Models for the aggregate structure of soot particles

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.

[1]  Michael P. Tolocka,et al.  Chemical species associated with the early stage of soot growth in a laminar premixed ethylene–oxygen–argon flame , 2005 .

[2]  M. Frenklach,et al.  Detailed modeling of soot formation in laminar premixed ethylene flames at a pressure of 10 bar , 1995 .

[3]  M. Maricq.  Coagulation dynamics of fractal-like soot aggregates , 2007 .

[4]  C. Sorensen,et al.  Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames. , 1992, Applied optics.

[5]  R. I. A. PATTERSON,et al.  The Linear Process Deferment Algorithm: A new technique for solving population balance equations , 2006, SIAM J. Sci. Comput..

[6]  Jasdeep Singh,et al.  Extending stochastic soot simulation to higher pressures , 2006 .

[7]  Magín Lapuerta,et al.  A method to determine the fractal dimension of diesel soot agglomerates. , 2006, Journal of colloid and interface science.

[8]  G. Thomas,et al.  In situ measurements of soot formation in simple flames using small angle X-ray scattering , 2005 .

[9]  M. Kostoglou,et al.  Cluster-cluster aggregation kinetics and primary particle growth of soot nanoparticles in flame by light scattering and numerical simulations. , 2002, Journal of colloid and interface science.

[10]  Chul Han Kim,et al.  Soot surface growth and oxidation in laminar diffusion flames at pressures of 0.1–1.0 atm , 2004 .

[11]  Hai Wang,et al.  Small-angle neutron scattering of soot formed in laminar premixed ethylene flames , 2002 .

[12]  Alberto C. Barone,et al.  Morphological characterization of the early process of soot formation by atomic force microscopy , 2003 .

[13]  S. Rogak,et al.  AN IMPROVED MOVING SECTIONAL AEROSOL MODEL OF SOOT FORMATION IN A PLUG FLOW REACTOR , 2006 .

[14]  Andreas Eibeck,et al.  Approximative solution of the coagulation–fragmentation equation by stochastic particle systems , 2000 .

[15]  W. Peukert,et al.  On the relevance of accounting for the evolution of the fractal dimension in aerosol process simulations , 2003 .

[16]  J. Wen,et al.  Numerical study of carbonaceous nanoparticle formation behind shock waves , 2006 .

[17]  D. E. Rosner,et al.  Bivariate Extension of the Quadrature Method of Moments for Modeling Simultaneous Coagulation and Sintering of Particle Populations. , 2001, Journal of colloid and interface science.

[18]  Ümit Özgür Köylü.  Quantitative analysis of in situ optical diagnostics for inferring particle/aggregate parameters in flames : Implications for soot surface growth and total emissivity , 1997 .

[19]  Sotiris E. Pratsinis,et al.  Population balance modeling of flame synthesis of titania nanoparticles , 2002 .

[20]  Hai Wang,et al.  Drag force, diffusion coefficient, and electric mobility of small particles. II. Application. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Antonello Barresi,et al.  Implementation of the population balance equation in CFD codes for modelling soot formation in turbulent flames , 2006 .

[22]  Michael Frenklach,et al.  Detailed kinetic modeling of soot aggregate formation in laminar premixed flames , 2005 .

[23]  Markus Kraft,et al.  Coupling a stochastic soot population balance to gas-phase chemistry using operator splitting , 2007 .

[24]  Fengshan Liu,et al.  Determination of the morphology of soot aggregates using the relative optical density method for the analysis of TEM images , 2006 .

[25]  Michael Frenklach,et al.  Numerical simulations of soot aggregation in premixed laminar flames , 2007 .

[26]  Tiago L. Farias,et al.  Fractal and projected structure properties of soot aggregates , 1995 .

[27]  Markus Kraft,et al.  Measurement and numerical simulation of soot particle size distribution functions in a laminar premixed ethylene-oxygen-argon flame , 2003 .

[28]  Andreas Eibeck,et al.  Stochastic interacting particle systems and nonlinear kinetic equations , 2003 .

[29]  Steven N. Rogak,et al.  A novel fixed-sectional model for the formation and growth of aerosol agglomerates , 2004 .

[30]  Hai Wang,et al.  Drag force, diffusion coefficient, and electric mobility of small particles. I. Theory applicable to the free-molecule regime. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  C. Jacobsen,et al.  X-ray scattering and spectroscopy studies on diesel soot from oxygenated fuel under various engine load conditions , 2005 .

[32]  Sotiris E Pratsinis,et al.  Soft- and hard-agglomerate aerosols made at high temperatures. , 2004, Langmuir : the ACS journal of surfaces and colloids.

[33]  S. D. Stasio,et al.  Small-angle neutron scattering study of soot particles in an ethylene-air diffusion flame , 2006 .

[34]  S. Friedlander,et al.  Bivariate population dynamics simulation of fractal aerosol aggregate coagulation and restructuring , 2006 .

[35]  M. Frenklach.  Method of moments with interpolative closure , 2002 .

[36]  Margaritis Kostoglou,et al.  Evolution of aggregate size and fractal dimension during Brownian coagulation , 2001 .

[37]  S. D. Stasio.  Electron microscopy evidence of aggregation under three different size scales for soot nanoparticles in flame , 2001 .

[38]  Fengshan Liu,et al.  Numerical simulation aided relative optical density analysis of TEM images for soot morphology determination , 2007 .

[39]  C. Oh,et al.  The Effect of Overlap between Monomers on the Determination of Fractal Cluster Morphology , 1997, Journal of colloid and interface science.

[40]  D. E. Rosner,et al.  Aggregate size distribution evolution for Brownian coagulation-sensitivity to an improved rate constant. , 2004, Journal of colloid and interface science.

[41]  D. E. Rosner,et al.  Bivariate moment simulation of coagulating and sintering nanoparticles in flames , 2002 .

[42]  S. L. Manzello,et al.  Morphology of soot collected in microgravity droplet flames , 2002 .

[43]  M. Maricq,et al.  The effective density and fractal dimension of soot particles from premixed flames and motor vehicle exhaust , 2004 .

[44]  C. McEnally,et al.  Investigation of the transition from lightly sooting towards heavily sooting co-flow ethylene diffusion flames , 2004 .

[45]  Michael Frenklach,et al.  Monte carlo simulation of soot aggregation with simultaneous surface growth-why primary particles appear spherical , 1998 .

[46]  J. Seinfeld,et al.  Evolution of nanoparticle size and mixing state near the point of emission , 2004 .

[47]  Steven N. Rogak,et al.  Study of soot growth in a plug flow reactor using a moving sectional model , 2005 .

[48]  D. Urban,et al.  Soot Formation in Laminar Premixed Ethylene/Air Flames at Atmospheric Pressure. Appendix G , 1997 .

[49]  S. Rogak,et al.  An aerosol model to predict size and structure of soot particles , 2004 .

[50]  Laplacian growth and diffusion limited aggregation: different universality classes. , 2001, Physical review letters.

[51]  Michael Frenklach,et al.  Graphene Layer Growth: Collision of Migrating Five-Member Rings - eScholarship , 2005 .

[52]  P. Meakin.  Effects of cluster trajectories on cluster-cluster aggregation: A comparison of linear and Brownian trajectories in two- and three-dimensional simulations , 1984 .

[53]  S. Rogak,et al.  A One-Dimensional Model for Coagulation, Sintering, and Surface Growth of Aerosol Agglomerates , 2003 .

[54]  Markus Kraft,et al.  Modes of neck growth in nanoparticle aggregates , 2008 .

[55]  D. Urban,et al.  Soot Formation in Laminar Premixed Methane/Oxygen Flames at Atmospheric Pressure. Appendix H , 1998 .

[56]  M. Kraft,et al.  A stochastic approach to calculate the particle size distribution function of soot particles in laminar premixed flames , 2003 .

[57]  M. Maricq,et al.  Soot size distributions in rich premixed ethylene flames , 2003 .

[58]  D. E. Rosner,et al.  Effective diameters for collisions of fractal-like aggregates: recommendations for improved aerosol coagulation frequency predictions. , 2002, Journal of colloid and interface science.

[59]  Michael Frenklach,et al.  Particle aggregation with simultaneous surface growth. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  Michael Frenklach,et al.  Monte-Carlo simulation of soot particle coagulation and aggregation: the effect of a realistic size distribution , 2005 .

[61]  H. Bockhorn,et al.  Kinetic modeling of soot formation with detailed chemistry and physics: laminar premixed flames of C2 hydrocarbons , 2000 .

[62]  Bin Zhao,et al.  Particle size distribution function of incipient soot in laminar premixed ethylene flames: effect of flame temperature , 2005 .

[63]  M. Frenklach,et al.  A detailed kinetic modeling study of aromatics formation in laminar premixed acetylene and ethylene flames , 1997 .

[64]  R. Jullien,et al.  The effects of restructuring on the geometry of clusters formed by diffusion‐limited, ballistic, and reaction‐limited cluster–cluster aggregation , 1988 .

[65]  Bin Zhao,et al.  A comparative study of nanoparticles in premixed flames by scanning mobility particle sizer, small angle neutron scattering, and transmission electron microscopy , 2007 .

[66]  C. Sorensen.  Light Scattering by Fractal Aggregates: A Review , 2001 .

[67]  Sotiris E. Pratsinis,et al.  Process simulation of gas-to-particle-synthesis via population balances: Investigation of three models , 2002 .