Particle Size Measurement

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Particle size measurement is the crucial technique in powder technology, as the properties of a powder are dependent upon its particle size distribution. This reference for industrial and academic researchers discusses a wide range of measurement techniques in detail, together with chapters on accurate sampling and surface area determination. This edition third was 1981 increases coverage of on- line analysis, reflecting the shift in emphasis of powder characterization toward in-process size analysis. Annotation c. Book News, Inc., Portland, OR
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Product Details

  • ISBN-13: 9789401066730
  • Publisher: Springer Netherlands
  • Publication date: 4/26/2012
  • Series: Powder Technology Series
  • Edition description: Softcover reprint of the original 1st ed. 1990
  • Pages: 806
  • Product dimensions: 6.00 (w) x 9.00 (h) x 1.66 (d)

Table of Contents

1 Sampling of powders.- 1.1 Introduction.- 1.2 Theory.- 1.3 Weight of sample required.- 1.4 Statistical considerations.- 1.5 Golden rules of sampling.- 1.6 Bulk sampling.- 1.6.1 Stored non-flowing material.- 1.6.2 Stored free-flowing material.- 1.6.3 Moving powders.- 1.6.4 Sampling from a moving stream of powder.- 1.6.5 Sampling from a conveyor belt or chute.- 1.6.6 Sampling from a bucket conveyor.- 1.6.7 Bag sampling.- 1.6.8 Sampling spears.- 1.6.9 Sampling from wagons and containers.- 1.6.10 Sampling from heaps.- 1.7 Slurry sampling.- 1.8 Sample dividing.- 1.8.1 Scoop sampling.- 1.8.2 Coning and quartering.- 1.8.3 Table sampling.- 1.8.4 Chute splitting.- 1.8.5 The spinning riffler.- 1.9 Miscellaneous devices.- 1.10 Reduction from laboratory sample to analysis sample.- 1.11 Reduction from analysis sample to measurement sample.- 1.12 Experimental tests of sample-splitting techniques.- 2 Sampling of dusty gases in gas streams.- 2.1 Introduction.- 2.2 Basic procedures.- 2.2.1 Sampling positions.- 2.2.2 Temperature and velocity surveys.- 2.2.3 Sampling points.- 2.3 Sampling equipment.- 2.3.1 Nozzles.- 2.3.2 Dust-sampling collector.- 2.3.3 Ancillary apparatus.- 2.3.4 On-line dust extraction.- 2.3.5 The Andersen stack sampler.- 2.4 Corrections for anisokinetic sampling.- 2.5 Probe orientation.- 2.6 Radiation methods.- 3 Sampling and sizing from the atmosphere.- 3.1 Introduction.- 3.2 Inertial techniques.- 3.3 Filtration.- 3.4 Electrostatic precipitation.- 3.5 Electrostatic charging and mobility.- 3.6 Thermal precipitation.- 3.7 The quartz microbalance.- 3.8 Optical sensing zone methods.- 3.8.1 Air Technology.- 3.8.2 Atcor Net 2000.- 3.8.3 Bausch and Lomb.- 3.8.4 Beckman.- 3.8.5 Centre for Air Environmental Studies.- 3.8.6 Climet Series 7000.- 3.8.7 Coulter Model 550 contamination monitor.- 3.8.8 Dynac.- 3.8.9 Gardner.- 3.8.10 G.C.A. Miniram.- 3.8.11 Insitec PCSV-P.- 3.8.12 Kratel Partoscope.- 3.8.13 Leitz Tyndalloscope.- 3.8.14 Met One particle counters.- 3.8.15 Pacific Scientific Hiac/Royco particle counting systems.- 3.8.16 Particle Measuring Systems.- 3.8.17 RAC particle monitors.- 3.8.18 Rotheroe and Mitchell digital dust indicator.- 3.8.19 Saab photometer.- 3.8.20 Sartorius.- 3.8.21 Sinclair.- 3.8.22 Techecology.- 3.8.23 TSI particle counters.- 3.8.24 The particulate volume monitor.- 3.9 Condensation nucleus counters.- 3.10 Diffusion battery.- 3.11 The aerodynamic particle size analyser.- 3.12 Miscellaneous techniques.- 4 Particle size, shape and distribution.- 4.1 Particle size.- 4.2 Particle shape.- 4.2.1 Shape coefficients.- 4.2.2 Shape factors.- 4.2.3 Applications of shape factors and shape coefficients.- 4.2.4 Shape indices.- 4.2.5 Shape regeneration by Fourier analysis.- 4.2.6 Fractal dimension characterization of textured surfaces.- 4.3 Determination of specific surface from size distribution data.- 4.3.1 Number distribution.- 4.3.2 Surface distribution.- 4.3.3 Volume distribution.- 4.4 Particle size distribution transformation between number, surface and mass.- 4.5 Average diameters.- 4.6 Particle dispersion.- 4.7 Methods of presenting size analysis data.- 4.8 Devices for representing the cumulative distribution curve as a straight line.- 4.8.1 Arithmetic normal distributions.- 4.8.2 The log-normal distribution.- 4.8.3 The Rosin-Rammler distribution.- 4.8.4 Mean particle sizes and specific surface evaluation for Rosin-Rammler distributions.- 4.8.5 Other particle size distribution equations.- 4.8.6 Simplification of two-parameter equations.- 4.8.7 Evaluation of non-linear distributions on log-normal paper.- 4.8.8 Derivation of shape factors from parallel log-normal curves.- 4.9 The law of compensating errors.- 4.10 Alternative notation for frequency distribution.- 4.10.1 Notation.- 4.10.2 Moment of a distribution.- 4.10.3 Transformation from qt(x) to qr(x).- 4.10.4 Relation between moments.- 4.10.5 Means of distributions.- 4.10.6 Standard deviations.- 4.10.7 Coefficient of variation.- 4.10.8 Applications.- 4.10.9 Transformation of abscissa.- 4.11 Phi-notation.- 4.12 Manipulation of the log-probability equation.- 4.12.1 Average sizes.- 4.12.2 Derived average sizes.- 4.12.3 Transformation of the log-normal distribution by count into one by weight.- 4.13 Relationship between median and mode of a log-normal distribution.- 4.14 An improved equation and graph paper for log-normal evaluations.- 4.14.1 Applications.- 5 Sieving.- 5.1 Introduction.- 5.2 Woven-wire and punched plate sieves.- 5.3 Electroformed micromesh sieves.- 5.4 British Standard specification sieves.- 5.5 Methods for the use of fine sieves.- 5.5.1 Machine sieving.- 5.5.2 Wet sieving.- 5.5.3 Hand sieving.- 5.5.4 Air-jet sieving.- 5.5.5 The sonic sifter.- 5.5.6 Felvation.- 5.5.7 Self-organized sieve (SORSI).- 5.6 Sieving errors.- 5.7 Mathematical analysis of the sieving process.- 5.8 Calibration of sieves.- 6 Microscopy.- 6.1 Introduction.- 6.2 Optical microscopy.- 6.2.1 Sample preparation.- 6.2.2 Particle size distributions from measurements on plane sections through packed beds.- 6.3 Particle size.- 6.4 Transmission electron microscopy (TEM).- 6.4.1 Specimen preparation.- 6.4.2 Replica and shadowing techniques.- 6.4.3 Chemical analysis.- 6.5 Scanning electron microscopy (SEM).- 6.6 Manual methods of sizing particles.- 6.6.1 Graticules.- 6.6.2 Training of operators.- 6.7 Semi-automatic aids to microscopy.- 6.8 Automatic counting and sizing.- 6.9 Automatic image analysis.- 6.10 Specimen improvement techniques.- 6.11 Statistical considerations governing the determination of size distributions by microscope count.- 6.11.1 Frequency distribution determination.- 6.11.2 Weight distribution determination.- 6.12 Conclusion.- 7 Interaction between particles and fluids in a gravitational field.- 7.1 Introduction.- 7.2 Relationship between drag coefficient and Reynolds number for a sphere settling in a liquid.- 7.3 The laminar flow region.- 7.4 Critical diameter for laminar flow settling.- 7.5 Particle acceleration.- 7.6 Errors due to the finite extent of the fluid.- 7.7 Errors due to discontinuity of the fluid.- 7.8 Brownian motion.- 7.9 Viscosity of a suspension.- 7.10 Calculation of terminal velocities in the transition region.- 7.11 The turbulent flow region.- 7.12 Non-rigid spheres.- 7.13 Non-spherical particles.- 7.13.1 Stokes’ region.- 7.13.2 The transition region.- 7.14 Concentration effects.- 7.15 Hindered settling.- 7.15.1 Low-concentration effects.- 7.15.2 High-concentration effects.- 7.16 Electro-viscosity.- 8 Dispersion of powders.- 8.1 Discussion.- 8.2 Theory of wetting.- 8.3 The use of glidants to improve flowability of dry powders.- 8.4 Density determination.- 8.5 Viscosity.- 8.6 Sedimentation systems.- 8.7 Densities and viscosities of some aqueous solutions.- 8.8 Standard powders.- 9 Incremental methods of particle size determination.- 9.1 Basic theory.- 9.1.1 Variation in concentration within a settling suspension.- 9.1.2 Relationship between density gradient and concentration.- 9.2 Resolution for incremental methods.- 9.3 The pipette method.- 9.3.1 Experimental errors.- 9.4 The photosedimentation technique.- 9.4.1 Introduction.- 9.4.2 Theory.- 9.4.3 The extinction coefficient.- 9.4.4 Photosedimentometers.- 9.4.5 Discussion.- 9.5 X-ray sedimentation.- 9.6 Hydrometers.- 9.7 Divers.- 9.8 The specific gravity balance.- 9.9 Appendix: Worked examples.- 9.9.1 Wide-angle scanning photosedimentometer: analysis of silica.- 9.9.2 Conversion from surface distribution to weight distribution.- 9.9.3 The LADAL X-ray sedimentometer: analysis of tungstic oxide.- 10 Cumulative methods of sedimentation size analysis.- 10.1 Introduction.- 10.2 Line-start methods.- 10.3 Homogeneous suspensions.- 10.4 Sedimentation balances.- 10.4.1 The Gallenkamp balance.- 10.4.2 The Sartorius balance.- 10.4.3 The Shimadzu balance.- 10.4.4 Other balances.- 10.5 The granumeter.- 10.6 The micromerograph.- 10.7 Sedimentation columns.- 10.8 Manometric methods.- 10.9 Pressure on the walls of the sedimentation tube.- 10.10 Decanting.- 10.11 The—-back-scattering method.- 10.12 Discussion.- 10.13 Appendix: An approximate method of calculating size distribution from cumulative sedimentation results.- 11 Fluid classification.- 11.1 Introduction.- 11.2 Assessment of classifier efficiency.- 11.3 Systems.- 11.4 Counterflow equilibrium classifiers in the gravitational field - elutriators.- 11.4.1 Water elutriators.- 11.4.2 Air elutriators.- 11.4.3 Zig-zag classifiers.- 11.5 Cross-flow gravity classifiers.- 11.5.1 The Warmain cyclosizer.- 11.5.2 The Humboldt particle size analyser TDS.- 11.5.3 The cross-flow elbow classifier.- 11.6 Counterflow equilibrium classifiers in the centrifugal field.- 11.6.1 The Bahco classifier.- 11.6.2 The BCURA centrifugal elutriator.- 11.6.3 Centrifugal elutriation in a liquid suspension.- 11.7 Cross-flow equilibrium classifiers in the centrifugal field.- 11.7.1 Analysette 9.- 11.7.2 The Donaldson classifier.- 11.7.3 The Micromeritics classifier.- 11.8 Other commercially available classifiers.- 11.9 Hydrodynamic chromatography.- 11.10 Sedimentation field flow fractionation (SFFF).- 12 Centrifugal methods.- 12.1 Introduction.- 12.2 Stokes’ diameter determination.- 12.3 Line-start technique.- 12.3.1 Theory.- 12.3.2 Line-start technique using a photometric method of analysis.- 12.3.3 Early instruments: the Marshall centrifuge and the MSA particle size analyser.- 12.3.4 The phoentrifuge.- 12.3.5 Disc phoentrifuges.- 12.3.6 The cuvette phoentrifuge.- 12.4 Homogeneous suspension.- 12.4.1 Sedimentation height small compared with distance from centrifuge axis.- 12.4.2 The Alpine sedimentation centrifuge.- 12.4.3 The Mikropul Sedimentputer.- 12.5 Cumulative sedimentation theory for a homogeneous suspension.- 12.6 Variable-time method (variation of P with t).- 12.7 Variable inner radius (variation of P with S).- 12.8 Shape of centrifuge tubes.- 12.9 Alternative theory (variation of P with S).- 12.10 Variable outer radius (variation of P with R).- 12.11 Incremental analysis with a homogeneous suspension.- 12.11.1 The Simcar centrifuge.- 12.11.2 General theory.- 12.12 The LADAL X-ray centrifuge.- 12.13 The LADAL pipette withdrawal centrifuge.- 12.13.1 Theory for the LADAL pipette withdrawal technique.- 12.14 The supercentrifuge.- 12.15 The ultracentrifuge.- 12.16 Conclusion.- 12.17 Appendix: Worked examples.- 12.17.1 Simcar centrifuge.- 12.17.2 X-ray centrifuge.- 12.17.3 LADAL pipette centrifuge.- 13 The electrical sensing zone method of particle size distribution determination (the Coulter principle).- 13.1 Introduction.- 13.2 Operation.- 13.3 Calibration.- 13.4 Evaluation of results.- 13.5 Theory.- 13.6 Effect of particle shape and orientation.- 13.7 Coincidence correction.- 13.8 Pulse shape.- 13.9 Multiple aperture method for powders having a wide size distribution.- 13.9.1 General.- 13.9.2 Sieving technique.- 13.9.3 Sedimentation technique.- 13.10 Carrying out a mass balance.- 13.11 End-point determination.- 13.12 Upper size limit.- 13.13 Commercial equipment.- 13.14 Conclusions.- 14 Radiation scattering methods of particle size determination.- 14.1 Introduction.- 14.2 Scattered radiation.- 14.2.1 The Rayleigh region ($$(D \ll \lambda )$$).- 14.2.2 The Rayleigh-Gans region ( D <—).- 14.3 State of polarization of the scattered radiation.- 14.4 Turbidity measurement.- 14.5 High-order Tyndall spectra (HOTS).- 14.6 Particle size analysis by light diffraction.- 14.7 Light-scattering equipment.- 14.8 Holography.- 14.9 Miscellaneous.- 15 Permeametry and gas diffusion.- 15.1 Flow of a viscous fluid through a packed bed of powder.- 15.2 Alternative derivation of Kozeny’s equation using equivalent capillaries.- 15.3 The aspect factor k.- 15.4 Other flow equations.- 15.5 Experimental applications.- 15.6 Preparation of powder bed.- 15.7 Constant-pressure permeameters.- 15.8 Constant-volume permeameters.- 15.9 Fine particles.- 15.10 Types of flow.- 15.11 Transitional region between viscous and molecular flow.- 15.12 Experimental techniques for determining Z.- 15.13 Calculation of permeability surface.- 15.14 Diffusional flow for surface area measurement.- 15.15 The relationship between diffusion constant and specific surface.- 15.16 Non-steady-state diffusional flow.- 15.17 Steady-state diffusional flow.- 15.18 The liquid phase permeameter.- 15.19 Application to hindered settling.- 16 Gas adsorption.- 16.1 Introduction.- 16.2 Theories of adsorption.- 16.2.1 Langmuir’s isotherm for ideal localized monolayers.- 16.2.2 BET isotherm for multilayer adsorption.- 16.2.3 The n-layer BET equation.- 16.2.4 Discussion of BET theory.- 16.2.5 Mathematical nature of the BET equation.- 16.2.6 Shapes of isotherms.- 16.2.7 Modifications of the BET equation.- 16.2.8 The Hüttig equation.- 16.2.9 The relative method of Harkins and Jura (HJr).- 16.2.10 Comparison between BET and HJr methods.- 16.2.11 The Frenkel-Halsey-Hill equation (FHH).- 16.2.12 The Dubinin-Radushkevich equation (D-R).- 16.2.13 The VA-t method.- 16.2.14 Kiselev’s equation.- 16.3 Experimental techniques - factors affecting adsorption.- 16.3.1 Degassing.- 16.3.2 Pressure.- 16.3.3 Temperature and time.- 16.3.4 Adsorbate.- 16.3.5 Interlaboratory tests.- 16.4 Experimental technique-volumetric methods.- 16.4.1 Principle.- 16.4.2 Volumetric apparatus for high surface area.- 16.4.3 Volumetric apparatus for low surface area.- 16.5 Experimental techniques - gravimetric methods.- 16.5.1 Principle.- 16.5.2 Single-spring balances.- 16.5.3 Multiple-spring balances.- 16.5.4 Beam balances.- 16.6 Continuous-flow gas chromatographic methods.- 16.6.1 Commercially available continuous-flow apparatus.- 16.7 Standard volumetric gas-adsorption apparatus.- 16.7.1 Worked example using BS4359 standard apparatus.- 16.8 Commercially available volumetric- and gravimetric-type apparatus.- 17 Other methods for determining surface area.- 17.1 Introduction.- 17.2 Calculation from size distribution data.- 17.3 Adsorption from solution.- 17.3.1 Orientation of molecules at the solid-liquid interface.- 17.3.2 Polarity of organic liquids and adsorbents.- 17.3.3 Drying of organic liquids and adsorbents.- 17.4 Methods of analysis of amount of solute adsorbed on to solid surfaces.- 17.4.1 Langmuir trough.- 17.4.2 Gravimetric method.- 17.4.3 Volumetric method.- 17.4.4 The Rayleigh interferometer.- 17.4.5 The precolumn method.- 17.5 Theory for adsorption from a solution.- 17.6 Quantitative methods for adsorption from a solution.- 17.6.1 Adsorption of non-electrolytes.- 17.6.2 Fatty acid adsorption.- 17.6.3 Adsorption of polymers.- 17.6.4 Adsorption of dyes.- 17.6.5 Adsorption of electrolytes.- 17.6.6 Deposition of silver.- 17.6.7 Adsorption of p-nitrophenol.- 17.6.8 Other systems.- 17.7 Theory for heat of adsorption from a liquid phase.- 17.7.1 Surface free energy of a fluid.- 17.7.2 Surface entropy and energy.- 17.7.3 Heat of immersion.- 17.8 Static calorimetry.- 17.9 Flow microcalorimetry.- 17.9.1 Experimental procedures-liquids.- 17.9.2 Calibration.- 17.9.3 Determination of the amount of solute adsorbed: the precolumn method.- 17.9.4 Gases.- 17.9.5 Application to the determination of surface area.- 17.10 Density method.- 18 Determination of pore size distribution by gas adsorption.- 18.1 Miscellaneous techniques.- 18.2 The Kelvin equation.- 18.3 The hysteresis loop.- 18.4 Relationship between the thickness of the adsorbed layer and the relative pressure.- 18.5 Classification of pores.- 18.6 The—s method.- 18.7 Pore size distribution determination of mesopores.- 18.7.1 Modelless method.- 18.7.2 Cylindrical core model.- 18.7.3 Cylindrical pore model.- 18.7.4 Parallel plate model.- 18.8 Analysis of micropores: the MP method.- 18.9 Miscellaneous.- 19 Mercury porosimetry.- 19.1 Introduction.- 19.2 Literature survey.- 19.3 Contact angle and surface tension for mercury.- 19.4 Commercial equipment.- 19.5 Theory for volume distribution determination.- 19.6 Theory for surface distribution determination.- 19.6.1 Cylindrical pore model.- 19.6.2 Modelless method.- 19.7 Theory for length distribution determination.- 19.8 Worked example.- 19.9 Hysteresis.- 19.10 Delayed intrusion.- 19.11 Anglometers.- 19.12 Assessment of mercury porosimetry.- 19.12.1 Effect of experimental errors.- 19.12.2 Effect of interconnecting pores.- 19.12.3 Effect of contact angle.- 19.12.4 Other errors.- 19.13 Comparison with other techniques.- 19.14 Correction factors.- 20 On-line particle size analysis.- 20.1 Introduction.- 20.2 Stream-scanning techniques.- 20.2.1 Brinkmann analyser.- 20.2.2 Climet particle counting systems.- 20.2.3 Flowvision.- 20.2.4 Hiac/Royco (Pacific Scientific) particle counters.- 20.2.5 Horiba particle size analysers.- 20.2.6 The Insitec particle counter.- 20.2.7 Kane May particle size analysers.- 20.2.8 Kratel Partascope.- 20.2.9 Lasentec.- 20.2.10 Met One liquid particle counter.- 20.2.11 Particle Measuring Systems.- 20.2.12 Polytec.- 20.2.13 Procedyne particle size analyser.- 20.2.14 Spectrex Prototron particle counter.- 20.2.15 Talbot optical-electronic method.- 20.2.16 Miscellaneous optical methods.- 20.2.17 Echo measurement.- 20.2.18 The Erdco acoustical counter.- 20.2.19 The Coulter on-line monitor.- 20.2.20 On-line automatic microscopy.- 20.2.21 Comparison between stream-scanning techniques.- 20.3 Field-scanning techniques.- 20.3.1 Some properties of size distributions of milled products.- 20.3.2 Static noise measurement.- 20.3.3 Ultrasonic attenuation measurements.- 20.3.4—-ray attenuation.- 20.3.5 X-ray attenuation and fluorescence.- 20.3.6 Low-angle laser light scattering.- 20.3.7 Classification devices.- 20.3.8 Hydrocyclones.- 20.3.9 Screening: the Cyclosensor.- 20.3.10 Automatic sieving machines.- 20.3.11 Gas-flow permeametry.- 20.3.12 Pressure drop in nozzles.- 20.3.13 Non-Newtonian rheological properties.- 20.3.14 Correlation techniques.- 20.3.15 Photon correlation spectroscopy.- Problems.- Appendix 1 Equipment and suppliers.- Appendix 2 Manufacturers’ and suppliers’ addresses.- Author index.

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