A New Moment Method for Solving the Coagulation Equation for Particles in Brownian Motion

REFERENCES

• Barrett , J. C. and Jheeta , J. S. 1996 . Improving the Accuracy of the Moments Method for Solving the Aerosol General Dynamic Equation . J. Aerosol Sci. , 27 : 1135 – 1142 .
   Web of Science ®Google Scholar
• Barrett , J. C. and Webb , N. A. 1998 . A Comparison of Some Approximate Methods for Solving the Aerosol General Dynamic Equation . J. Aerosol Sci. , 29 : 31 – 39 .
   Web of Science ®Google Scholar
• Chan , T. L. , Lin , J. Z. , Zhou , K. and Chan , C. K. 2006 . Simultaneous Numerical Simulation of Nano and Fine Particle Coagulation and Dispersion in a Round Jet . J. Aerosol Sci. , 37 : 1545 – 1561 .
   Web of Science ®Google Scholar
• Frenklach , M. 1985 . Dynamics of Discrete Distribution for Smoluchowski Coagulation Model . J. Coll. Interface Sci. , 108 : 237 – 242 .
   Web of Science ®Google Scholar
• Frenklach , M. 2002 . Method of Moments with Interpolative Closure . Chem. Engineer. Sci. , 57 : 2229 – 2239 .
   Web of Science ®Google Scholar
• Frenklach , M. and Harris , S. J. 1987 . Aerosol Dynamics Modeling Using the Method of Moments . J. Coll. Interface Sci. , 118 : 252 – 261 .
   Web of Science ®Google Scholar
• Friedlander , S. K. 2000 . Smoke, Dust, and Haze. Fundamentals of Aerosol Dynamics , Oxford University Press .
   Google Scholar
• Gelbard , F. and Seinfeld , J. H. 1980 . Simulation of Multicomponent Aerosol Dynamics . J. Coll. Interface Sci. , 78 : 485 – 501 .
   Web of Science ®Google Scholar
• Gordon , R. G. 1968 . Error Bounds in Equilibrium Statistical Mechanics . Journal Mathematical Physics , 9 : 655 – 672 .
   Web of Science ®Google Scholar
• Hulbert , H. M. and Katz , S. 1964 . Some Problems in Particle Technology: A Statistical Mechanical Formulation . Chem. Engineer. Sci. , 19 : 555 – 574 .
   Web of Science ®Google Scholar
• Lee , K. W. 1983 . Change of Particle Size Distribution During Brownian Coagulation . J. Coll. Interface Sci. , 92 : 315 – 325 .
   Web of Science ®Google Scholar
• Lee , K. W. , Chen , H. and Gieseke , J. A. 1984 . Log-Normally Preserving Size Distribution for Brownian Coagulation in the Free-Molecule Regime . Aerosol Sci. Technol. , 3 : 53 – 62 .
   Web of Science ®Google Scholar
• Lee , K. W. and Chen , H. 1984 . Coagulation Rate of Polydisperse Particles . Aerosol Sci. Technol. , 3 : 327 – 334 .
   Web of Science ®Google Scholar
• Lee , K. W. , Lee , Y. J. and Han , D. S. 1997 . The Log-Normal Size Distribution Theory for Brownian Coagulation in the Low Knudsen Number Regime . J. Coll. Interface Sci. , 188 : 486 – 492 .
   Web of Science ®Google Scholar
• Lin , J. Z. , Chan , T. L. , Lin , S. , Zhou , K. , Zhou , Y. and Lee , S. C. 2007 . Effects of Coherent Structures on Nanoparticle Coagulation and Dispersion in a Round Jet . Intl. J. Nonlinear Sci. Numer. Simul. , 8 : 45 – 54 .
   Web of Science ®Google Scholar
• McGraw , R. 1997 . Description of Aerosol Dynamics by the Quadrature Method of Moments . Aerosol Sci. Technol. , 27 : 255 – 265 .
   Web of Science ®Google Scholar
• Morgan , N. M. , Wells , C. G. , Goodson , M. J. , Kraft , M. and Wagner , W. 2006 . A New Numerical Approach for the Simulation of the Growth of Inorganic Nanoparticles . J. Computational Physics , 211 : 638 – 658 .
   Web of Science ®Google Scholar
• Muller , H. 1928 . Zur Allgemeinen Theorie Der Raschen Koagulation . Kolloideihefte , 27 : 223 – 250 .
   Google Scholar
• Pratsinis , S. E. 1988 . Simultaneous Nucleation, Condensation, and Coagulation in Aerosol Reactor . J. Coll. Interface Sci. , 124 : 416 – 417 .
   Web of Science ®Google Scholar
• Pratsinis , S. E. and Kim , K. S. 1989 . Particle Coagulation, Diffusion and Thermophoresis in Laminar Tube Flows . J. Aerosol Sci. , 20 : 101 – 111 .
   Web of Science ®Google Scholar
• Settumba , N. and Garrick , S. C. 2003 . Direct Numerical Simulation of Nanoparticle Coagulation in a Temporal Mixing Layer via a Moment Method . J. Aerosol Sci. , 34 : 149 – 167 .
   Web of Science ®Google Scholar
• Smoluchowski , V. 1917 . Versuch Einer Mathematischen Theorie Der Koagulationskinetik Kollider Losungen . Zeitschrift für Physikalische Chemie , 92 : 29 – 168 .
   Google Scholar
• Talukdar , S. S. and Swihart , M. T. 2004 . Aerosol Dynamics Modeling of Silicon Nanoparticle Formation During Silane Pyrolysis: A Comparison of Three Solution Methods . J. Aerosol Sci. , 35 : 889 – 908 .
   Web of Science ®Google Scholar
• Upadhyay , R. R. and Ezekoye , O. A. 2003 . Evaluation of the 1-Point Quadrature Approximation in QMOM for Combined Aerosol Growth Laws . J. Aerosol Sci. , 34 : 1665 – 1683 .
   Web of Science ®Google Scholar
• Wells , C. G. and Kraft , M. 2005 . Direct Simulation and Mass Flow Stochastic Algorithms to Solve a Sintering-Coagulation Equation . Monte Carlo Methods and Applications , 11 : 175 – 198 .
   Google Scholar
• Williams , M. M. R. 1986 . Some Topics in Nuclear Aerosol Dynamics . Progress in Nuclear Energy , 17 : 1 – 52 .
   Web of Science ®Google Scholar
• Wright , D. L. , McGraw , R. and Rosner , D. E. 2001 . Bivariate Extension of the Quadrature Method of Moments for Modeling Simultaneous Coagulation and Sintering of Particle Populations . J. Coll. Interface Sci. , 236 : 242 – 251 .
   PubMed Web of Science ®Google Scholar
• Yu , M. Z. , Lin , J. Z. and Chan , T. L. 2006 . Large Eddy Simulation of a Planar Jet Flow with Nanoparticle Coagulation . Acta Mechanica Sinica , 22 : 293 – 300 .
   Web of Science ®Google Scholar
• Yu , M. Z. , Lin , J. Z. and Chen , L. H. 2007 . Nanoparticle Coagulation in a Planar Jet Via Moment Method . Appl. Math. Mech. , 28 : 1445 – 1453 .
   Google Scholar
• Yu , M. Z. , Lin , J. Z. and Chan , T. L. 2008a . Numerical Simulation of Nanoparticle Synthesis in Diffusion Flame Reactor . Powder Technology , 181 : 9 – 20 .
   Web of Science ®Google Scholar
• Yu , M. Z. , Lin , J. Z. and Chan , T. L. 2008b . Effect of Precursor Loading on Non–Spherical TiO2 Nanoparticle Synthesis in a Diffusion Flame Reactor . Chem. Engineer. Sci. , 63 : 2317 – 2329 .
   Web of Science ®Google Scholar