Theory of Particle Formation and Growth in Oxide Synthesis Flames

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Abstract
This work discusses those factors which determine ultimate particle size in the synthesis of pyrogenic silica. Pyrogenic or fumed silicas are produced commercially through the combustion of a premixed stream of silicon tetrachloride, hydrogen and air. Because of their minute size, silica particles assume translational velocities and collision frequencies characteristic of large gas molecules. When chemical reaction and nucleation times are short relative to the total formation period; growth, theoretically, approaches a rate which is independent of the early history of the system and is determined solely by the frequency of Brownian collisions. Under these conditions, the logarithm of particle size is directly proportional to the logarithm of growth time. In commercial flames, secondary air is inducted into the flame jet, causing particles to cool below their fusion temperature. Under such circumstances, the growth time and thus the ultimate particle size is a strong function of initial flame temperature. Theoretical disappearance rates have been formulated using a Brownian collision-coalescence model and are compared with results obtained from a commercial burner operating at a variety of flame temperatures and concentrations. Inspection of the literature suggests that the collision-coalescence mechanism of growth applies to numerous other oxide and carbon forming flames where reactions are fast relative to quench times, supersaturation ratios are high and particles are small relative to mean-free molecular paths.