Mathematical Modelling of Mechanical Alloying - Harris, John Richard (2002)
This thesis applies Smoluchowski's coagulation-fragmentation equations to model the mechanical alloying process. Mechanisms operating during the milling process are reviewed. In the first instance, models are developed that predict the size distribution of a single milled powder while ignoring mixing phenomena. A methodology is developed that allows experimentally measured sieve-fractions to be converted into volumetric cluster size distributions. Model parameters describing the rate of aggregation and fragmentation are obtained by fitting the model's predicted average particle size data over time to that measured in experiments. Different size-dependent aggregation and fragmentation rates are tested in many milling scenarios and the most realistic size-dependence of rates is found.