Particle shape elongation

Particles shape. Elongated particles sieve more slowly than compact particles. 

Particle Shape. Whereas the Stokes particle is assumed to be a sphere, very few real soHds are actually spherical. Flat and elongated particles sediment slower than spheres. For maximum sedimentation rate, the particle should be as spherical as possible. 

While the shape factor, introduced in the previous section, provides a quantitative definition or description of particle shape, there are other descriptors such as flakiness ratio, flakiness index, elongation index and angularity number which are also found to be in vogue. 

Characterization of the particle shape is generally described by the deviation from sphericity, as in the case of ellipsoids where the ratio of the two radii is the measure of deviation. The surface and volume are important properties aflected by the overall shape of a particle. A more complicated relationship for particle characterization was described by Heywood, who introduced shape coefficients such as surface and volume coefficients and elongation and flatness ratios [42]. 

Fig. 5.22 (A-D) Scheme of Au nanoparticle growth between bilayers (A) nucleation at bilayer interfaces and bulk-like growth when particle size is smaller than the lamellar d spacing (B) once the transversal particle size is larger than the d spacing, growth is slowed by the bilayers, the transversal Au3+flux being limited, leadingto elongated particles shapes (C) when the constraint exerted by the particles on the bilayers is...

Note that we have only presented a few examples. Bulk density is a measure of how well particles pack together in a defined volinne. It depends on the shape of the particles comprising the powder. Most of the organic compounds (pharmaceuticals) will exhibit elongated shaped particles. Note that at least 50% of the voliunes presented in 4.1.12 are. in most cases, unoccupied space, i.e.-porosity. We conclude that if someone measures the particle size and the size distribution, we need to know exactly what was measured, often in terms of the particle shape. Particle size is customarily measured in terms of two-dimensioned (physical eispect) or three-dimensioned (volume) values. However, the particle size is often deseribed in terms of spheroidal diameters even though the peirticles may be aclcular in nature. 

We have already discussed measurement of particle size by the use of particle dimensions in Section II. where particle shape as relating to particle size was a major concern. Note that even though the shape of the particle may be quite elongated, the stated size wiU be predicated upon a spheroidal shape. The stated (measured) size of a PSD based upon weight will depend upon how well the particles were separated into fractions. For example, if we use a set of sieves to separate particle fractions, the fractions of particles measured may, or may not, be a function of shape. Acicular particles will not pass through a given screen the same way as... 

Many uses of aggregates require cubical particle shapes (see sections 8.3.3 and 8.5.4). Products which are excessively flaky may be brought within specification by the use of de-flaking screens. These may have transverse, elongated or slotted apertures, and may incorporate weirs or baffles to improve the presentation of slabby particles. In some cases, such screens simply remove a size fraction which has been found to be particularly flaky. 

Equation 2.65 defines the useful quantity known as the specific surface area, i.e. the surface area per unit mass of solid. The constant F( = fsjfv = /31a) may be called the overall, surface-volume or specific surface shape factor. For spheres and cubes, F = 6. For other shapes F > 6. For an octahedron fy = J 2) 3,fs = 2 /3 and F = 7.35. Values of F 10 are frequently encountered in comminuted solids, and much higher values may be found for flakes and plate-like crystals. If the particles are elongated or needle-shaped, their volume and surface area may be calculated on the assumption that they are... 

Figure 9.28. Effect of particle shape on the caking of crystals a) large uniform granular crystals good) b) non-uniform granular crystals poor) (c) large uniform elongated crystals poor) d) non-uniform elongated crystals very bad)...

---