Mathematical modelling of a ternary particle system for determining the critical size ratio in a chemically reacting condition

The paper discusses the effect of particle size ratios in a chemically reacting condition for a typical case of the preparation of vanadium carbide by aluminothermic reduction followed by in situ carburization. The ternary particle system involved in this preparation is comprised of vanadium oxide, aluminium (Al) and carbon (C). A mathematical model has been developed to predict the critical particle size ratio of the oxides of vanadium and Al, which would give the best possible arrangement of the reductant and oxides of vanadium to satisfy the stoichiometry as well as the monolayer formation of fines over the carrier (coarse) particle for the efficient reduction reaction. This model also helps the selection of the C particle size, which is the third component of the ternary system chosen in this study.