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We study a general class of systems of interacting particles that randomly interact to form new or different particles. In addition to the distribution of particles we consider the fluxes, defined as the rescaled number of jumps of each type that take place in a time interval. We prove a dynamic large deviations principle for the fluxes under general assumptions that include mass-action chemical kinetics. This result immediately implies a dynamic large deviations principle for the particle distribution.

A detailed population balance model is used to perform a parametric sensitivity study on the computed optical band gap (OBG) of polycyclic aromatic hydrocarbons (PAHs) in a laminar co-flow ethylene diffusion flame. Assuming that the OBG of PAHs in soot can be estimated by the energy difference between the highest occupied and lowest unoccupied molecular orbitals in single PAHs, OBG may be correlated with the number of aromatic rings in PAHs. This allows insights into which are the key species involved in the formation of soot. PAH size distributions are computed along the centreline and in the wings of the flame. We compare our simulations with experimentally determined soot volume fraction and OBG (derived from extinction measurements) from the literature. It is shown that the model predicts reasonably well the soot volume fraction and OBG throughout the flame. We find that the computed OBG is most sensitive to the size of the smallest PAH which is assumed to contribute to the OBG. The best results are obtained accounting for PAH contribution in both gas and particle phases assuming a minimum size of ovalene (10 rings). This suggests that the extinction measurements show a significant absorption by PAHs in the gas phase at the visible wavelength that is used, which has been demonstrated by experiments in the literature. It is further shown that PAH size distributions along the centreline and in the wings are unimodal at larger heights above burner. Despite the different soot particle histories and residence times in the flame, the PAH size associated with both modes are similar which is consistent with the near-constant OBG that is observed experimentally. The simulations indicate that the transition from the gas phase to soot particles begins with PAHs with as few as 16 aromatic rings, which is consistent with experimental observations reported in the literature.

This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. The weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.

The error arising from the delocalization of the coagulation interaction in stochastic particle methods is studied. The model under consideration includes advection, coagulation, and inception. Stochastic particle methods depend on several discretization parameters, due to the finite number of particles, the decoupling of transport and interaction (time step), and the spatial delocalization of the interaction (cell size). The paper studies the dependence on the cell size of the steady state solution obtained in the infinite-particle-number limit. Sufficient conditions for second order approximation are provided. Examples are given, where only first order approximation is observed.

A detailed PAH growth model is developed, which is solved using a kinetic Monte Carlo algorithm. The model describes the structure and growth of planar PAH molecules, and is referred to as the kinetic Monte Carlo–aromatic site (KMC-ARS) model. A detailed PAH growth mechanism based on reactions at radical sites available in the literature, and additional reactions obtained from quantum chemistry calculations are used to model the PAH growth processes. New rates for the reactions involved in the cyclodehydrogenation process for the formation of 6-member rings on PAHs are calculated in this work based on density functional theory simulations. The KMC-ARS model is validated by comparing experimentally observed ensembles on PAHs with the computed ensembles for a C2H2 and a C6H6 flame at different heights above the burner. The motivation for this model is the development of a detailed soot particle population balance model which describes the evolution of an ensemble of soot particles based on their PAH structure. However, at present incorporating such a detailed model into a population balance is computationally unfeasible. Therefore, a simpler model referred to as the site-counting model has been developed, which replaces the structural information of the PAH molecules by their functional groups augmented with statistical closure expressions. This closure is obtained from the KMC-ARS model, which is used to develop correlations and statistics in different flame environments which describe such PAH structural information. These correlations and statistics are implemented in the site-counting model, and results from the site-counting model and the KMC-ARS model are in good agreement. Additionally the effect of steric hindrance in large PAH structures is investigated and correlations for sites unavailable for reaction are presented.

A new, advanced soot particle model is developed that describes soot particles by their aromatic structure, including functional site descriptions and a detailed surface chemistry mechanism. A methodology is presented for the description of polyaromatic hydrocarbon (PAH) structures by their functional sites. The model is based on statistics that describe aromatic structural information in the form of easily computed correlations, which were generated using a kinetic Monte Carlo algorithm to study the growth of single PAH molecules. A comprehensive surface reaction mechanism is presented to describe the growth and desorption of aromatic rings on PAHs. The model is capable of simulating whole particle ensembles which allows bulk properties such as soot volume fraction and number density to be found, as well as joint particle size and surface area distributions. The model is compared to the literature-standard soot model [J. Appel, H. Bockhorn, M. Frenklach, Combust. Flame 121 (2000) 122–136] in a plug-flow reactor and is shown to predict well the experimental results of soot mass, average particle size, and particle size distributions at different flow times. Finally, the carbon/hydrogen ratio and the distribution of average PAH sizes in the ensemble, as predicted by the model, are discussed.

New bivariate models for soot particle structure are introduced to qualitatively replicate observed particle shapes and are found to offer quantitative improvements over older single-variable models. Models for the development of particle shape during surface growth and for particle collision diameters are described and implemented along with two models taken from other published work. Using a stochastic approach, bivariate soot particle distributions are calculated for the first time. Distributions calculated for the new models are found to be insensitive to the collision diameter model used for coagulation. The total mass of soot produced in a laminar premixed flame is found to vary by no more than 20% as the model for the geometric effects of chemical reactions on the surface of particles is changed. Histories of individual particles are analyzed and show the limitations of collector particle techniques for predicting the evolution of aggregate shape descriptors.

The feasibility of coupling a stochastic soot algorithm to a deterministic gas-phase chemistry solver is investigated for homogeneous combusting systems. A second-order splitting technique was used to decouple the particle population and gas phase in order to solve. A numerical convergence study is presented that demonstrates convergence with splitting step size and particle count for a batch reactor and a perfectly stirred reactor. Simulation results are presented alongside experimental data for a plug flow reactor (PFR) and are compared to a method of moments simulation of a perfectly stirred reactor. Coupling of the soot and chemistry solvers is shown to converge for both systems; however, numerical instabilities present significant challenges in the PSR case. Comparison with the experimental data for a PFR showed good agreement of the soot mass and reasonable agreement of the particle size distribution. Two different soot particle models were used to simulate the PFR: a spherical particle model and a surface–volume model that takes some account of particle shape. The results for the two models are compared. Additionally, the stochastic soot solver is used to track the evolution of the C/H ratio of individual soot particles in the PFR for the first time.

In this paper, the prediction of a soot model [J. Appel, H. Bockhorn, M. Frenklach, Combust. Flame 121 (2000) 122–136] is compared to a recently published set of highly detailed soot particle size distributions [B. Zhao, Z. Yang, Z. Li, M.V. Johnston, H. Wang, Proc. Combust. Inst. 30 (2005)]. A stochastic approach is used to obtain soot particle size distributions (PSDs). The key features of the measured and simulated particle size distributions are identified and used as a simple way of comparing PSDs. The sensitivity of the soot PSDs to the parameters defining parts of the soot model, such as soot inception, particle and PAH collision efficiency and enhancement, and surface activity is investigated. Incepting soot particle size is found to have a very significant effect on the small-size end of the PSDs, especially the position of the trough for a bimodal soot PSDs. A new model for the decay in the surface activity is proposed in which the activity of the soot particle depends only on the history of that particle and the local temperature in the flame. This is a first attempt to use local flame variables to define the surface aging which has major impact on the prediction of the large-size end of the PSDs. Using these modifications to the soot model it is possible to improve the agreement between some of the points of interest in the simulated and measured PSDs. The paper achieves the task to help advance the soot models to predict soot PSD in addition to soot volume fraction and number density, which has been the focus of the literature.

A class of coagulation weight transfer functions is constructed, each member of which leads to a stochastic particle algorithm for the numerical treatment of population balance equations. These algorithms are based on systems of weighted computational particles and the weight transfer functions are constructed such that the number of computational particles does not change during coagulation events. The algorithms also facilitate the simulation of physical processes that change single particles, such as growth, or other surface reactions. Four members of the algorithm family have been numerically validated by comparison to analytic solutions to simple problems. Numerical experiments have been performed for complex laminar premixed flame systems in which members of the class of stochastic weighted particle methods were compared to each other and to a direct simulation algorithm. Two of the weighted algorithms have been shown to offer performance advantages over the direct simulation algorithm in situations where interest is focused on the larger particles in a system. The extent of this advantage depends on the particular system and on the quantities of interest.