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Particulate Morphology - 1st Edition - ISBN: 9780123969743, 9780123971845

Particulate Morphology

1st Edition

Mathematics Applied to Particle Assemblies

Author: Keishi Gotoh
Paperback ISBN: 9780323282574
eBook ISBN: 9780123971845
Hardcover ISBN: 9780123969743
Imprint: Elsevier
Published Date: 21st March 2012
Page Count: 96
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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.

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.


Researchers and students in chemical engineering, materials science and mathematics

Table of Contents


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


No. of pages:
© Elsevier 2012
21st March 2012
Paperback ISBN:
eBook ISBN:
Hardcover ISBN:

About the Author

Keishi Gotoh

Keishi Gotoh

Affiliations and Expertise

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

Ratings and Reviews