This thesis develops and applies a new detailed population balance model to study the aerosol synthesis of titanium dioxide nanoparticles. It begins by exploring whether the morphological data captured by an existing detailed particle model can be used in a milling model to relate particle morphology and ultimately the particle synthesis conditions to the behaviour of particles in the milling process. The study identifies limitations in the existing particle model and informs the development of a new detailed particle model. A new, detailed, geometrical particle model is introduced that tracks the size and position of individual primary particles and their relationship with neighbouring primaries in an aggregate. The particle model forms part of a detailed population balance model that can describe the morphological evolution of aggregate particles under inception, coagulation, growth, sintering and coalescence, while resolving the neck radius, free surface area and volume of each individual primary, as well as the fractal-like structure of each aggregate. The model removes the need to assume a fractal dimension and prefactor when calculating the particle gyration and collision diameters, and permits the visualisation of particles. The process sub-models are tested and the convergence behaviour is investigated for a simple batch reactor test case. The synthesis of TiO2 aggregates from TTIP precursor in a lab-scale hot wall reactor is simulated. A two-step simulation methodology is presented to apply the model to a stagnation flame. The methodology extends an existing two-step method, where a detailed population balance model is applied as a post-processing step to flame profiles obtained from a fully-coupled simulation with gas-phase chemistry, flow dynamics and a simple particle model. The new methodology addresses a previously unidentified issue in employing the post-processing step to simulate flames with steep temperature gradients. A corrective sample volume scaling term is introduced to account for the effect of thermophoresis. Finally, the new detailed particle model and methodology are used to simulate the synthesis of titanium dioxide nano-aggregates in a stagnation flame. Model predictions are evaluated against experimental results by comparing experimental measurements from transmission electron microscopy (TEM) data with identical, simulated quantities. A parametric sensitivity study is performed to investigate key model parameters.