Particulate Morphology

Particulate Morphology, 1st Edition

Mathematics Applied to Particle Assemblies

Particulate Morphology, 1st Edition,Keishi Gotoh,ISBN9780123971845





This book proposes a new scholarly basis for powder science and technology, and also for engineering sciences, which allows users to learn new applied mathematics.

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Key Features

  • Concisely explains various mathematics and tools applied to the subject.
  • Incorporates multiple fields to give a clear view of the application of mathematics in powder technology.


Encompassing over fifty years of research, Professor Gotoh addresses the correlation function of spatial structures and the statistical geometry of random particle assemblies. In this book morphological study is formed into random particle assemblies to which various mathematics are applied such as correlation function, radial distribution function and statistical geometry. This leads to the general comparison between the thermodynamic state such as gases and liquids and the random particle assemblies. Although structures of molecular configurations change at every moment due to thermal vibration, liquids can be regarded as random packing of particles. Similarly, gaseous states correspond to particle dispersion. If physical and chemical properties are taken away from the subject, the remainder is the structure itself. Hence, the structural study is ubiquitous and of fundamental importance. This book will prove useful to chemical engineers working on powder technology as well as mathematicians interested in learning more about the subject.


Researchers and students in chemical engineering, materials science and mathematics

Keishi Gotoh

Affiliations and Expertise

Toyohashi Sozo University and Toyohashi University of Technology, Toyohashi, Japan

Particulate Morphology, 1st Edition


1. Spatial Structure of Random Dispersion of Equal Spheres in One Dimension

1.1 Discrete System

1.2 Continuous System


2. Spatial Structure of Random Dispersion of Equal Spheres in Two Dimensions

2.1 Outline of Computer Simulation Experiments

2.2 Structure of Random Dispersion

2.3 Measurement of Dispersed State of Disk Particles


3. Preliminary Mathematics

3.1 Laplace Transform and Inversion Formula

3.2 Fourier Transform and Spectral Density

4. Radial Distribution Function

4.1 Definition of Radial Distribution Function

4.2 Ornstein–Zernike Equation

4.3 Solving Procedure

4.4 Analytic Solution by Percus–Yevick Approximation

4.5 Radial Distribution Function of Multisized Particle System

4.6 Radial Distribution Function of Binary-Sized Particle System and Applications


5. Sample Size for Measuring Particle Concentration

5.1 Distribution Functions

5.2 Sample Size of Measurement


6. Introduction to Statistical Thermodynamics

6.1 Quantum States of Steady Thermal Vibration

6.2 Analytical Dynamics and Generalized Coordinates

6.3 Stationary Distribution and Partition Function

6.4 Number Density and Distribution Function

6.5 Equation of State for Gases

7. Particulate Morphology

7.1 Random Packing

7.2 Random Dispersion

7.3 Molecular System and Particle Assemblies


Closing Remarks

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