A Study of the Physical Significance of Three‐Dimensional signature waveforms

Abstract

It has been shown that the projected area of a rotating fineparticle can be used to construct a signature waveform which is descriptive of some aspects of the three‐dimensional morphology of a fineparticle. If the fineparticle is rotated systematically about two mutually independent axes, through two sets of 90 degrees rotations, the signature waveform can be related to the surface area of the convex hull. It could be that the convex hull of a fineparticle is related to its fluid dynamic behaviour and its ability to modify the effective viscosity of a fluid in its suspension. This type of significance of different types of Cauchy signature waveforms are discussed. The concept of three‐dimensional signature waveforms is extended to cover the structural shape waveform and the fractal waveforms which, respectively, describe the spatial structure and the ruggedness of a fineparticle profile. The possible utilization of all three types of waveforms to describe in a complete manner the three‐dimensional structure of a rugged fineparticle is discussed.

Fractal Surfaces

“…The usual approach to using these projected profiles is to "unroll" them as a plot of radius vs. angle, perform harmonic (Fourier) analysis, and then apply statistical classification techniques to determine the particular frequencies that can distinguish particulate classes in any given instance (Ehrlich and Weinberg 1970;Beddow, Philip et al 1977;Flook 1982;Kaye, Leblanc et al 1983;Barth and Sun 1985;Kaye 1985b;Russ 1989;Klasa 1991). This was illustrated in Chapter 4, Figure 21.…”

Agglomeration of Chain-Like Combustion Aerosols Due to Brownian Motion

“…In our discussion of fractals so far, we have been describing only the density fractal of an infinite or very large cluster. However, structural fractals are also very useful for describing the rugged boundaries of fine particles (Kaye et al, 1984;Kaye, 1986). Kaye (1986) made a comparison between a straight line and a set of lines with varying degrees of curviness, and showed that all of these lines have a topological dimension of unity.…”

“…These fractal dimensions can also be related to the aspect ratios (length of the profile divided by its width) of the agglomerates, which can then be related to their aerodynamic properties (Kaye et al, 1984).…”

What Use are Fractals?

“…However, when we come to consider a respirable dust such as those present in a fumed smoke such as diesel exhaust soot, there is no simple way to relate the lodgability and surface reactivity of the dust to the aerodynamic diameter. We hope to be able to link the fractal dimension of the agglomerated structure to the physical behaviour of the agglomerate in a viscous fluid [49]. Shellac spheres have physical diameters identical with their aerodynamic diameters and can be used to illustrate the aerodynamic diameter of fractionated dust in a direct manner [54].…”