In this article, the evolution of in-flame soot species in a slow speed, buoyancy-driven diffusion flame is thoroughly studied with the implementation of the population balance approach in association with computational fluid dynamics (CFD) techniques. This model incorporates interactive fire phenomena, including combustion, radiation, turbulent mixing, and all key chemical and physical formation and destruction processes, such as particle inception, surface growth, oxidation, and aggregation. The in-house length-based Direct Quadrature Method of Moments (DQMOM) soot model is fully coupled with all essential fire sub-modelling components and it is specifically constructed for low-speed flames. Additionally, to better describe the combustion process of the parental fuel, ethylene, the strained laminar flamelet model, which considers detailed chemical reaction mechanisms, is adopted. Numerical simulation is validated against a self-conducted co-flow slot burner experimental measurement. A comprehensive assessment of the effect of adopting different nucleation laws, oxidation laws, and various fractal dimension and diffusivity values is performed. The results suggest the model employing Moss law of nucleation, modified NSC law of oxidation, and adopting a fractal dimension value of 2.0 and Schmidt number of 0.9 yields the simulation result that best agreed with experimental data.