods
English language
24 pages
sale 15% off
Preview
sale 15% off
Preview

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
---------------------- Page: 1 ----------------------
ISO 20998-3:2017(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2017, Published in Switzerland

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form

or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior

written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of

the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2017 – All rights reserved
---------------------- Page: 2 ----------------------
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

© ISO 2017 – All rights reserved iii
---------------------- Page: 3 ----------------------
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

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).

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: 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
iv © ISO 2017 – All rights reserved
---------------------- Page: 4 ----------------------
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.
© ISO 2017 – All rights reserved v
---------------------- Page: 5 ----------------------
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.

© ISO 2017 – All rights reserved 1
---------------------- Page: 6 ----------------------
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
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
x median size (50th percentile)
x the 90th percentile of the cumulative PSD
α attenuation spectrum
β, β′ compressibility of the liquid and particle, respectively
mean compressibility of the slurry
δ thermal wave skin depth
δ viscous wave skin depth
η viscosity of the liquid
κ thermal conductivity
ρ, ρ′ density of the liquid and particle, respectively
mean density of the slurry
ρ* mean density at the complementary concentration (1-ϕ)
2 © ISO 2017 – All rights reserved
---------------------- Page: 7 ----------------------
ISO 20998-3:2017(E)
ϕ volume concentration of the dispersed phase
ϕ maximum volume concentration of the dispersed phase (maximum packing)

ϕ concentration at which the skin depth becomes equal to the interparticle distance

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.
δ = (1)
ρωC
δ = (2)
© ISO 2017 – All rights reserved 3
---------------------- Page: 8 ----------------------
ISO 20998-3:2017(E)
Key
δ skin depth (μm)
f frequency (MHz)
δ viscous wave skin depth
δ thermal wave skin depth
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/
 
 
 
dx=   −1 (3)
 
 
 
 
 
where
ϕ is the maximum volume concentration based on the packing arrangement;
x is the sphere diameter.
For random packing, ϕ typically has a value of approximately 0,6.

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

4 © ISO 2017 – All rights reserved
---------------------- Page: 9 ----------------------
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:
 
 
η 1
 
 
d =⋅φ +1 (4)
 
 ρπ 
 
 

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.

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
product of particle size and square root of ultrasonic frequency (m·Hz )
__________
water
___ ___
. . hexadecane
Figure 2 — Estimate of ϕ (approximate concentration at which nonlinear effects
may become evident) calculated for water and for hexadecane
© ISO 2017 – All rights reserved 5
---------------------- Page: 10 ----------------------
ISO 20998-3:2017(E)
Key
f frequency (MHz)
x particle diameter (mm)

Figure 3 — Contour plot of ϕ for water, as a function of frequency and particle diameter

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

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

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

6 © ISO 2017 – All rights reserved
---------------------- Page: 11 ----------------------
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.
© ISO 2017 – All rights reserved 7
---------------------- Page: 12 ----------------------
ISO 20998-3:2017(E)

— 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.
8 © ISO 2017 – All rights reserved
---------------------- Page: 13 ----------------------
...

Questions, Comments and Discussion

Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.