Particle Size and Sizing Methods

In this chapter, the basic definitions of the equivalent diameter for an individual particle of irregular shape and its corresponding particle sizing techniques are presented. Typical density functions characterizing the particle size distribution for polydispersed particle systems are introduced. Several formulae expressing the particle size averaging methods are given. Basic characteristics of various material properties are illustrated. 

Particles used in practice for gas-solid flows are usually nonspherical and polydispersed. For a nonspherical particle, several equivalent diameters, which are usually based on equivalences either in geometric parameters (e.g., volume) or in flow dynamic characteristics (e.g., terminal velocity), are defined. Thus, for a given nonspherical particle, more than one equivalent diameter can be defined, as exemplified by the particle shown in Fig. 1.2, in which three different equivalent diameters are defined for the given nonspherical particle. The selection of a desired definition is often based on the specific process application intended. 

Source T. Allen s Particle Size Measurements, Chapman Hall, 1990. 

United States Department of Agriculture (USDA) classification 

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This account of the kinetics of reactions between (inorganic) solids commences with a consideration of the reactant mixture (Sect. 1), since composition, particle sizes, method of mixing and other pretreatments exert important influences on rate characteristics. Some comments on experimental methods are included here. Section 2 is concerned with reaction mechanisms formulated to account for observed behaviour, including references to rate processes which involve diffusion across a barrier layer. This section also includes a consideration of the application of mechanistic criteria to the classification of the kinetic characteristics of solid-solid reactions. Section 3 surveys rate processes identified as the decomposition of a solid catalyzed by a solid. Section 4 reviews other types of solid + solid reactions, which may be conveniently subdivided further into the classes... 

TTiere are several particle sizing methods, all based upon sedimentation and Stokes Law. If a particle is suspended in a fluid (which may be gas, or any liquid), the force of resistance to movement by the particle will be proportional to the particle s velocity, v, and its radius, r, vis-... 

Methods for making both forms solvent-soluble were the subject of many patents and closely guarded industrial secrets, but much of the mystery was cleared up in two papers by Gerstner [23] and Smith and Easton [24] published in 1966, by which time X-ray diffraction, electron microscopy and disc centrifuge particle sizing methods had been brought to bear on the problem. 

Agut et al. (2011) assessed the different technology transfer options and reported that within Sanofi-Aventis that option 1 (comparative testing) is the approach of choice for critical methodologies, i.e. assay, degradation products, and in some cases water content and dissolution. Option 2 (co-validation) is reserved for less-critical methodologies, i.e. residual solvents by gas chromatography (GC), water content, dissolution and particle size methods whereas, option 4 (transfer waiver) is restricted to pharmacopoeial compendial methods, i.e. appearance, pH, particulate matter, etc. 

The sizing methods involve both classical and modem instrumentations, based on a broad spectrum of physical principles. The typical measuring systems may be classified according to their operation mechanisms, which include mechanical (sieving), optical and electronic (microscopy, laser Doppler phase shift, Fraunhofer diffraction, transmission electron miscroscopy [TEM], and scanning electron microscopy [SEM]), dynamic (sedimentation), and physical and chemical (gas adsorption) principles. The methods to be introduced later are briefly summarized in Table 1.2. A more complete list of particle sizing methods is given by Svarovsky (1990). 

Microscopy remains the principal standard method of particle sizing and of shape and morphological classification. Though often tedious and time consuming in its application, it remains a standard by which individual particles can be classified with confidence and most particle sizing methods are referenced. 

Detection limit, quantification limit, accuracy, and specificity are not normally considered appropriate for validation of particle sizing methods. 

The author of these recommendations added that the validation of particle sizing technique cannot be completed with the first batch of a sample, as data are insufficient to fully validate the procedure at this stage. It is not always important to know the absolute particle size of the first batch manufactured, but it is important to know how the second and subsequent batches compare with it. The validation of a particle size method should be in phases, with parts completed when the first sample is analyzed and other data completed or added later, for example, prior to the regulatory filing. Calibration or verification of an instrument being used is assumed to be normal part of GMP and may be used as a suitability assessment. " ... 

This paper focuses on the application of two particle sizing methods, laser diffraction spectroscopy and ultrasonic attenuation spectroscopy, to the characterization of suspensions of filmed powders. 

In most applications more than one particle is observed. As each individual may have its own particle size, methods for data reduction have been introduced. These include the particle-size distribution, a variety of model distributions, and moments (or averages) of the distribution. One should also note that these methods can be extended to other particle attributes. Examples include pore size, porosity, surface area, color, and electrostatic charge distributions, to name but a few. 

Polydispersed aerosols are used for the efficiency-by-particle size method. Upstream and downstream measurements are made using optical particle counting devices at a variety of flow rates. The dust-holding capacity of a filter is a measurement of the synthetic dust loaded onto a filter under established procedures and a measurement of the pressure drop as the loading increases. 

Increasing interest in detailed experimental analysis of two-phase flows has led to a number of review papers on single point laser measurements. A more general overview on two-phase flow measurements was given for example by Taylor (1994) focusing on current activities in PDA development and PIV applications in two-phase flows. Applications of LDA and PDA for analyzing flows with combustion were reviewed by Heitor et al. (1993), and a more industrial orientated review on particle sizing methods can be found in Black et al. (1996). 

The specific, particle sizing method chosen depends on the type of. size information needed and the chemical and physical properties of the sample. In addition to the three techniques discussed here, molecular sieving, electrical conductance, microscopy, capillary hydrodynamic chromatography, light obscuration counting, field-flow fractionation, Doppler anemometry, and ultrasonic spectrometry-are commonly applied. Huch of the particle sizing methods has its advantages and drawbacks for particular samples and analyses. 

Before choosing a particle sizing technique, examination of the samples under a microscope is usually wise becau.se the range of sizes and shapes present can then he estimated. Most particle size methods are sensitive to particle shape and all are limited with respect to the particle size range. Particles with approximately spherical shapes are measured most accurately. Needles and other shapes that differ significantly from spherical are often analyzed by microscopy. 

Table 12.3 Particle size methods and size ranges...

It must be remembered that different particle size methods yield different results. Because they respond differently to shape and wientation, they measure different prc erties and equate to different equivalent diametos, as discussed in Section 12.2.2. It is equally important to understand that an instrument that serves well for one particular problem will not necessarily do the job for a different problem. 

There is no universal particle size method or instmment that can satisfy all the varied criteria and needs, and furthermore, it is highly unlikely that sudi a device will materialize within the foreseeable future. Indeed, no new principles or methodology have been wimessed in many decades. This does not, however, imply nor say that there have been no new developments or improvements in the field of particle size measurements. Quite to the contrary, there have been many new and exciting developments of interest and value to research as well as industry. 

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