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This paper introduces a new iterative scheme for solving the discrete Smoluchowski equation and explores the numerical convergence properties of the method for a range of kernels admitting analytical solutions, in addition to some more physically realistic kernels typically used in kinetics applications. The solver is extended to spatially dependent problems with non-uniform velocities and its performance investigated in detail. NRF (Natl Research Foundation, S’pore) Accepted version

This work proposes a kinetic model and an inception pathway for the flame synthesis of silica nanoparticles from tetraethoxysilane (TEOS). The kinetic model for the decomposition of TEOS is developed by generating reactions involving species that were reported in high concentrations at equilibrium. Flux and sensitivity analyses are then performed to identify the main reaction pathways. The parameters for these reactions are systematically fitted to experimental data using low discrepancy (LD) sequences and response surfaces. The main product of TEOS decomposition is deduced to be silicic acid (Si(OH)4). To increase computational efficiency, the kinetic model has been reduced by determining the level of importance (LOI) of each species and retaining only the important ones. This reduced kinetic model is then coupled to a detailed population balance model using an operator splitting technique. New particle inception and surface growth steps have been incorporated into the particle model in which particles form and grow by the interaction of Si(OH)4 monomers. Coagulation and sintering of particles are also included in the model and the material dependent sintering parameters have been determined by fitting the model to experimental values of collision and primary particle diameters using LD sequences. The particle size distributions and computer-generated TEM-style images have been generated and good agreement with experiments is observed. The gas-phase reactor composition and the temporal evolution of particle size at different temperatures are also presented.

The aim of this work is to present a new detailed multivariate population balance model to describe the aerosol synthesis of silica nanoparticles from tetraethoxysilane (TEOS). The new model includes a chemical representation of the silica particles to facilitate a detailed chemical description of particle processes. Silica nanoparticles are formed by the interaction of silicic acid monomers (Si(OH) 4 ) in the gas-phase as reported in a previous study. A multidimensional population balance model is developed where each particle is described by its constituent primary particles and the connectivity between these primaries. Each primary, in turn, has internal variables that describe its chemical composition, i.e., the number of Si, free O and OH units. Different particle processes, such as inception, surface reaction, coagulation, sintering, and intra-particle reactions, are formulated from first-principles that alter the particle ensemble and are two-way coupled to the gas-phase. The free parameters in the model are estimated by fitting the model response to experimental values of collision and primary particle diameters using low discrepancy Sobol sequences followed by the simultaneous perturbation stochastic approximation algorithm. The simulation results are finally presented at different process conditions. A strong dependence of particle properties on process temperature and inlet concentration is observed. The desirable operating conditions for different industrial applications are also highlighted. This work illustrates the significance of adopting a multidimensional approach to understand, and hence control, complex nanoparticle synthesis processes.

This paper investigates the first part of a two-stage methodology for the detailed fully coupled modelling of nanoparticle formation in turbulent reacting flows. We use a projected fields (PF) method to approximate the joint composition probability density function (PDF) transport equation that describes the evolution of the nanoparticles. The method combines detailed chemistry and the method of moments with interpolative closure (MoMIC) population balance model in a commercial computational fluid dynamics (CFD) code. We show details of the implementation and present an extensive set of numerical experiments and validation. We consider the example of the chloride process for the industrial synthesis of titania. We show good agreement with experimental data and present fully coupled detailed chemistry CFD simulations of nanoparticle formation in a representative ‘slot’ reactor geometry. The simulations show that inception occurs in a mixing zone near the reactor inlets. Most of the nanoparticle mass is due to surface growth downstream of the mixing zone with a narrower size distribution occurring in the regions of higher surface growth. The predicted temperature and particle properties are compared to a perfect mixing case. The implications for the second part of the methodology, where it is proposed to post-process the data using a more detailed particle model, are discussed critically.

This paper compares two mean reaction rate closures for turbulent reacting flow: the Stochastic Fields (SF) method and the Direct Quadrature Method of Moments using the Interaction by Exchange with the Mean micromixing model (DQMoM-IEM). The methods have many common features and have received significant attention in recent literature, yet have not been systematically compared. We present both methods in the same mathematical framework and compare their numerical performance. In addition, we introduce antithetic sampling as a variance reduction technique to increase the efficiency of the SF algorithm. We extend the methodology to take advantage of this development and show details of the implementation of each method in a commercial computational fluid dynamics code. We present a systematic investigation and consider both axisymmetric and 3D formulations of a problem known from the literature. DQMoM-IEM showed excellent agreement with experimental and transported probability density function data. SF gave reasonable agreement, but retained a minor grid-dependence not seen with DQMoM-IEM and did not fully resolve the sub-grid segregation of the species. The antithetic sampling was demonstrated to significantly increase the efficiency of the axisymmetric SF cases.

This paper investigates a mean reaction rate closure for turbulent reacting flows called the Direct Quadrature Method of Moments using the Interaction by Exchange with the Mean micromixing model (DQMoM-IEM). The method was first introduced for reacting flows by Fox (Computational Models for Turbulent Reacting Flows, Cambridge University Press, 2003). We present a systematic study that considers several important new aspects of the method. In particular we introduce a new analytic expression for the DQMoM-IEM source terms. We present a rigourous numerical investigation and discuss problems of boundedness and singularity in detail. We introduce a filter function to overcome these issues in the general case and present analytic integrals for special cases of specific terms. We extend the methodology to take advantage of these developments and show details of the implementation in a commercial computational fluid dynamics (CFD) code. We present an extensive set of numerical experiments and validation. The method is proven for a problem known from the literature which includes an isothermal dimerisation process. Experimental and transported probability density function (PDF) data compare reasonably well. The method is discussed critically and areas for further research are suggested to make the method more practical.

An unusual group of human B-cell tumors with cellular features of chronic lymphocytic leukemia or lymphoplasmacytoid leukemia, together with high levels of a monoclonal IgG serum protein, has been investigated. Analysis of tumor-derived VH genes of neoplastic B lymphocytes was used to determine the clonal relationship between the IgM expressed or secreted by the tumor cells and the IgG serum paraprotein. In all five cases, VH gene sequences showed transcripts of IgM and IgG of common clonal origin. Sequences were derived from VH3 (4 of 5) and VH1 (1 of 5) families and were all highly somatically mutated with strong evidence for antigen selection. There was no intraclonal variation detectable in either IgM or IgG sequences. In 3 of 5 cases, in which monoclonal IgM and IgG were found in serum, the VH genes combined to Cμ or Cγ showed identical mutational patterns. However, in 2 of 5 cases, in which IgM was confined to cell expression with only monoclonal IgG in serum, sequences of the VH transcripts of IgM and IgG showed many shared mutations but also numerous differences. In these cases, the level of mutation was similar in IgM and IgG and both appeared to be antigen selected. In summary, the final neoplastic event in this group of tumors has apparently occurred at the point of isotype switch from IgM to IgG, leading to dual isotype synthesis. In the group that secreted both isotypes, the mutation pattern was identical, indicating either synthesis by a single cell, or silencing of mutational activity before switching. In the group that did not secrete IgM, cells of each isotype were distinct and reflected a divergent mutational history.

IgM-secreting plasma cell tumors are rare variants of typical isotype-switched multiple myeloma with a similar disease outcome. To probe the origin and clonal history of these tumors, we have analyzed VH gene sequences in 6 cases. Potentially functional tumor-derived VH genes were all derived from VH3, with the V3-7 gene segment being used by 4 of 6. All were somatically mutated, with a mean deviation from germline sequence of 5.2% (range, 3.1% to 7.1%). The distribution of replacement mutations was consistent with antigen selection in 4 of 6 cases, and no intraclonal heterogeneity was observed. Clonally related switched isotype transcripts were sought in 4 cases, and Cγ transcripts with tumor-derived CDR3 sequence were identified in 2 of 4. These findings indicate that IgM-secreting myelomas are arrested at a postfollicular stage at which somatic mutation has been silenced. Isotype switch variants show the cell of origin to be at the IgM to IgG switch point. These features indicate that the final neoplastic event has occurred at a stage immediately before that of typical isotype-switched myeloma. One possibility is that IgM myeloma involves the previously identified precursor cell of typical myeloma.