The mathematical description of a new detailed particle model for polydisperse aggregate particles is presented. An aggregate particle is represented as a collection of overlapping spherical primary particles and the model resolves the composition, radius and position coordinates of each individual primary to form a detailed geometrical description of aggregate morphology. Particles transform under inception, coagulation, surface growth, sintering and coalescence processes. The new particle description is used to model the aerosol synthesis of titanium dioxide (TiO 2) aggregates from titanium tetraisopropoxide (TTIP) precursor. TiO 2 particles are formed through collision-limited inception and growth reactions of Ti(OH) 4 from the gasphase, produced from the thermal decomposition of TTIP. Coupling between the particle population balance and detailed gas-phase chemistry is achieved by operator splitting. A numerical study is performed by simulating a simple batch reactor test case to investigate the convergence behaviour of key functionals with respect to the maximum number of computational particles and splitting time step. Finally, a lab-scale hot wall reactor is simulated to demonstrate the advantages of a detailed geometrical description. Simulated particle size distributions were in reasonable agreement with experimental data. Further evaluation of the model and a parametric sensitivity study are recommended.

Numerical simulation of soot formation in a laminar premixed burner-stabilised benchmark ethylene stagnation flame was performed with a new detailed population balance model employing a two-step simulation methodology. In this model, soot particles are represented as aggregates composed of overlapping primary particles, where each primary particle is composed of a number of polycyclic aromatic hydrocarbons (PAHs). Coordinates of primary particles are tracked, which enables simulation on particle morphology and provides more quantities that are directly comparable to experimental observations. Parametric sensitivity study on the computed particle size distributions (PSDs) shows that the rate of production of pyrene and the collision efficiency have the most significant effect on the computed PSDs. Sensitivity of aggregate morphology to the sintering rate is studied by analysing the simulated primary particle size distributions (PPSDs) and transmission electron microscopy (TEM) images. The capability of the new model to predict PSDs in a premixed stagnation flame is investigated. Excellent agreement between the computed and measured PSDs is obtained for large burner-stagnation plate separation (≥ 0.7 cm) and for particles with mobility diameter larger than 6 nm, demonstrating the ability of this new model to describe the coagulation process of aggregate particles.

A two-step simulation methodology is presented that allows a detailed particle model to be used to resolve the complex morphology of aggregate nanoparticles synthesised in a stagnation flame. In the first step, a detailed chemical mechanism is coupled to a one-dimensional stagnation flow model and spherical particle model solved using method of moments with interpolative closure. The resulting gas-phase profile is post-processed with a detailed stochastic population balance model to simulate the evolution of the population of particles, including the evolution of each individual primary particle and their connectivity with other primaries in an aggregate. A thermophoretic correction is introduced to the post-processing step through a simulation volume scaling term to account for thermophoretic transport effects arising due to the steep temperature gradient near the stagnation surface. The methodology is evaluated by applying it to a test case: the synthesis of titanium dioxide from titanium tetraisopropoxide (TTIP) precursor. The thermophoretic correction is shown to improve the fidelity of the post-process to the first fully-coupled simulation, and the methodology is demonstrated to be feasible for simulating the morphology of aggregate nanoparticles formed in a stagnation flame, permitting the simulation of quantities that are directly comparable to experimental observations.