Particle size measurement. Volume 1, Powder sampling and particle size measurement: 5th ed

Acknowledgements xv Preface to the the fifth edition xvii Preface to the the first edition xix Editor's foreword xx i Powder sampling 1 Introduction 1 Sample selection 2 Sampling stored material 4 1.3.1 Sampling stored non-flowing material 5 1.3.2 Sampling stored free-flowing material 7 Sampling flowing streams 8 1.4.1 Sampling from a conveyor belt 9 1.4.2 Point samplers 10 1.4.3 Sampling from falling streams 12 1.4.4 Stream sampling ladles 13 1.4.5 Traversing cutters 14 1.4.6 Sampling dusty material 16 1.4.7 Moving flap sampler 17 Sample reduction 19 1.5.1 Scoop sampling 19 1.5.2 Cone and quartering 20 1.5.3 Table sampling 2 0 1 .5.4 Chute splitting 22 1.5.5 The rotary sample divider 23 1 .5.6 Miscellaneous sampling devices 2 3 Sluny sampling 2 4 Reduction of laboratory sample to measurement sample 27 Number of samples required 2 8 Theoretical statistical emrs on a number basis 3 1 Practical statistical errors on a number basis 3 3 Theoretical statistical errors on a weight basis 35 Practical statistical errors on a weight basis 3 6 Experimental tests of sampling techniques 37 Weight of smple requircd 3 8 1.14.1 Gross sample 3 8 1.14.2 Sampling by incrcmcnts 4 0 vi Contents Data presentation and interpretation 44 Introduction 44 Particle size 4 5 Average diameters 5 0 Particle dispersion 54 Particle shape 5 4 2.5.1 Shape coefficients 5 5 2.5.2 Shapefactors 56 2.5.3 Shape regeneration by Fourier analysis 58 2.5.4 Fractal dimensions characterization of textured surfaces 59 2.5.5 Other methods of shape analysis 62 2.5.6 Sorting by shape 6 2 Determination of specific surface from size distribution data 6 2 2.6.1 from a number count 63 2.6.2 from a surface count 6 3 2.6.3 from a volume (mass) count 6 4 Tabular presentation of particle size distribution 6 5 Graphical presentation of size distribution data 68 2.8.1 Presentation on linear graph paper 68 Standard forms of distribution functions 6 9 Arithmetic normal distribution 69 2.10.1 Manipulation of the normal equation 7 1 The log-normal distribution 7 2 2.1 1.1 Relationship between number mean sizes for a log-normal distribution 74 2.1 1.2 Derived mean sizes 77 2.1 1.3 Transformation between log-normal distributions 7 8 2.1 1.4 Relationship between median and mode of a log-normal equation 7 9 2.1 1.5 An hpmved equation and graph paper for log-normal evaluations 8 0 2.1 1.6 Application 80 Johnson's SB distribution 8 1 Rosin-Rarnmler, Bemet-Sperling formula 83 Other distribution laws 8 4 2.14.1 Simplification of two-parameter equations 8 5 2.14.2 Comments 8 6 The law of compensating errors 8 6 Evaluation of non linear distributions on log-normal paper 88 2.16.1 Bimodal intersecting distributions 93 2.16.2 Bimodal non-intersecting distributions 9 3 2.16.3 Other distributions 94 2.16.4 Applications of log-normal plots 94 2.16.5 Curve fitting 94 Contents vii Alternative notations for frequency distribution 2.17.1 Notation 2.17.2 Moment of a distribution 2.17.3 Transformation from qt(x) to q d x ) . 2.17.4 Relation between moments 2.17.5 Means of distributions 2.17.6 Standard deviations 2.17.7 Coefficient of variation 2.17.8 Applications 2.1 7.9 Transformation of abscissae Phi-notation Particle size by image analysis 112 Introduction 112 Optical microscopy 113 3.2.1 Upper size limit 114 3.2.2 Lower size limit 114 Sample preparation 115 Measurement of plane sections through packed beds 117 Particle size 117 Calibration 11 8 3.6.1 Linear eyepiece graticules 118 3.6.2 Globe and circle graticules 120 Training of operators 120 Experimental techniques 12 1 Determination of particle size distribution by number 122 Conditions governing a weight size determination 124 3.10.1 Illustrative example of the calculation of a size distribution by weight 125 Quantitative image analysis 128 3.1 1 .I Calibration of image analyzers 128 3.1 1.2 Experimental procedures 128 3.1 1.3 Commercial quantitative image analysis systems. 1 37 3.1 1.4 On-line microscopy 140 Electron microscopy 140 Transmission electron microscopy 14 1 3.1 3.1 Specimen preparation for TEM 142 3.13.2 Replica and shadowing techniques 145 3.1 3.3 Chemical analysis 145 Scanning electron microscopy 146 Other scanning electron microscopy techniques 148 Errors involved in converting a number to a volume count 148 Particle size analysis by sieving Introduction Woven-wire and punched plate sieves Electroforrned micromesh sieves viii Contents Woven-wire and punched plate sieves Electroformed micromesh sieves Standard sieves Mathematical analysis of the sieving process Calibration of sieves Sieving emrs Methods of sieving Amount of sample Hand sieving Machine sieving Wet sieving 4.12.1 Manual 4.12.2 Wet sieving by machine Air-Jet sieving The Sonic Sifter The Seishin Robot Sifter Automatic systems 4.16.1 The Gradex particle size analyzer 4.1 6.2 Labcon automatic sieve system Ultrasonic sieving The sieve cascadograph Felvation Self organized sieves (SORSI) Shape separation Correlation with light scattering data Conclusions Fluid classification Introduction Assessment of classifier efficiency Systems Counter-flow equilibrium classifiers in a gravitational field-elutriators Cross-flow gravitational classification 5.5.1 The Warmain Cyclosizer 5.5.2 The Humboldt particle size analyzer TDS Counter-flow centrifugal classifiers Cross-flow centrifugal classifiers Zig-zag classifiers Cross-flow elbow classifier Fractionation methods for particle size measurement Hydrodynamic chromatography Capillary hydrodynamic fractionation Capillary zone electrophoresis Size exclusion chromatography Ficld flow fractionation 5.15.1 Sedimentation field flow fractionation Contents ix 5.15.2 Time-delayed-exponential SF3 5.15.3 Thermal field flow fractionation 5.15.4 Magnetic field flow fractionation 5.15.5 Flow field flow fractionation 5.15.6 Steric field flow fractionation The Matec electro-acoustic system EAS-8000 Continuous SPLIT fractionation Classification by decantation Interaction between fluids and particles Introduction Settling of a single homogeneous sphere under a gravitational force 6.2.1 Relationship between settling velocity and particle size 6.2.2 Calculation of particle size in the laminar flow region Size limits for gravity sedimentation 6.3.1 Upper size limit 6.3.2 Lower size limit Time for terminal velocity to be attained Wall effects Errors due to discontinuity of the fluid Viscosity of a suspension Non-rigid spheres Non-spherical particles 6.9.1 Stokes region 6.9.2 Transition region Relationship between drag coefficient and Reynolds number in the transition region The turbulent flow region Concentration effects Hindered settling 6.13.1 Low concentration effects 6.13.2 High concentration effects Electro-viscosity Dispersion of powders 6.15.1 Dry powder dispersion 6.15.2 The use of glidants to improve flowability of dry powdels 6.15.3 Wet powder dispersion 6.15.4 Role of dispersing agents 6.15.5 Wetting a powder 6.15.6 Determination of contact angle (6) 6.15.7 Deagglornerating wetted clumps 6.15.8 Suspension stability 6.15.9 Tests of dispersion quality x Contents Sedimentation theory Powder density Liauid viscositv ~egolutiono f &dimenring suspensions Concentration changes in a suspension settling under gravity Relationship between density gradient and concentration 7.5.1 Hydrometers Theory for the gravity photosedimentation technique 7.6.1 The Beer-Lamben law 7.6.2 The extinction coefficient Theory for concentration determination with the x-ray gravitational sedimentation technique Theory for mass oversize distribution determination for cumulative, homogeneous, gravitational sedimentation Stokes equation for centrifugal sedimentation 7.9.1 General theory Stokes diameter determination for cumulative and incremental line-start techniques 7.10.1 Incremental, line-start, centrifugal technique 7.10.2 Homogeneous, cumulative, centrifugal technique 7.10.3 Sedimentation distance small compared with distance from centrifuge axis Line-start technique using a photocentrifuge 7.1 1.1 Introduction 7.1 1.2 Homogeneous mode 7.1 1.3 Line-start mode Theory for mass oversize distribution determination for cumulative, homogeneous, centrifugal sedimentation Theory for mass oversize distribution determination for incremental, homogeneous, centrifugal sedimentation 7.13.1 General theory 7.13.2 Variable time method 7.13.3 Variable inner radius (pipette withdrawal) 7.1 3.4 Variable measurement radius (scanning x-ray centrifuge) Sedimentation methods of particle size measurement Introduction Homogeneous incremental gravitational sedimentation 8.2.1 The pipette method of Andreasen 8.2.2 The photosedimentation technique 8.2.3 X-ray sedimentation 8.2.4 Hydrometers and divers Homogeneous cumulative gravitational sedimentation Contents xi 8.3.1 Introduction 8.3.2 Balances 8.3.3 Sedimentation columns Line-start incremental gravitational sedimentation 8.4.1 Photosedimentation Line-start cumulative gravitational sedimentation 8.5.1 Introduction 8.5.2 Methods Homogeneous incremental centrifugal sedimentation 8.6.1 Introduction 8.6.2 The Simcar pipette disc centrifuge 8.6.3 The Ladal pipette disc centrifuge 8.6.4 The Ladal x-ray disc centrifuge 8.6.5 The Du Pont/Brookhaven scanning x-ray disc centrifugal sedimentometer (BI-XDC) 8.6.6 The BI-DCP disc @hoto)centrifuge Cuvet photocentrifuges Homogeneous cumulative centrifugal sedimentation 8.8.1 Methods Line-start incremental centrifugal sedimentation 8.9.1 Disc photocentrifuges Line-start cumulative centrifugal sedimentation 8.10.1 MSA analyzer Particle size analysis using non-invasive dielectric sensors Conclusions Stream scanning methods of particle size measurement Introduction The electrical sensing zone method (The Coulter hinciple) 9.2.1 Introduction 9.2.2 Operating principle 9.2.3 Theory for the electrical sensing zone method 9.2.4 Effect of particle shape and orientation 9.2.5 Pulse shape 9.2.6 Effect of coincidence 9.2.7 Multiple aperture method for powders having a wide size range 9.2.8 Calibration 9.2.9 Carrying out a mass balance 9.2.10 Oversize counts on a mass basis using the Coulter Counter 9.2.1 1 Apparatus 9.2.12 Limitations of the method 9.2.1 3 Coulter Multisizer mass balance calculation for BCR 70 standard quartz powder Fiber length analysis xii Contents Optical particle counters 9.4.1 Aemmetrics Eclipse particle size analyzer 9.4.2 Hiac/Royco 9.4.3 Kratel Partascope 9.4.4 Kratel Partograph 9.4.5 Climet 9.4.6 Particle Measuring Systems 9.4.7 Howvision 9.4.8 Polytec HC (high concentration optical counter) 9.4.9 Lasentec 9.4.10 GdaiCIS 9.4.1 1 Spectrex Protovon 9.4.12 Spectrex PCT-1 laser particle counter 9.4.13 Procedyne 9.4.14 KaneMay 9.4.15 Met One 9.4.16 Erdco acoustical counter 9.4.17 Micro Pure Systems acoustic particle monitors (Moni tek) 9.4.1 8 Rion laser based liquidborne particle counter 9.4.19 FaleyStatus8000 9.4.20 Kowa Nanolyzerm PC-30 and PC-500 9.4.2 1 Malvem Autocounters 9.4.22 Particle Sizing Systems Accusizerm 770 9.4.23 AWK electronic sieve analyzer 9.4.24 PMT universal size distribution measuring systems 9.4.25 Canty Vision System 9.4.26 Contamination Control Systems Aerodynamic time-of flight measurement 9.5.1 Amherst API Aemsizer 9.5.2 The TSI Aerodynamic Particle Sizer APS 33B Laser phasemppler principle 9.6.1 BXRAL. PPLisatek and L2F 9.6.2 Hosokawa Mikropul E-Spart Analyzer 9.6.3 Aemmetrics phaseDoppler particle analyzer (APDPA) 9.6.4 Dantec Particle Dynamic Analyzer Interferometers 9.7.1 The TSI Liquitrakm interferometer Flow ultramicroscope 9.8.1 ISPA image analysis system Measurement of the size distribution of drops in dispersions Dupont electrolytic grain size analyzer TSI condensation particle counter TSI diffusion battery Contents xiii 9.13 TSI diffusional particle sizer 9.14 Differential mobility analyzer (DMA) 9.15 Scanning mobility particle sizer (SMPS) 9.16 Atmospheric particle counters 10 Field scanning methods of particle size measurement 10.1 Introduction 10.2 Effect of comminution on particle size distribution 10.3 Single point analyzers 10.3.1 Static noise measurement 10.3. 2 Ultrasonic attenuation. 10.3.3 $-ray attenuation 10.3.4 X-ray attenuation and fluorescence 10.3.5 Counter-flow classifiers 10.3.6 Hydrocyclones 10.3.7 The cyclosensor 10.3.8 Automatic sieving machines 10.3.9 Gas flow permearnetry 10.3.10 Correlation techniques 10.4 Low angle laser light scattering (LALLS) 10.4.1 Introduction 10.4.2 Theoretical basis for LALLS instruments 10.4.3 Commercial instruments 10.5 Optical incoherent space frequency analysis 10.6 Small angle x-ray scattering (SAXS) 10.7 Ultrasonic attenuation 10.8 Photon correlation specmscopy (PCS) 10.8.1 Introduction 10.8.2 Principles 10.8.3 Through dynamic light scattering 1 0.8.4 Particle size 10.8.5 Concentration effects 10.8.6 Particle interaction 10.8.7 Particle size effects 10.8.8 Polydispersity 10.8.9 The controlled reference method 10.8.10 Commercial equipment 1 0.8.1 1 Discussion 10.8.12 Diffusion wave spectroscopy (DWS) 10.9 Insitec Ensemble Particle Concentration-Size (EPCS) Systems 10.10 Turbo-Power Model TPO-400 10.11 Turbidity 10.12 Transient turbidity 10.13 Concentration monitors 10.14 Shape discrimination xiv Contents 11 Industrial applications of particle size measurement 1 1.1 Introduction 1 1.2 Industrial diamonds 1 1.3 Control of oversize particles 1 1.4 Starry night 1 1.5 Control of adhesive additives 1 1.6 Video-tape 1 1.7 Curve fitting 11.8 Effect of size distribution on filter efficiency 1 1.9 Predicting pigment gloss and hiding power 1 1.10 Strength of engineering plastics 1 1.1 1 Homogeneity control of ceramic paste 1 1.12 Flowability 1 1.13 Elimination of intra-lot variability by mixing 1 1.14 Mixing and segregation 1 1.15 Comminution 1 1.16 Attrition 1 1.17 Instnunent evaluation 1 1.17.1 Introduction 1 1.17.2 Evaluation procedure 11.17.3 Definition of accuracy 11.17.4 Definition of reproducibility 1 1.17.5 Mean accuracy and reproducibility 11.17.6 Discussion 1 1.18 Summary Appendix Manufacturers and suppliers Author index Subject index