A detailed particle model for polydisperse aggregate particles

Abstract

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.

Modelling soot formation in a benchmark ethylene stagnation flame with a new detailed population balance model

“…More detailed discussion regarding this data structure including its merits and constraints can be found in Ref. [52]. The volume of a primary particle is calculated based on the mass of its component PAHs and the soot density ρ, represented as…”

“…1, v(p i ) can also be given by the volume of a sphere of radius r i minus the volume of the caps created by overlaps with its neighbors as described by the equations in Ref. [52,54]. This approach of describing aggregate particles as overlapping polydispersed primary particles is based on the work of Mitchell and Frenklach [23], Morgan et al [24], Eggersdorfer et al [54,55] and Lindberg et al [52].…”

“…The detailed model equations can be found in [52]. Particle properties that are of interest in population balance simulations, such as collision diameter (d c ) and mobility diameter (d m ), can be defined based on the aforementioned particle type space.…”

“…A more detailed description can be found in Ref. [52]. Surface growth PAHs in a primary particle can grow via surface reactions with gas-phase species, which is described by the KMC-ARS model [36,41,42].…”

A hybrid particle-number and particle model for efficient solution of population balance equations

“…Sander et al [15] and Lindberg et al [11] describe treatment of sintering for the current type space, assuming grain boundary diffusion to define the characteristic sintering time. It would be simple to extend this detailed particle model to track the relative positions of primary particles in each aggregate in order to resolve collisions and surface changes in more detail, as presented by our co-workers in Lindberg et al [53].…”