Particle Size Measurement

ISBN-13: 9789401066730 / Angielski / Miękka / 2012 / 806 str.

Terence Allen

Opis

Powder technology is a subject in its own right, and powder characterization is central to an understanding of this discipline. In the eight years since the printing of the third edition of Particle Size Measurement there have been two big changes in my life. After thirty years of academia I have returned to industry, and after a lifetime in Great Britain I have emigrated to the United States. In industry the initial demand is to relate powder properties to product performance and then to maintain powder consistency. This requires on-line or rapid off-line analysis which, in turn, has led to the demand for a whole range of new instruments whose primary function is process monitoring. Historically, chemical engineering courses have concentrated on the be- haviour of fluids, and engineers enter industry relatively unschooled in the subject of powder behaviour . Yet, when my colleagues Reg Davies and John Boughton surveyed three thousand Dupont products, they discovered that 80% involved powder at some stage of their manufacture. The results of this survey illustrate the need for more training in this key subject. This edition reflects the changing image of powder characterization towards in-process size analysis. Hence the chapter covering on-line analysis has been largely re-written. Apart from this, I have expanded certain sections and describe the new instruments that have been introduced since the last edition.

Spis treści

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 photocentrifuge.- 12.3.5 Disc photocentrifuges.- 12.3.6 The cuvette photocentrifuge.- 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.