Particle shape distribution

The most complete information that can be obtained in dispersion analysis comes from the determination ofparticle size distributionfunction (in some cases one may be interested in obtaining particle shape distribution). Some methods yield only the information on the average particle size, which in some cases may be accompanied by some conditional distribution width. These terms require a more detailed discussion, as different methods may yield different size distribution functions and average sizes for the same disperse system. 

Figure 9.23 TEM images showing morphology of shape-specific particles, shape distribution diagrams, and Arrhenius plots for each nanoshape. (Reprinted with permission from [242]. Copyright 2005 American Chemical Society.)...

Fiarticle morphology porosity, relative length scale of polymer and pore phases, particle shape, distribution of phases in high-impact polypropylene Interphase heat and mass transfer phenomena Intraphase heat and mass transfer phenomena Observed kinetics, rate limiting steps Phase equilibrium, monomer sorption and desorption in polymer phase, diffusion Fbrticle agglomeration Micromixi ng... 

The most common tests involve analytical data such as particle size, particle size distribution, and particle shape. The standard method for more granular materials and coarser powders is sieve analysis [153], whereas for fine materials laser diffraction is well established [154]. If the particle shape and particle shape distribution are of special interest, optical systans are preferred, in which a multitude of single particles are detected by a camera and pictures of the particles may be analyzed [155],... 

Important bulk properties are bulk density, compressibility, internal coefficient of friction, external coefficient of friction, particle size and particle size distribution, and particle shape and particle shape distribution. 

This chapter will highlight the factors of packing (bulk density, voidage), rate of flow, compressibility of packing, flowability, failure properties and angle of internal friction, cohesion, strength and adhesion. The factors of particle size distribution, specific surface area and particle shape distribution have already been dealt with elsewhere (Stanley-Wood 2000, 2005). 

Spartakov A, Trusov A, Vojtylov V. Magnetooptical determination of particle shape distribution in colloids. Colloid Surf A Physicochem Eng Asp 2002 209(2-3) 131-137. 

This ideal case is rarely if ever encountered in practice in general there will be a distribution of particle sizes rather than a single size, and in addition there will usually be a range of particle shapes, many of them highly irregular. 

The term essentially a drag coefficient for the dust cake particles, should be a function of the median particle size and particle size distribution, the particle shape, and the packing density. Experimental data are the only reflable source for predicting cake resistance to flow. Bag filters are often selected for some desired maximum pressure drop (500—1750 Pa = 3.75-13 mm Hg) and the cleaning interval is then set to limit pressure drop to a chosen maximum value. 

Filler particle si2e distribution (psd) and shape affect rheology and loading limits of filled compositions and generally are the primary selection criteria. On a theoretical level the influence of particle si2e is understood by contribution to the total energy of a system (2) which can be expressed on a unit volume basis as ... 

Deterrnination of the specific surface area can be made by a variety of adsorption measurements or by air-permeability deterrninations. It is customary to calculate average particle size from the values of specific surface by making assumptions regarding particle size distribution and particle shape, ie, assume it is spherical. 

Apparent Density. This term refers to the weight of a unit volume of loose powder, usually expressed in g/cm (l )- The apparent density of a powder depends on the friction conditions between the powder particles, which are a function of the relative surface area of the particles and the surface conditions. It depends, furthermore, on the packing arrangement of the particles, which depends on the particle size, but mainly on particle size distribution and the shape of the particles. 

The characteristics of a powder that determine its apparent density are rather complex, but some general statements with respect to powder variables and their effect on the density of the loose powder can be made. (/) The smaller the particles, the greater the specific surface area of the powder. This increases the friction between the particles and lowers the apparent density but enhances the rate of sintering. (2) Powders having very irregular-shaped particles are usually characterized by a lower apparent density than more regular or spherical ones. This is shown in Table 4 for three different types of copper powders having identical particle size distribution but different particle shape. These data illustrate the decisive influence of particle shape on apparent density. (J) In any mixture of coarse and fine powder particles, an optimum mixture results in maximum apparent density. This optimum mixture is reached when the fine particles fill the voids between the coarse particles. 

The value of pigments results from their physical—optical properties. These ate primarily deterrniaed by the pigments physical characteristics (crystal stmcture, particle size and distribution, particle shape, agglomeration, etc) and chemical properties (chemical composition, purity, stabiUty, etc). The two most important physical—optical assets of pigments are the abiUty to color the environment in which they ate dispersed and to make it opaque. 

The most commonly measured pigment properties ate elemental analysis, impurity content, crystal stmcture, particle size and shape, particle size distribution, density, and surface area. These parameters are measured so that pigments producers can better control production, and set up meaningful physical and chemical pigments specifications. Measurements of these properties ate not specific only to pigments. The techniques appHed are commonly used to characterize powders and soHd materials and the measutiag methods have been standardized ia various iadustries. 

Some particle size measuring techniques ate more particle shape sensitive than others. Data obtained by different methods can be significantly different, and whenever a particle size is reported, the measuring technique and conditions should always be mentioned. Even using the same equipment, the extremes of the distributions (low and high 10%) are usually not readily reproducible. 

Rehydration Bonded Alumina. Rehydration bonded aluminas are agglomerates of activated alumina, which derive their strength from the rehydration bonding mechanism. Because more processing steps are involved in the manufacture, they are generally more expensive than activated aluminum hydroxides. On the other hand, rehydration bonded aluminas can be produced in a wider range of particle shape, surface area, and pore size distribution. 

The particle size deterrnined by sedimentation techniques is an equivalent spherical diameter, also known as the equivalent settling diameter, defined as the diameter of a sphere of the same density as the irregularly shaped particle that exhibits an identical free-fall velocity. Thus it is an appropriate diameter upon which to base particle behavior in other fluid-flow situations. Variations in the particle size distribution can occur for nonspherical particles (43,44). The upper size limit for sedimentation methods is estabHshed by the value of the particle Reynolds number, given by equation 11 ... 

Particle-Size Distribution. Particle size, crystal shape, and distribution of vanillin ate important and gready affect parameters such as taste. 

Zinc dust is smaller in particle size and spherical in shape, whereas zinc powder is coarser in size and irregular in shape. The particle size of zinc dust, important in some appHcations, is controUed by adjusting the rate of condensation. Rapid cooling produces fine dust, slower condensation coarse dust. In the case of zinc powder, changes in the atomization parameters can be employed to change particle size to some degree. The particle size distributions for commercial zinc powders range from 44 to 841 p.m (325—20 mesh). The purity of zinc powders is 98—99.6%. 

In addition to surface area, pore size distribution, and surface chemistry, other important properties of commercial activated carbon products include pore volume, particle size distribution, apparent or bulk density, particle density, abrasion resistance, hardness, and ash content. The range of these and other properties is illustrated in Table 1 together with specific values for selected commercial grades of powdered, granular, and shaped activated carbon products used in Hquid- or gas-phase appHcations (19). 

Glassification. Classification (2,12,26,28) or elutriation processes separate particles by the differences in how they settle in a Hquid or moving gas stream. Classification can be used to eliminate fine or coarse particles, or to produce a narrow particle size distribution powder. Classification by sedimentation iavolves particle settling in a Hquid for a predetermined time to achieve the desired particle size and size distribution or cut. Below - 10 fim, where interparticle forces can be significant, gravitational-induced separation becomes inefficient, and cyclone and centrifugation techniques must be used. Classification also separates particles by density and shape. Raw material separation by differential sedimentation is commonly used in mineral processiag. 

Properties Affecting Solids Mixing Wide differences among properties such as particle-size distribution, density, shape, and surface characteristics (such as elec trostatic charge) may m e blending very difficult. In fact, the properties of the ingredients dominate the mixing operation. The most commonly observed characteristics of solids are as follows ... 

Although it is entirely possible for erosion-corrosion to occur in the absence of entrained particulate, it is common to find erosion-corrosion accelerated by a dilute dispersion of fine particulate matter (sand, silt, gas bubbles) entrained in the fluid. The character of the particulate, and even the fluid itself, substantially influences the effect. Eight major characteristics are influential particle shape, particle size, particle density, particle hardness, particle size distribution, angle of impact, impact velocity, and fluid viscosity. 

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