Degree Name

Doctor of Philosophy


Department of Materials Engineering


Porosity is one of the most important properties of particulate materials, and it has been well known that there is a strong dependence of porosity on particle size distribution. This thesis will present a study of the packing of particles with special reference to the porosity and its estimation of particulate mixtures.

An attempt has been made to establish a general theory of the random packing of particles. The existence of two packing mechanisms, viz. the filling mechanism and the occupation mechanism, is demonstrated and the result is used to explain the limitations of the existing mathematical models. The porosity of multi-size (component) mixtures of particles can be predicted from the experimental results of binary mixtures. Based on this idea, the three models, i.e. the linear, mixture and linear-mixture packing models, which can not only provide a qualitative but also quantitative description of the relationship between theporosity and the size distribution of particulate materials, are developed. The possible limitation of the linear and mixture packing models are discussed respectively. However,the linear-mixture packing model, as it consideres the filling and occupation mechanisms, can express the real packing structure of a packing for all situations. The model is suggested as a general model for the porosity estimation of multi-component mixtures of particles.

The experimental theory with mixtures is briefly introduced, and its application in the porosity calculation of particulate mixtures is discussed. It is argued that the study of the packing of particles is to a large degree the study of the methods used to characterize particulate system. From this point of view, the importance and the usefulness of this methodology is illustrated by some examples.

The properties of a real size distribution of particulate materials are systematically discussed. In order to avoid possible conceptual problems and difficulty in dealing with a distribution, some boundary conditions are given, which results in a search for an alternative to the existing functions in the literature. Johnson's S B function is suggested to represent all the unimodal size distribution of particulate materials. Its applicability is proved from the theory of distributions in statistics. It is shown that most of the commonly used two-parameter functions can be converted into the S B function. The methods of fitting curves with special reference to its uses in powder technology is also discussed.