A new numerical approach for the simulation of the growth of inorganic nanoparticles

In this paper we derive and test an extended mass-flow type stochastic particle algorithm for simulating the growth of nanoparticles that are formed in flames and reactors. The algorithm incorporates the effects of coagulation that dominates such systems, along with a particle source and surface growth. We simulate three different configurations for the creation of nanoparticles. The oxidation of SiH"4 to SiO"2 and Fe(CO)"5 to Fe"2O"3 in premixed H"2/O"2/Ar flames were investigated under different initial concentrations of SiH"4 and Fe(CO)"5, respectively. In addition, the oxidation of TiCl"4 to TiO"2 in a plug-flow reactor was investigated. A simple reaction mechanism for the conversion of Fe(CO)"5 to Fe"2O"3 was suggested, based on prior experimental data along with estimated transport properties for the species considered in this system. The simulation results were compared to experimental data available in the literature. re.

[1]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[2]  Markus Kraft,et al.  An efficient stochastic algorithm for simulating Nano-particle dynamics , 2002 .

[3]  Wolfgang Wagner,et al.  An Efficient Stochastic Algorithm for Studying Coagulation Dynamics and Gelation Phenomena , 2000, SIAM J. Sci. Comput..

[4]  Robert J. Kee,et al.  PREMIX :A F ORTRAN Program for Modeling Steady Laminar One-Dimensional Premixed Flames , 1998 .

[5]  P. Roth,et al.  Oxidation of Fe atoms by O2 based on Fe- and O-concentration measurements , 2002 .

[6]  Michael Frenklach,et al.  Aerosol dynamics modeling using the method of moments , 1987 .

[7]  D. Steinberg,et al.  Technometrics , 2008 .

[8]  Daniel T. Gillespie,et al.  The Stochastic Coalescence Model for Cloud Droplet Growth. , 1972 .

[9]  C. Sparrow The Fractal Geometry of Nature , 1984 .

[10]  Karl Sabelfeld,et al.  Stochastic particle methods for Smoluchowski coagulation equation: variance reduction and error estimations , 2003, Monte Carlo Methods Appl..

[11]  M. Smoluchowski,et al.  Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen , 1927 .

[12]  Robert J. Kee,et al.  A FORTRAN COMPUTER CODE PACKAGE FOR THE EVALUATION OF GAS-PHASE, MULTICOMPONENT TRANSPORT PROPERTIES , 1986 .

[13]  Babovsky Hans On a Monte Carlo scheme for Smoluchowski’s coagulation equation , 1999 .

[14]  Benjamin Jourdain,et al.  A stochastic approach for the numerical simulation of the general dynamics equation for aerosols , 2003 .

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

[16]  M. Hounslow A discretized population balance for continuous systems at steady state , 1990 .

[17]  CoalescenceDavid J. Aldous Stochastic Coalescence , 1998 .

[18]  P. Roth,et al.  Kinetics of the Fe-Atom Condensation Based on Fe−Concentration Measurements † , 2003 .

[19]  W. Wagner,et al.  Numerical study of a stochastic particle method for homogeneous gas-phase reactions , 2003 .

[20]  Rosner,et al.  Monte Carlo Simulation of Particle Aggregation and Simultaneous Restructuring. , 1999, Journal of colloid and interface science.

[21]  S. Pratsinis,et al.  Kinetics of Titanium(IV) Chloride Oxidation , 1990 .

[22]  Patrick T. Spicer,et al.  Titania formation by TiCl4 gas phase oxidation, surface growth and coagulation , 2002 .

[23]  Sotiris E. Pratsinis,et al.  Monte Carlo simulation of particle coagulation and sintering , 1994 .

[24]  Andreas Eibeck,et al.  Stochastic Particle Approximations for Smoluchoski’s Coagualtion Equation , 2001 .

[25]  Markus Kraft,et al.  Two approaches to the simulation of silica particle synthesis , 2002 .

[26]  M. Smoluchowski,et al.  Drei Vortrage uber Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen , 1916 .

[27]  Markus Kraft,et al.  Direct Simulation and Mass Flow Stochastic Algorithms to Solve a Sintering-Coagulation Equation , 2005, Monte Carlo Methods Appl..

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

[29]  Robert J. Kee,et al.  CHEMKIN-III: A FORTRAN chemical kinetics package for the analysis of gas-phase chemical and plasma kinetics , 1996 .

[30]  P. Roth,et al.  Formation and characteristics of Fe2O3 nano-particles in doped low pressure H2/O2/Ar flames , 2001 .

[31]  P. Roth,et al.  Formation and Growth of Sio2 Particlesin Low Pressure H2/O2/Ar Flames Doped with Sih4 , 1997 .