Particulate Morphology: Mathematics Applied to Particle Assemblies

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.

Preface

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

2. Spatial Structure of Random Dispersion of Equal Spheres in Two-Dimension

3. Preliminary Mathematics

4. Radial Distribution Function

5. Sample Size for Measuring Particle Concentration

6. Introduction to Statistical Thermodynamics

7. Structural Comparison of Molecular System and particle Assemblies: Particle Morphology

Closing Remarks