Particle silhouette

Meloy, T. P. (1977), Fast Fourier transforms applied to shape analysis of particle silhouettes to obtain morphological data, Powder Technology, 17, 27-35. 

In 1969 and 1971 Meloy presented papers in which fast Fourier transforms were used to process particle silhouettes as signals [47,48] and this work was extended in 1977 [49,50]. One of their main conclusions was that particles have signatures which depend on and not on and they proposed the equation ... 

Beddow [42] showed how a number of particle silhouette shapes could be analyzed and reproduced by Fourier transforms. Gotoh and Finney [52] proposed a mathematical method for expressing a single, three-dimensional body by sectioning as an equivalent ellipsoid having the same volume, surface area and projected area as the original body. 

Normand, M.D. and Peleg, M. 1986. Determination of the fractal dimension of a particle silhouette using image-processing techniques. Powder Technol. 45, 271-275. 

Peleg, M. and Normand, M.D. 1985b. Mechanical stability as the limit to the fractal dimension of solid particle silhouettes. Powder Technol. 43, 187-188. 

The most severe limitation of optical transmission microscopy is its small depth of focus, which is about 10 pm at a magnification of lOOx and about 5 pm at lOOOx. This means that, for a sample having a wide range of sizes, only a few particles are in focus in any field of view. Further, in optical transmission microscopy, the edges of the particles are blurred due to diffraction effects. This is not a problem with particles larger than about 5 pm since they can be studied by reflected light, but only transmission microscopy, with which silhouettes are seen, can be used for smaller particles. 

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... 

Figure 239. Silhouettes of particles of carbon black morphologies (a) spherical and individual, (b) agglomerated into approximately spherical shapes, (c) agglomerated linearly and (d) agglomerated into linear but branched systems (Taylor, 1997).

Once the various samples of oil and debris have been collected it is desirable to view them with a metallurgical microscope. To present the particles in an acceptable manner, the sample bottle is drawn through a 0.8 mm Millipore Isopore filter using a standard filter assembly with vacuum pump. This particular filter is used because it is transparent when examining the particles in transmitted lighting conditions that can yield silhouette images useful for computer-based analyses. 

LaserNet, produced by the US Naval Research Laboratory already extracts size and silhouette features of wear debris in oil and can also assess machine condition using information on particle size distribution. 

Figure 2.3.2 from Kaye (1995) shows silhouettes of dynamically equivalent particles. The more nonspherical the actual particle, the larger it needs to be in order for it to settle with the same terminal velocity. The spheres to the right are Stokes diameters, those to the left aerodjmamic diameters. Since uranium dioxide is far denser than 1000 kg/m, the two diameters differ the most for this type of particle. 

Fig. 2.3.2. Silhouettes of several different particle types along with their equivalent aerodynamic and Stokesian diameters from Kaye (1995)...

The utility of microscopic size measurements of irregular particles often depends on the ability to convert the measured sizes to other equivalent diameters that describe the behavior rather than the geometry of the particles. The most useful of these diameters is the equivalent volume diameter, which can be combined with the dynamic shape factor (Section 3.5) to describe the aerodynamic properties of a particle. The volume shape factor relates the voliune of a particle, v, to one of the silhouette diameters described before and is defined, for the projected area diameter, by... 

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