# BS ISO 20998-2-2013

BSI Standards Publication BS ISO 20998-2:2013 Measurement and characterization of particles by acoustic methods Part 2: Guidelines for linear theoryBS ISO 20998-2:2013 BRITISH STANDARD National foreword This British Standard is the UK implementation of ISO 20998-2:2013. The UK participation in its preparation was entrusted to Technical Committee LBI/37, Particle characterization including sieving. A list of organizations represented on this committee can be obtained on request to its secretary. This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. © The British Standards Institution 2013. Published by BSI Standards Limited 2013 ISBN 978 0 580 74526 3 ICS 19.120 Compliance with a British Standard cannot confer immunity from legal obligations. This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 August 2013. Amendments issued since publication Date Text affectedBS ISO 20998-2:2013 © ISO 2013 Measurement and characterization of particles by acoustic methods — Part 2: Guidelines for linear theory Caractérisation des particules par des méthodes acoustiques — Partie 2: Théorie linéaire INTERNATIONAL STANDARD ISO 20998-2 First edition 2013-08-15 Reference number ISO 20998-2:2013(E)BS ISO 20998-2:2013ISO 20998-2:2013(E)ii © ISO 2013 – All rights reserved COPYRIGHT PROTECTED DOCUMENT © ISO 2013 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 Case postale 56 • CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyright@iso.org Web www.iso.org Published in SwitzerlandBS ISO 20998-2:2013ISO 20998-2:2013(E)© ISO 2013 – All rights reserved iii Contents Page Foreword iv Introduction v 1 Scope . 1 2 Normative references 1 3 T erms and definitions . 1 4 Symbols and abbreviated terms . 2 5 Mechanism of attenuation (dilute case) 4 5.1 Introduction 4 5.2 Excess attenuation coefficient . 4 5.3 Specific attenuation mechanisms . 5 5.4 Linear models 5 6 Determination of particle size 7 6.1 Introduction 7 6.2 Inversion approaches used to determine PSD . 8 6.3 Limits of application. 9 7 Instrument qualification 9 7.1 Calibration 9 7.2 Precision . 9 7.3 Accuracy .10 8 Reporting of results 11 Annex A (informative) Viscoinertial loss model 12 Annex B (informative) ECAH theory and limitations 13 Annex C (informative) Example of a semi-empirical model 16 Annex D (informative) It er ati v e fitting 19 Annex E (informative) Physical parameter values for selected materials .21 Annex F (informative) Practical example of PSD measurement .22 Bibliography .30BS ISO 20998-2:2013ISO 20998-2:2013(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. 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. 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 meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information The committee responsible for this document is ISO/TC 24, Particle characterization including sieving, Subcommittee SC 4, Particle characterization. ISO 20998 consists of the following parts, under the general title Measurement and characterization of particles by acoustic methods: — Part 1: Concepts and procedures in ultrasonic attenuation spectroscopy — Part 2: Guidelines for linear theoryiv © ISO 2013 – All rights reservedBS ISO 20998-2:2013ISO 20998-2:2013(E) Introduction It is well known that ultrasonic spectroscopy can be used to measure particle size distribution (PSD) in colloids, dispersions, and emulsions (References [1][2][3][4]). The basic concept is to measure the frequency-dependent attenuation or velocity of the ultrasound as it passes through the sample. The attenuation spectrum is affected by scattering or absorption of ultrasound by particles in the sample, and it is a function of the size distribution and concentration of particles (References [5][6][7]). Once this relationship 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 off-line 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 be observed directly in real time (Reference [8]). These data can be used in process control schemes to improve both the manufacturing process and the product performance. ISO 20998 consists of two parts: — 20998-1 introduces the terminology, concepts, and procedures for measuring ultrasonic attenuation spectra; — 20998-2 provides guidelines for determining particle size information from the measured spectra for cases where the spectrum is a linear function of the particle volume fraction. A further part addressing the determination of particle size for cases where the spectrum is not a linear function of volume fraction is planned.© ISO 2013 – All rights reserved vBS ISO 20998-2:2013BS ISO 20998-2:2013Measurement and characterization of particles by acoustic methods — Part 2: Guidelines for linear theory 1 Scope This part of ISO 20998 describes ultrasonic attenuation spectroscopy methods for determining the size distributions of a particulate phase dispersed in a liquid at dilute concentrations, where the ultrasonic attenuation spectrum is a linear function of the particle volume fraction. In this regime, particle– particle interactions are negligible. Colloids, dilute dispersions, and emulsions are within the scope of this part of ISO 20998. The typical particle size for such analysis ranges from 10 nm to 3 mm, although particles outside this range have also been successfully measured. For solid particles in suspension, size measurements can be made at concentrations typically ranging from 0,1 % volume fraction up to 5 % volume fraction, depending on the density contrast between the solid and liquid phases, the particle size, and the frequency range. NOTE See References [9][10]. For emulsions, measurements may be made at much higher concentrations. These ultrasonic methods can be used to monitor dynamic changes in the size distribution. While it is possible to determine the particle size distribution from either the attenuation spectrum or the phase velocity spectrum, the use of attenuation data alone is recommended. The relative variation in phase velocity due to changing particle size is small compared to the mean velocity, so it is often difficult to determine the phase velocity with a high degree of accuracy, particularly at ambient temperature. Likewise, the combined use of attenuation and velocity spectra to determine the particle size is not recommended. The presence of measurement errors (i.e. “noise”) in the magnitude and phase spectra can increase the ill-posed nature of the problem and reduce the stability of the inversion. 2 Normative references The following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. 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 3 T erms a nd definiti ons For the purposes of this document, the terms and definitions in ISO 20998-1 and the following apply. 3.1 c o e f f i c i e n t o f v a r i a t i o n ratio of the standard deviation to the mean value INTERNATIONAL ST ANDARD ISO 20998-2:2013(E) © ISO 2013 – All rights reserved 1BS ISO 20998-2:2013ISO 20998-2:2013(E) 3.2 dimensionless size parameter representation of particle size as the product of wave number and particle radius 3.3 particle radius one-half of the particle diameter 3.4 wave number ratio of 2π to the wavelength 4 Symbols and abbreviated terms A matrix representing the linear attenuation model A n coefficients of series expansion in ECAH theory a particle radius c speed of sound in liquid C p specific heat at constant pressure C PF particle projection area divided by suspension volume CV coefficient of variability (ratio of the standard deviation to the mean value) E extinction at a given frequency ECAH Epstein-Carhart-Allegra-Hawley (theory) f i frequency H identity matrix h n Hankel functions of the first kind I transmitted intensity of ultrasound I 0 incident intensity of ultrasound i the imaginary number inv() matrix inverse operation K extinction efficiency (extinction cross section divided by particle projection area) K matrix representation of the kernel function (the ultrasonic model) K T transpose of matrix K k(f, x) kernel function k c , k T , k s wave numbers of the compressional, thermal, and shear waves ka dimensionless size parameter P n Legendre polynomials PSD particle size distribution2 © ISO 2013 – All rights reservedBS ISO 20998-2:2013ISO 20998-2:2013(E) q solution vector (representation of the PSD) q 3 (x) volume weighted density function of the PSD Q 3 (x) volume weighted cumulative PSD s standard deviation x particle diameter x 10 the 10 thpercentile of the cumulative PSD x 50 median size (50 thpercentile) x 90 the 90 thpercentile of the cumulative PSD x min minimum particle size in a sample x max maximum particle size in a sample α total ultrasonic attenuation coefficient α attenuation spectrum absolute attenuation coefficient divided by the frequency, = (α/f) α exc excess attenuation coefficient, α exc= α – α L α exc’ alternate definition of excess attenuation coefficient where α exc ’ = α – α int α exp measured attenuation spectrum a int intrinsic absorption coefficient of the dispersion α L attenuation coefficient of the continuous (liquid) phase α mod attenuation spectrum predicted by the model, given a trial PSD α P attenuation coefficient of the discontinuous (particulate) phase α sc elastic scattering component of the attenuation coefficient α th thermal loss component of the attenuation coefficient α vis viscoinertial loss component of the attenuation coefficient β T volume thermal expansion coefficient Δ error in the fit, Δ Tikhonov regularization factor Δl thickness of the suspension layer ΔQ 2 fraction of the total projection area containing a certain particle size class η viscosity of the liquid κ thermal conductivity© ISO 2013 – All rights reserved 3BS ISO 20998-2:2013ISO 20998-2:2013(E) λ ultrasonic wavelength μ shear modulus ρ, ρ density of the liquid and particle, respectively ϕ volume concentration of the dispersed phase χ 2 chi-squared value Ψ c compression wave Ψ s shear wave Ψ T thermal wave ω angular frequency (i.e. 2π times the frequency) 5 Mechanism of attenuation (dilute case) 5.1 Introduction As ultrasound passes through a suspension, colloid, or emulsion, it is scattered and absorbed by the discrete phase with the result that the intensity of the transmitted sound is diminished. The attenuation coefficient is a function of ultrasonic frequency and depends on the composition and physical state of the particulate system. The measurement of the attenuation spectrum is described in ISO 20998-1. 5.2 Ex c ess att enuation c oefficient The total ultrasonic attenuation coefficient, α, is due to viscoinertial loss, thermal loss, elastic scattering, and the intrinsic absorption coefficient, α int , of the dispersion (References [1][10]): (1) The intrinsic absorption is determined by the absorption of sound in each homogenous phase of the dispersion. For pure phases, the attenuation coefficients, denoted α Lfor the continuous (liquid) phase and α Pfor the discontinuous (particulate) phase, are physical constants of the materials. In a dispersed system, intrinsic absorption occurs inside the particles and in the continuous phase, therefore, (2) The excess attenuation coefficient is usually defined to be the difference between the total attenuation and the intrinsic absorption in pure (particle-free) liquid phase (References [4][7]): (3) With this definition, the excess attenuation coefficient is shown to be the incremental attenuation caused by the presence of particles in the continuous phase. Combining Formulae (1), (2), and (3), it can be seen that (4)4 © ISO 2013 – All rights reservedBS ISO 20998-2:2013ISO 20998-2:2013(E) The viscoinertial, thermal, and elastic scattering terms depend on particle size, but α Land α Pdo not. Thus, the excess attenuation coefficient contains a term that does not depend on size. When working with aqueous dispersions and rigid par