A.F. Vetter

Morphological fourier descriptors

Abstract The Fourier method of particle profile representation is presented and discussed. Rotationally invariant size and shape terms are derived from the Fourier particle profile representation. The shape terms are demonstrated to be rotationally invariant as well as magnification (size) invariant. The size and shape terms proposed are shown to include all the available information about the boundary of a particle profile. Mathematical and statistical interpretations of the size and shape terms proposed are demonstrated. Some actual and potential applications are discussed.

A simple relationship between particle shape effects and density, flow rate and Hausner Ratio

Abstract A study has been made of the relative magnitudes of particle shape effects on three bulk solids properties. The bulk solids used in this study were small plastic pellets of regular shapes and sizes. Experimental results indicate that variations in particle normal and tangential not-roundness have marked effects on the apparent density, flow rate and Hausner Ratio of the bulk solids. The not-roundness is the standard deviation of the radial distribution of the particle profile. It is a particle shape characteristic derived from morphological analysis. A simple relation of the form P(bulk property) = P(ideal) + P(deviation) is proposed and tested, in which P indicates the property under test. P(ideal) indicates the value of the property for perfect spheres; P(deviation accounts for the effect of particle shape.

On relating some particle profile characteristics to the profile fourier coefficients

Abstract This paper describes a preliminary investigation of the problems inherent in the development of an interface between a particle shape pre-processor and a binary computer. In the experiment described, the set of data points of the particle profiles are converted into sets of Fourier coefficients, which in turn are converted to features that appear to be capable of human operator assessment. Real particle profiles are analyzed to yield features which are tested for clustering tendencies in the pattern space. Advantages and disadvantages of the method are discussed.

A refined method of particle shape representation

Abstract A new method using parametric Fourier descriptors to represent particle shape is discussed. This method is compared with the ( R , θ) method described elsewhere [1]. The problem of profile re-entrance inherent in the ( R , θ) method is solved completely.

A shape-modified size correction for terminal settling velocity in the intermediate region

Abstract The terminal velocity of arbitrarily shaped sand particles was experimentally studied in the intermediate (or transition) Reynolds number region (2

A generalized method of morphological analysis (the (R,S) method)

Abstract Two methods to describe particle shape using a truncated Fourier series to represent the particle profile are presented. These are the (R,θ) and the (φ,l) methods. The advantages and disadvantages of each method are discussed and a new third method, called the (R,S) method, is proposed. The (R,S) method is shown to include advantages not common to the (R,θ) and the (φ,l) methods. The (R,S) method may have physical applications most pronounced in dendritic problems. Analogous size and shape terms [4] in the (R,S) method are presented. The mathematical and statistical interpretations of the size and shape terms are presented and analoged with those proposed [4] in the (R,θ) method. The disadvantages of the (R,S) method are discussed.

Acid—zinc reaction predictably affects particle morphology☆

Abstract The results in this investigation indicate that change of particle morphology as a chemical reaction progresses can be separated into two stages and that each can be predictably described by particle morphological analysis. The first stage involves the smoothing out of peaks and corners of the particle. The overall tendency of this stage is to attain a more regular geometry. In the second stage, new points of attack at the smoothed particle surface begin to develop and continue to develop as the reaction progresses. Both of these two stages of development can be reflected in a simple parameter which is the sum of the Fourier coefficients describing the particle shape. At the first stage this sum decreases, whereas at the second stage it increases again. Those more vulnerable points that are attacked could depend on the surface fine structure, positions of crystal defects and impurities within, rather than the shape of the particle. Although the first stage begins developing at the moment the chemical reaction is started, the second stage might occur at a much later time or be completely missing, depending on particle surface characteristics. In some cases the two stages may overlap to a certain extent but they are still separated far enough to make practical predictions meaningful. The above conclusions are drawn from studies of particles reacting in a homogeneous surrounding medium. For particles reacting in non-homogeneous surrounding, further investigations are necessary.

Effects of particle shape on two-phase flow in pipes

Abstract The results of this study show that particles with the same sphericity but of different shapes behave differently in slurry flow. Also, a quantitative relationship between pressure drop and particle morphological descriptors is determined. Five different shapes of particles with the same volume and surface area are used in this experiment. Each set of particles was circulated in a 24 ft long, 4 in ID Plexiglas pipe by a single-speed slurry pump. By changing the solids concentration of each set of particles, the pressure drop characteristics of the system were obtained.

Chemical disintegration of coal in triaxial stress fields

Abstract This paper studies the effects of stress and flow rate on comminution rates of a coal sample. Chemical disintegration of coal involves introducing a solvent or comminution reagent into a coal seam and converting the monolithic coal into a particulate slurry of coal particles. A 2.5 molar solution of methanol and sodium hydroxide solution at 55 °C was used as the chemical reagent and its comminution ability was studied under different applied stress and solvent flow rates. The comminution rates ranged from 19.5 to 1.2 mg/(cm2·h) as the overburden stress was increased from 0 to 17 MPa. The results showed a substantial increase in the comminution rate at stresses higher than 10 MPa and the disintegrated particles demonstrated a high degree of angularity, indicative of physical breakage. It was also shown that the fracturing rates increased with a rise in the solvent flow rate.

Morphological analysis of fine particle mixtures

Abstract Three analytical methods are used to estimate the morphological composition of binary and ternary powder particle mixtures. These are the mean value correlation method, the discrimination analysis method and a newly developed combination matrix method. The most accurate technique is the combination matrix method, which gave an estimate of the morphological composition of a mixture with a 0.04 × 10−2 mean squared error.