Effective diameters for collisions of fractal-like aggregates: recommendations for improved aerosol coagulation frequency predictions.

Fractal-like aggregate (FA-) drag has been previously calculated/correlated/reported, but "mobility diameter" information is not sufficient to make rational calculations of Brownian coagulation rates (for, say, population-balance modeling). Indeed, until now, only conjectures about gyration-radius scaling behavior have been used to predict FA-FA collision cross sections! But such "scaling relations" are untrustworthy even for FA momentum-, energy-, and mass-transfer purposes, and improved FA-collision rate constants (appearing as "kernels" in the coagulation balance integro-PDE) are overdue. Our premise is that FA collision rates in the free-molecule regime can be predicted using a gas-kinetic type formulation. If (a) carrier gas mean free path and FA persistence length are much larger than any characteristic FA size, (b) FA number density is low, (c) FA velocity and position are uncorrelated, and (d) there is a "hard-sphere" interaction between primary particles of different FAs, such a theory is developed/applied here. We introduce an effective collision diameter, , depending on the geometries of the two participating FAs. Quasi-MC calculations are reported for large ensembles of pairs of FAs, each computer-generated using a tunable cluster-cluster (CC)-algorithm. Our results differ from frequently used theoretical estimates based only on FA gyration (or mobility) radii and D(f). They also confirm that, if the size disparity of the colliding FAs is large, obtained by simply assigning individual diameters to each FA are significantly overestimated. Modified collision rate expressions for FA-coagulation modeling are suggested.

[1]  L. Sander,et al.  Diffusion-limited aggregation, a kinetic critical phenomenon , 1981 .

[2]  Filippov.  Drag and Torque on Clusters of N Arbitrary Spheres at Low Reynolds Number. , 2000, Journal of colloid and interface science.

[3]  R. Jullien,et al.  A cluster-cluster aggregation model with tunable fractal dimension , 1994 .

[4]  D. E. Rosner,et al.  Effect of Radiative Heat Transfer on the Coagulation Dynamics of Combustion-Generated Particles , 1994 .

[5]  H. Baum,et al.  Simulation of aerosol agglomeration in the free molecular and continuum flow regimes , 1986 .

[6]  S. Friedlander.  Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics , 2000 .

[7]  D. E. Rosner,et al.  Boundary layer coagulation effects on the size distribution of thermophoretically deposited particles , 1989 .

[8]  Sotiris E. Pratsinis,et al.  Flame aerosol synthesis of ceramic powders , 1998 .

[9]  C. Sorensen,et al.  Two-Dimensional Soot , 2001 .

[10]  A. M. Brasil,et al.  Evaluation of the Fractal Properties of Cluster?Cluster Aggregates , 2000 .

[11]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[12]  Paul Meakin,et al.  Fractal aggregates in geophysics , 1991 .

[13]  Constantine M. Megaridis,et al.  Morphological Description of Flame-Generated Materials , 1990 .

[14]  Forman A. Williams,et al.  Sooting and disruption in spherically symmetrical combustion of decane droplets in air , 1988 .

[15]  R. Botet,et al.  Aggregation and Fractal Aggregates , 1987 .

[16]  Christopher M. Sorensen,et al.  Aerogelation in a Flame Soot Aerosol , 1998 .

[17]  Steven N. Rogak,et al.  Stokes drag on self-similar clusters of spheres , 1990 .

[18]  Doraiswami Ramkrishna,et al.  Population Balances: Theory and Applications to Particulate Systems in Engineering , 2000 .

[19]  C. Sorensen,et al.  Aggregation Kernel Homogeneity for Fractal Aggregate Aerosols in the Slip Regime , 2001 .

[20]  Rémi Jullien,et al.  Scaling of Kinetically Growing Clusters , 1983 .

[21]  A. V. Filippov,et al.  Phoretic Motion of Arbitrary Clusters of N Spheres , 2001 .

[22]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases : an account of the kinetic theory of viscosity, thermal conduction, and diffusion in gases , 1954 .

[23]  Suyuan Yu,et al.  MC simulation of aerosol aggregation and simultaneous spheroidization , 2001 .

[24]  James W. Gentry,et al.  Structural analysis of soot agglomerates , 1987 .

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

[26]  D. E. Rosner,et al.  Experimental studies of soot particle thermophoresis in nonisothermal combustion gases using thermocouple response techniques , 1985 .

[27]  C. Sorensen,et al.  Diffusive mobility of fractal aggregates over the entire Knudsen number range. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Lourdes F. Vega,et al.  Vapor−Liquid Equilibria and Critical Behavior of Heavy n-Alkanes Using Transferable Parameters from the Soft-SAFT Equation of State , 2001 .

[29]  J. Seinfeld.  Atmospheric Chemistry and Physics of Air Pollution , 1986 .

[30]  R. Flagan,et al.  Coagulation of aerosol agglomerates in the transition regime , 1992 .

[31]  Steven N. Rogak,et al.  Measurement of Mass Transfer to Agglomerate Aerosols , 1991 .

[32]  R. Nakamura,et al.  Free molecular gas drag on fluffy aggregates , 1996 .

[33]  C. Sorensen,et al.  Light scattering study of fractal cluster aggregation near the free molecular regime , 1997 .

[34]  C. Sorensen,et al.  Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis , 1993 .

[35]  C. N. Davies,et al.  The Mechanics of Aerosols , 1964 .

[36]  D. E. Rosner,et al.  Thermophoretic Effects on Particles in Counterflow Laminar Diffusion Flames , 1993 .

[37]  R. Jullien,et al.  GEOMETRICAL PROPERTIES OF AGGREGATES WITH TUNABLE FRACTAL DIMENSION , 1997 .

[38]  S. Friedlander,et al.  Enhanced power law agglomerate growth in the free molecule regime , 1993 .

[39]  A. Randolph,et al.  Theory of Particulate Processes: Analysis and Techniques of Continuous Crystallization , 1971 .

[40]  D. E. Rosner,et al.  Size- and Structure-lnsensitivity of the Thermophoretic Transport of Aggregated “Soot” Particles in Gases , 1991 .

[41]  D. E. Rosner,et al.  In situ light-scattering measurements of morphologically evolving flame-synthesized oxide nanoaggregates. , 1999, Applied optics.

[42]  U. Baltensperger,et al.  Scaling behaviour of physical parameters describing agglomerates , 1990 .

[43]  D. E. Rosner,et al.  Prediction and correlation of accessible area of large multiparticle aggregates , 1994 .

[44]  D. E. Rosner,et al.  Transport Processes in Chemically Reacting Flow Systems , 1986 .

[45]  S. Pratsinis,et al.  Self-preserving size distributions of agglomerates , 1995 .

[46]  Robert J. Santoro,et al.  Aerosol dynamic processes of soot aggregates in a laminar ethene diffusion flame , 1993 .

[47]  G. Bird.  Molecular Gas Dynamics and the Direct Simulation of Gas Flows , 1994 .

[48]  D. E. Rosner,et al.  Translation Brownian Diffusion Coefficient of Large (Multiparticle) Suspended Aggregates , 1995 .

[49]  Paul Meakin,et al.  Collisions between point masses and fractal aggregates , 1989 .

[50]  T. Witten,et al.  Long-range correlations in smoke-particle aggregates , 1979 .

[51]  M. Williams,et al.  Aerosol science : theory and practice : with special applications to the nuclear industry , 1991 .

[52]  John H. Seinfeld,et al.  Fundamentals of Air Pollution Engineering , 1988 .

[53]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[54]  Daniel E. Rosner,et al.  Morphological evolution of nanoparticles in diffusion flames : Measurements and modeling , 1997 .

[55]  J. Ferziger,et al.  Mathematical theory of transport processes in gases , 1972 .

[56]  D. E. Rosner,et al.  Microstructural descriptors characterizing granular deposits , 1992 .

[57]  J. Helble.  Combustion aerosol synthesis of nanoscale ceramic powders , 1998 .

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

[59]  Ümit Özgür Köylü,et al.  Computational Evaluation of Approximate Rayleigh–Debye–Gans/Fractal-Aggregate Theory for the Absorption and Scattering Properties of Soot , 1995 .

[60]  P. Meakin.  Formation of fractal clusters and networks by irreversible diffusion-limited aggregation , 1983 .