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The purpose of this study is to present a newly proposed and developed sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method for solving the population balance equation for the weighted fraction coagulation process in aerosol dynamics with high computational accuracy and efficiency.

In the new SAMWFMC method, the jump Markov process is constructed as the weighted fraction Monte Carlo (WFMC) method (Jiang and Chan, 2021) with a fraction function. Both adjustable and constant fraction functions are used to validate the computational accuracy and efficiency. A new merging scheme is also proposed to ensure a constant-number and constant-volume scheme.

The new SAMWFMC method is fully validated by comparing with existing analytical solutions for six benchmark test cases. The numerical results obtained from the SAMWFMC method with both adjustable and constant fraction functions show excellent agreement with the analytical solutions and low stochastic errors. Compared with the WFMC method (Jiang and Chan, 2021), the SAMWFMC method can significantly reduce the stochastic error in the total particle number concentration without increasing the stochastic errors in high-order moments of the particle size distribution at only slightly higher computational cost.

The WFMC method (Jiang and Chan, 2021) has a stringent restriction on the fraction functions, making few fraction functions applicable to the WFMC method except for several specifically selected adjustable fraction functions, while the stochastic error in the total particle number concentration is considerably large. The newly developed SAMWFMC method shows significant improvement and advantage in dealing with weighted fraction coagulation process in aerosol dynamics and provides an excellent potential to deal with various fraction functions with higher computational accuracy and efficiency.

The purpose of this study is to investigate the aerosol dynamics of the particle coagulation process using a newly developed weighted fraction Monte Carlo (WFMC) method.

The weighted numerical particles are adopted in a similar manner to the multi-Monte Carlo (MMC) method, with the addition of a new fraction function (α). Probabilistic removal is also introduced to maintain a constant number scheme.

Three typical cases with constant kernel, free-molecular coagulation kernel and different initial distributions for particle coagulation are simulated and validated. The results show an excellent agreement between the Monte Carlo (MC) method and the corresponding analytical solutions or sectional method results. Further numerical results show that the critical stochastic error in the newly proposed WFMC method is significantly reduced when compared with the traditional MMC method for higher-order moments with only a slight increase in computational cost. The particle size distribution is also found to extend for the larger size regime with the WFMC method, which is traditionally insufficient in the classical direct simulation MC and MMC methods. The effects of different fraction functions on the weight function are also investigated.

Stochastic error is inevitable in MC simulations of aerosol dynamics. To minimize this critical stochastic error, many algorithms, such as MMC method, have been proposed. However, the weight of the numerical particles is not adjustable. This newly developed algorithm with an adjustable weight of the numerical particles can provide improved stochastic error reduction.

The purpose of this paper is to study the evolution and growth of aerosol particles in a turbulent planar jet by using the newly developed large eddy simulation (LES)-differentially weighted operator splitting Monte Carlo (DWOSMC) method.

The DWOSMC method is coupled with LES for the numerical simulation of aerosol dynamics in turbulent flows.

Firstly, the newly developed and coupled LES-DWOSMC method is verified by the results obtained from a direct numerical simulation-sectional method (DNS-SM) for coagulation occurring in a turbulent planar jet from available literature. Then, the effects of jet temperature and Reynolds number on the evolution of time-averaged mean particle diameter, normalized particle number concentration and particle size distributions (PSDs) are studied numerically on both coagulation and condensation processes. The jet temperature and Reynolds number are shown to be two important parameters that can be used to control the evolution and pattern of PSD in an aerosol reactor.

The coupling between the Monte Carlo method and turbulent flow still encounters many technical difficulties. In addition, the relationship between turbulence, particle properties and collision kernels of aerosol dynamics is not yet well understood due to the theoretical limitations and experimental difficulties. In the present study, the developed and coupled LES-DWOSMC method is capable of solving the aerosol dynamics in turbulent flows.

The purpose of this paper is to study the complex aerosol dynamic processes by using this newly developed stochastically weighted operator splitting Monte Carlo (SWOSMC) method.

Stochastically weighted particle method and operator splitting method are coupled to formulate the SWOSMC method for the numerical simulation of particle-fluid systems undergoing the complex simultaneous processes.

This SWOSMC method is first validated by comparing its numerical simulation results of constant rate coagulation and linear rate condensation with the corresponding analytical solutions. Coagulation and nucleation cases are further studied whose results are compared with the sectional method in excellent agreement. This SWOSMC method has also demonstrated its high numerical simulation capability when used to deal with simultaneous aerosol dynamic processes including coagulation, nucleation and condensation.

There always exists conflict and tradeoffs between computational cost and accuracy for Monte Carlo-based methods for the numerical simulation of aerosol dynamics. The operator splitting method has been widely used in solving complex partial differential equations, while the stochastic-weighted particle method has been commonly used in numerical simulation of aerosol dynamics. However, the integration of these two methods has not been well investigated.

The purpose of this paper is to study the soot formation and evolution by using this newly developed Lagrangian particle tracking with weighted fraction Monte Carlo (LPT-WFMC) method.

The weighted soot particles are used in this MC framework and is tracked using Lagrangian approach. A detailed soot model based on the LPT-WFMC method is used to study the soot formation and evolution in ethylene laminar premixed flames.

The LPT-WFMC method is validated by both experimental and numerical results of the direct simulation Monte Carlo (DSMC) and Multi-Monte Carlo (MMC) methods. Compared with DSMC and MMC methods, the stochastic error analysis shows this new LPT-WFMC method could further extend the particle size distributions (PSDs) and improve the accuracy for predicting soot PSDs at larger particle size regime.

Compared with conventional weighted particle schemes, the weight distributions in LPT-WFMC method are adjustable by adopting different fraction functions. As a result, the number of numerical soot particles in each size interval could be also adjustable. The stochastic error of PSDs in larger particle size regime can also be minimized by increasing the number of numerical soot particles at larger size interval.

The purpose of this paper is to study nanoparticles diffusion and coagulation processes in a twin-jet.

Large eddy simulation (LES) and Taylor-series expansion moment method (TEMOM) are employed to deal with a nanoparticle-laden twin-jet flow.

The numerical results show that the interaction of the two jets and turbulence eddy structures rolling-up, paring and shedding in flow sharply affects particles number concentration. Particle diameter grows quickly at the interfaces of jets. Coagulation shows more obvious effect at initial stage than that in the subsequent period. Then diffusion makes the particle diameter distribution much more uniform.

In recent years a great number of attentions have been focussed on the issue of particulate dynamics processes including diffusion, coagulation and deposition, etc. However, up to now few works have been focus on the nanoparticles coagulation and dispersion in turbulent flows. The investigation on the diffusion and coagulation process of nanoparticles using TEMOM in a twin-jet flow has not been found.

The purpose of this paper is to investigate competitive effect of source strength and coagulation on the evolution of aerosol size distribution with a continuous source.

A theoretical model was proposed in which the nanoparticle population balance equation with respect to particle size was solved by the sectional method.

It was found two modes appear when a nanoparticle system was injected by a continuous source.

Through tracing the evolution of particle size distribution with different source strength, the characteristics of two modes as well as their lag-time to approach steady state were deeply investigated.

The purpose of this paper is to investigate aerosol evolution in a planar mixing layer from a Lagrangian point of view. After using Monte Carlo (MC) method to simulate the evolution of aerosol dynamics along particles trajectories, the particles size distributions are obtained, which are unavailable in mostly used methods of moments.

Nucleation and growth of dibutyl phthalate (DBP) particles are simulated using the quadrature method of moments in a planar mixing layer, where a fast hot stream with DBP vapor is mixing with a slow cool stream without vapor. Trajectories of aerosol particles are recorded. MC method is used to simulate the aerosol evolution along trajectories.

Investigation on aerosol evolution along the trajectories prompts to classify these trajectories into three groups: first, trajectories away from the active nucleation zone; second, trajectories starting from the active nucleation zone; and third, trajectories crossing over the active nucleation zone. Particle size distributions (psds) along selected representative trajectories are investigated. The psd evolution exhibits interesting behavior due to the synthetic effects of nucleation and condensation. Condensation growth tends to narrow down the psd, and form a sharp front on the side of big particle size. Nucleation is able to broaden the psd through generating the smallest particles. The duration and strength of nucleation have significant effect on the shape of psd.

As far as the authors knowledge, it is the first simulation of aerosol evolution that takes a Lagrangian point of view, and uses MC simulation along particles trajectories to provide the particles size distribution.

The effects of amount of conventional surfactant sodium dodecyl sulfate in the synthesis of carboxylated acrylic latices prepared by semicontinuous emulsion polymerization method were investigated. The properties considered were particle size and colloidal stability by addition of sodium chloride solution, on the latex system and water sorption, tensile strength at break and elongation, on latex films. It was found that the surfactant concentration had an important effect on the above mentioned properties. The particle size decreases with increasing surfactant concentration and the colloidal stability has a maximum value. The critical coagulation concentration value found in this work, seems to indicate an additional stabilisation of latex particles, due to a steric factor. The water uptake and the mechanical behaviour of latex films are affected considerably when SDS concentration rises. In conclusion, depending on the final use of latex, there is an optimal surfactant concentration for which the properties are appropriate.

Polyurethane (PU) anionomer having 2‐ethoxymethacrylate terminal groups was prepared in a methyl methacrylate/n‐butyl acrylate mixture as a reactive diluent, following a prepolymer mixing process. This prepolymer‐acrylic monomer mixture was chain extended in a water/surfactant solution using different dispersion speeds. Stability tests of PU‐acrylic monomer dispersions before polymerization were performed at different temperatures by following the particle size evolution. After the dispersion process the kinetics of batch emulsion polymerization at 70°C using different concentrations of initiator was investigated. Data are compared with published results of batch emulsion copolymerization of methyl methacrylate/n‐butyl acrylate. The effect of triethylamine, used in the prepolymer synthesis, on the emulsion polymerization of acrylic monomers was also studied. The kinetic results indicate that during emulsion polymerization of PU acrylic mixture, some coagulation takes place, mainly due to changes in ionic strength of the medium, before stable latex particles are formed. The presence of the PU prepolymer seems not to affect the kinetics of batch copolymerization of methyl methacrylate/n‐butyl acrylate monomers.