1、BSI Standards PublicationBS ISO 20998-2:2013Measurement andcharacterization of particles byacoustic methodsPart 2: Guidelines for linear theoryBS ISO 20998-2:2013 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of ISO 20998-2:2013.The UK participation in its preparati
2、on was entrusted to TechnicalCommittee LBI/37, Particle characterization including sieving.A list of organizations represented on this committee can beobtained on request to its secretary.This publication does not purport to include all the necessaryprovisions of a contract. Users are responsible fo
3、r its correctapplication. The British Standards Institution 2013. Published by BSI StandardsLimited 2013ISBN 978 0 580 74526 3ICS 19.120Compliance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was published under the authority of theStandards Policy and S
4、trategy Committee on 31 August 2013.Amendments issued since publicationDate Text affectedBS ISO 20998-2:2013 ISO 2013Measurement and characterization of particles by acoustic methods Part 2: Guidelines for linear theoryCaractrisation des particules par des mthodes acoustiques Partie 2: Thorie linair
5、eINTERNATIONAL STANDARDISO20998-2First edition2013-08-15Reference numberISO 20998-2:2013(E)BS ISO 20998-2:2013ISO 20998-2:2013(E)ii ISO 2013 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2013All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utili
6、zed 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 ISOs member body in the country of the requester.ISO copyright
7、 officeCase postale 56 CH-1211 Geneva 20Tel. + 41 22 749 01 11Fax + 41 22 749 09 47E-mail copyrightiso.orgWeb www.iso.orgPublished in SwitzerlandBS ISO 20998-2:2013ISO 20998-2:2013(E) ISO 2013 All rights reserved iiiContents PageForeword ivIntroduction v1 Scope . 12 Normative references 13 Terms and
8、 definitions . 14 Symbols and abbreviated terms . 25 Mechanism of attenuation (dilute case) 45.1 Introduction 45.2 Excess attenuation coefficient . 45.3 Specific attenuation mechanisms . 55.4 Linear models 56 Determination of particle size 76.1 Introduction 76.2 Inversion approaches used to determin
9、e PSD . 86.3 Limits of application. 97 Instrument qualification 97.1 Calibration 97.2 Precision . 97.3 Accuracy . 108 Reporting of results 11Annex A (informative) Viscoinertial loss model 12Annex B (informative) ECAH theory and limitations 13Annex C (informative) Example of a semi-empirical model 16
10、Annex D (informative) Iterative fitting 19Annex E (informative) Physical parameter values for selected materials .21Annex F (informative) Practical example of PSD measurement .22Bibliography .30BS ISO 20998-2:2013ISO 20998-2:2013(E)ForewordISO (the International Organization for Standardization) is
11、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 represent
12、ed 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 t
13、his 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
14、Directives, Part 2. www.iso.org/directivesAttention 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 developm
15、ent of the document will be in the Introduction and/or on the ISO list of patent declarations received. www.iso.org/patentsAny 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 t
16、erms and expressions related to conformity assessment, as well as information about ISOs adherence to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL: Foreword - Supplementary informationThe committee responsible for this document is ISO/TC 24, Particle characteriza
17、tion 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 lin
18、ear theoryiv ISO 2013 All rights reservedBS ISO 20998-2:2013ISO 20998-2:2013(E)IntroductionIt is well known that ultrasonic spectroscopy can be used to measure particle size distribution (PSD) in colloids, dispersions, and emulsions (References 1234). The basic concept is to measure the frequency-de
19、pendent 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 567). Once this relat
20、ionship 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 qua
21、lity 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, dispersi
22、on, 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 measurin
23、g 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 spectru
24、m 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 theory1 ScopeThis part of ISO 20998 describes ultrasonic attenuation spectrosc
25、opy 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, particleparticle interactions are negligible. Colloids, dilute dis
26、persions, 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 concentration
27、s 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 910.For emulsions, measurements may be made at much higher concentrations. These ultrasonic
28、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
29、 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 recomm
30、ended. 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 referencesThe following documents, in whole or in part, are normatively referenced in this document and a
31、re 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 particulat
32、e propertiesISO 20998-1:2006, Measurement and characterization of particles by acoustic methods Part 1: Concepts and procedures in ultrasonic attenuation spectroscopy3 Terms and definitionsFor the purposes of this document, the terms and definitions in ISO 20998-1 and the following apply.3.1coeffici
33、ent of variationratio of the standard deviation to the mean valueINTERNATIONAL STANDARD ISO 20998-2:2013(E) ISO 2013 All rights reserved 1BS ISO 20998-2:2013ISO 20998-2:2013(E)3.2dimensionless size parameterrepresentation of particle size as the product of wave number and particle radius3.3particle
34、radiusone-half of the particle diameter3.4wave numberratio of 2 to the wavelength4 Symbols and abbreviated termsA matrix representing the linear attenuation modelAncoefficients of series expansion in ECAH theorya particle radiusc speed of sound in liquidCpspecific heat at constant pressureCPFparticl
35、e projection area divided by suspension volumeCV coefficient of variability (ratio of the standard deviation to the mean value)E extinction at a given frequencyECAH Epstein-Carhart-Allegra-Hawley (theory)fifrequencyH identity matrixhnHankel functions of the first kindI transmitted intensity of ultra
36、soundI0incident intensity of ultrasoundi the imaginary numberinv() matrix inverse operationK extinction efficiency (extinction cross section divided by particle projection area)K matrix representation of the kernel function (the ultrasonic model)KTtranspose of matrix Kk(f, x) kernel functionkc, kT,
37、kswave numbers of the compressional, thermal, and shear waveska dimensionless size parameterPnLegendre polynomialsPSD particle size distribution2 ISO 2013 All rights reservedBS ISO 20998-2:2013ISO 20998-2:2013(E)q solution vector (representation of the PSD)q3(x) volume weighted density function of t
38、he PSDQ3(x) volume weighted cumulative PSDs standard deviationx particle diameterx10the 10thpercentile of the cumulative PSDx50median size (50thpercentile)x90the 90thpercentile of the cumulative PSDxminminimum particle size in a samplexmaxmaximum particle size in a sample total ultrasonic attenuatio
39、n coefficient attenuation spectrum absolute attenuation coefficient divided by the frequency, = (/f)excexcess attenuation coefficient, exc= Lexcalternate definition of excess attenuation coefficient where exc = intexpmeasured attenuation spectrumaintintrinsic absorption coefficient of the dispersion
40、Lattenuation coefficient of the continuous (liquid) phasemodattenuation spectrum predicted by the model, given a trial PSDPattenuation coefficient of the discontinuous (particulate) phasescelastic scattering component of the attenuation coefficientththermal loss component of the attenuation coeffici
41、entvisviscoinertial loss component of the attenuation coefficientTvolume thermal expansion coefficienterror in the fit, = expmod Tikhonov regularization factorl thickness of the suspension layerQ2fraction of the total projection area containing a certain particle size class viscosity of the liquid t
42、hermal conductivity ISO 2013 All rights reserved 3BS ISO 20998-2:2013ISO 20998-2:2013(E) ultrasonic wavelength shear modulus, density of the liquid and particle, respectively volume concentration of the dispersed phase2chi-squared valueccompression wavesshear waveTthermal wave angular frequency (i.e
43、. 2 times the frequency)5 Mechanism of attenuation (dilute case)5.1 IntroductionAs 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 i
44、s 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 Excess attenuation coefficientThe total ultrasonic attenuation coefficient, , is due to viscoinertial loss, th
45、ermal loss, elastic scattering, and the intrinsic absorption coefficient, int, of the dispersion (References 110): =+visthscint(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 Lfor
46、the continuous (liquid) phase and 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,int()+1LP(2)The excess attenuation coefficient is usually defined to b
47、e the difference between the total attenuation and the intrinsic absorption in pure (particle-free) liquid phase (References 47):excL= (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. C
48、ombining Formulae (1), (2), and (3), it can be seen that excvis th sc PL=+() (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 Land Pdo not. Thus, the excess attenuation coefficient contains a
49、term that does not depend on size. When working with aqueous dispersions and rigid particles, this term can often be neglected, so thatexcvis th sc+ (5)However, in some emulsions, the ultrasonic absorption in the oily phase can be significant. In that case, the definition of the excess attenuation coefficient given in Formula (3) may be modified asexc=int(6)In this situation, Formula (5) is still valid. It shou
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