Determination of particle shape

Particle shape is of the greatest importance for agglomeration. Typical characteristics are particle roundness or the general overall shape and surface roughness. For some binding mechanisms and/or agglomeration methods, the particle shape is the most decisive particle characteristic. 

To overcome this problem, particles can be described by polar coordinates. A radius vector is drawn from the center of gravity to the particle surface. By using the radius and the two polar coordinate angles, all points on the particle surface can be described. This technique can define the shape of a particle surface to any desired degree of accuracy. 

A whole series of orthonormal functions can be used to interpret the information. The most familiar and applicable are the Fourier functions. Before being able to compose a particle shape descriptor in the polar system by the use of Fourier functions, one must realize that all that is normally known of a particle is its silhouette or profile. Therefore, methods must be found to interpret information from cuts through the particle or scans of portions of the surface area and connect it with overall shape. It is assumed that the silhouette of any cut or sample of the surface will give all information, such as roughness and other physical parameters, needed to describe the entire particle surface. Thus, unless the silhouette of a particle misses a unique, dominant feature of the particle shape, it will be representative of the particle. By sampling 

The methods are very complicated and require a large number of discrete items of information to describe a particle shape reasonably well they actually produce the signature of the particle, particularly if the coefficients are coupled with their respective phase angle. Meloy found that, in spite of a considerable scatter of data points, the log-log plot of coefficient amplitudes yields a straight line. He named this the law of morphological coefficients and defined the concept of random particles whereby, by definition and under certain assumptions, a random particle has a straight line as its signature. 

Until now, most of the analytical work done on particles using these techniques has assumed that the particle was essentially a sphere and has measured the deviation from sphericity, e.g. by using orthonormal functions, such as the Fourier set. New approaches define families of macroenvelopes which, instead 

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Considerable attention is also given to the methods that need to be used to adequately characterise a filler for use in thermoplastic applications, particularly the determination of particle shape and size. 

B. Determination of Particle Shape from Intrinsic Viscosity. 333... 

Part 2 Determination of particle size — Test sieves, nominal size of apertures Part 3 Determination of particle shape of aggregates — Flakiness index Part 4 Determination of particle shape of aggregates — Shape index... 

Part 3 Determination of particle shape of aggregates - Flakiness index . 

Source Reproduced from CEN EN 933-3, Tests for geometrical properties of aggregates - Part 3 Determination of particle shape - Flakiness index,... 

There are a large number of transformation models which can be used to analyze the image dimensional parameters in the determination of particle shape. Some methods require additional information of particle surface area, volume or thickness to give better estimates of shape but for most purposes, a simple approach is often preferred. The common treatment of data, namely, breadth, length, perimeter, and area to reflect the particle shape (1,2) is given as follows ... 

Previously, we demonstrated the ability of infrared spectroscopy to measure particle size in streams of ash, coal, and silica (18). The size determinations are based on Mie theory, which provides a general relationship between particle size and the wavelength dependence of infrared light scattering. Here we focus on the determination of particle shape, in addition to size, and report in-situ measurements of both titania and silica particles formed in a diffusion flame reactor. 

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. 

Size. The precise determination of particle size, usually referred to as the particle diameter, can actually be made only for spherical particles. For any other particle shape, a precise determination is practically impossible and particle size represents an approximation only, based on an agreement between producer and consumer with respect to the testing methods (see Size measurement of particles). 

Surfa.ce, Any reaction between two powder particles starts on the surface. The amount of surface area compared to the volume of the particle is, therefore, an important factor in powder technology. The particle—surface configuration, whether it is smooth or contains sharp angles, is another. The particle surface area depends strongly on the method of production, as shown in Table 1. The method of production usually determines the particle shape. 

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. 

There are various methods for the determination of the surface area of solids based on the adsorption of a mono-, or polymolecular layer on the surface of the solid. These methods do not measure the particle diameter or projected area as such, but measure the available surface per gram or milliliter of powder. The surface measured is usually greater than that determined by permeability methods as the latter are effectively concerned with the fluid taking the path of least resistance thru the bed, whereas the adsorbate will penetrate thru the whole of the bed as well as pores in the powder particles. These methods appear to be more accurate than surface areas calculated from weight averages or number averages of particle size because cracks, pores, and capillaries of the particles are included and are independent of particle shape and size... 

Some particles, particularly the biogenous ones, are prone to alteration as they settle onto the sediments and then imdergo burial. The likelihood of particle preservation is generally enhanced in settings where the trip to the seafloor is short and burial rates are fast. The time a particle takes to settle onto the seafloor is determined by water depth and particle sinking rates. The latter is a function of particle shape and density. Seawater... 

Diagrammatic representation of scattering data on large particles, obtained at different angles but at the same concentration, constructed by plotting sin (.6y2)AR(6) versus sin(0/2), or q AR 9) versus q, and used for the determination of molecular shape. For definitions of symbols, see Definition 3.3.12. 

The effect of particle shape was not determined, but is expected to be of minor importance. 

Having determined cp experimentally, one may roughly (to the first approximation) evaluate the viscosity of the plastisol. The real plastisols of course are not ideal dispersed systems, and their viscosity as a rule is essentially different from that given in Eq. (3.1). This results not only from the low accuracy of

particle shape from the ideal sphere (K / 2.5), but also from the strong influence of a number of factors which will be discussed below on the basis of the available published data. 

Influence of Particle-Shape and Moisture on Porosity—Graton and Fraser (1935) examined the influence of particle-shape on porosity under dry and wet conditions. All samples studied by these investigators passed an 18- and were retained on 35-mesh Tyler screens. Their results for several materials are shown in Table 29. The loose state was the arrangement assumed by the particles when poured into the test container. The compact state was achieved by tapping the test container. In the wet state the material was first wetted and poured into the measuring container filled with water. After the desired packing was obtained, the material was dried at 110 deg C, collected, then weighed and its volume determined. It is to be noted in Table 29 that wet materials pack more loosely than dry materials. 

Determination of Surface-Shape Factor—The shape-factor is one which, when multiplied by the square of the diameter of a hypothetical particle having an average surface, gives the true surface. The shape-factor is given by Eq (3-41)... 

Particle behavior is a function of particle size, density, surface area, and shape. These interact in a complex manner to give the total particle behavior pattern [28], The shape of a particle is probably the most difficult characteristic to be determined because there is such diversity in relation to particle shape. However, particle shape is a fundamental factor in powder characterization that will influence important properties such as bulk density, permeability, flowability, coatablility, particle packing arrangements, attrition, and cohesion [33-36], Consequently it is pertinent to the successful manipulation of pharmaceutical powders that an accurate definition of particle shape is obtained prior to powder processing. 

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