Effect of Mixing on the Nucleation and Growth of Titania Particles

Aerosol processes that produce titania particles by reacting gaseous precursors (such as titanium tetrachloride) initially must mix the precursor into the oxidizer at elevated temperatures to initiate the formation of product. Oftentimes the rate of reaction is sufficiently large as to be mixing limited. Thus the rate of mixing of the reacting species will control the chemistry and morphological properties of the particles that are produced. The interplay between mixing, nucleation, and growth in these systems is difficult to observe experimentally due to the small time scales that are involved and the spatial limitations of most diagnostics. An alternative approach is direct numerical simulation (DNS). DNS refers to a class of numerical solutions of the three-dimensional time-dependent governing equations for a particular system in which no turbulence modeling assumptions are made. To within the precision of the numerical algorithm, DNS can be thought of as a numerical experiment. Here we apply DNS to the mixing, reaction, nucleation, and growth of titania particles formed from the reaction of titanium tetrachloride with oxygen. The simulation solves for the velocity, species concentration, and eight moments of the particle size distribution using a combination of a pseudospectral method (for the velocity) and a compact finite difference scheme (for all of the scalars). The results show that increasing the rate of mixing increases the rate of particle formation while decreasing the variance in the particle size distribution. However, for a given extent of reaction, poorer mixing leads to larger mean particle sizes and larger standard deviations. The results are most easily interpreted in terms of the reaction volume between the unmixed reactants, where most of the reaction occurs. Based on this analysis, we present rules of thumb for controlling the particle size distribution in aerosol reactors.