Modelling the mechanisms of microsilica particle formation and growth

Thesis

Microsilica particles arise as a byproduct of silicon furnace operation, created inside high temperature flames due to the combustion reaction of silicon monoxide with oxygen. These nanoparticles, which grow as silicon dioxide vapour condenses on the surface of existing particles, are used in a variety of composite materials. The size and quality of the particles affect the performance of the material used for such applications, and hence control of these quantities is of importance to manufacturers.

Motivated by this, we derive a mathematical model that connects local fluid flow, thermal and chemical conditions of the furnace to the formation and growth of microsilica particles. Since the regions where microsilica particles form are local to a very thin reaction zone, we focus on the dynamics within the flame front. We first study two distinct reductions of the model: the case of initially well-mixed or spatially homogeneous chemical species, and the case of initially separated chemical species. In the latter case, the one-dimensional domain is given by a cross section of the reaction zone and diffusion plays a dominant role in providing material to a combustion front. In order to incorporate fluid flow, we extend the previous work to 2-D by considering a mixing layer approach, that is, by assuming two parallel flows entering the domain with distinct velocities, temperatures, and concentrations. We study how the mixing layer evolves as both streams interact, and how mixing affects the formation and growth of particles. In all cases, we provide asymptotic approximations under various limits and neglecting the effect of the particles on the chemicals and temperature, and numerical solutions of the full model. Our results suggest that oxygen availability and a sufficiently high temperature are essential for the combustion reactions to occur, strongly influencing the width of the reaction zone and the particle size distribution. Furthermore, when the flow is almost uniform, fewer particles form and more of the total mass corresponds to large particles, in contrast with the non-uniform case.

Authors: González-Fariña, R

• DOI: 10.5287/ora-bdv7yvdkz
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: silica fume; particle growth; reaction-diffusion system; combustion; microsilica; silicon furnace; particle nucleation; asymptotic analysis; mathematical modelling; mixing layer; moment equations
• Subjects: Combustion; Reaction-diffusion equations; Asymptotic expansions; Aerosols; Mathematical models; Applied mathematics; Fluids