Determination of the Scalar Friction Factor for Nonspherical Particles and Aggregates Across the Entire Knudsen Number Range by Direct Simulation Monte Carlo (DSMC)

REFERENCES

• Allen , M. D. and Raabe , O. G. 1982 . Re-Evaluation of Millikan's Oil Drop Data for the Motion of Small Particles in Air . J. Aerosol Sci. , 13 : 537
   Web of Science ®Google Scholar
• Allen , M. D. and Raabe , O. G. 1985 . Slip Correction Measurements of Spherical Solid Aerosol-Particles in an Improved Millikan Apparatus . Aerosol Sci. Technol. , 4 : 269 – 286 .
   Web of Science ®Google Scholar
• Annis , B. K. , Malinauskas , A. P. and Mason , E. A. 1972 . Theory of Drag on Neutral or Charged Spherical Aerosol Particles . J. Aerosol Sci. , 3 : 55 – 64 .
   Google Scholar
• Bird , G. A. 1994 . Molecular Gas Dynamics and the Direct Simulation of Gas Flows , Oxford : Clarendon .
   Google Scholar
• Bleiholder , C. , Wyttenbach , T. and Bowers , M. T. 2011 . A Novel Projection Approximation Algorithm for the Fast and Accurate Computation of Molecular Collision Cross Sections (I). Method . Int. J. Mass Spectrom. , 308 : 1 – 10 .
   Web of Science ®Google Scholar
• Brady , J. F. and Sierou , A. 2001 . Accelerated Stokesian Dynamics Simulations . J. Fluid Mech. , 448 : 115 – 146 .
   Web of Science ®Google Scholar
• Buckingham , E. 1914 . On Physical Similar Systems; Illustrations of the Use of Dimensional Equations . Phys. Rev. , 4 : 345 – 376 .
   Web of Science ®Google Scholar
• Buckingham , E. 1915 . Model Experiments and the Forms of Empirical Equations . Trans. ASME , 37 : 263 – 296 .
   Google Scholar
• Buckley , R. L. and Loyalka , S. K. 1989 . Cunningham Correction Factor and Accommodation Coefficient: Interpretation of Millikan's Data . J. Aerosol Sci. , 20 : 347 – 349 .
   Web of Science ®Google Scholar
• Cai , J. and Sorensen , C. M. 1994 . Diffusion of Fractal Aggregates in the Free Molecular Regime . Phys. Rev. E , 50 ( 5 ) : 3397 – 3400 .
   Web of Science ®Google Scholar
• Cercignani , C. and Pagani , C. D. 1968 . Flow of a Rarified Gas Past an Axisymmetric Body. I. General Remarks . Phys. Fluids , 11 : 1395 – 1399 .
   Web of Science ®Google Scholar
• Cercignani , C. , Pagani , C. D. and Bassanini , P. 1968 . Flow of a Rarefied Gas Past an Axisymmetic Body. II. Case of a Sphere . Phys. Fluids , 11 : 1399 – 1403 .
   Web of Science ®Google Scholar
• Chan , P. and Dahneke , B. 1981 . Free-Molecule Drag on Straight Chains of Uniform Spheres . J. Appl. Phys. , 52 : 3106 – 3110 .
   Web of Science ®Google Scholar
• Chandrasekhar , S. 1943 . Stochastic Problems in Physics and Astronomy . Rev. Mod. Phys. , 15 : 1 – 89 .
   Google Scholar
• Chapman , S. and Cowling , T. G. 1970 . The Mathematical Theory of Non-Uniform Gases , Cambridge : Cambridge University Press .
   Google Scholar
• Chen , Z. Y. , Deutch , J. M. and Meakin , P. 1984 . Translational Friction Coefficient of Diffusion Limited Aggregates . J. Chem. Phys. , 80 ( 6 ) : 2982 – 2983 .
   Web of Science ®Google Scholar
• Chen , Z. Y. , Weakliem , P. C. and Meakin , P. 1988 . Hydrodynamic Radii of Diffusion-Limited Aggregates and Bond-Percolation Clusters . J. Chem. Phys. , 89 ( 9 ) : 5887 – 5889 .
   Web of Science ®Google Scholar
• Cheng , Y. S. , Allen , M. D. , Gallegos , D. P. , Yeh , H. C. and Peterson , K. 1988 . Drag Force and Slip Correction of Aggregate Aerosols . Aerosol Sci. Technol. , 8 ( 3 ) : 199 – 214 .
   Web of Science ®Google Scholar
• Cho , K. , Hogan , C. J. and Biswas , P. 2007 . Study of the Mobility, Surface Area, and Sintering Behavior of Agglomerates in the Transition Regime by Tandem Differential Mobility Analysis . J. Nanopart. Res. , 9 : 1003 – 1012 .
   Web of Science ®Google Scholar
• Chun , J. and Koch , D. L. 2005 . A Direct Simulation Monte Carlo Method for Rarefied Gas Flows in the Limit of Small Mach Number . Phys. Fluids , 17 ( 10 ) ):107107-107107-14
   PubMed Web of Science ®Google Scholar
• Dahneke , B. E. 1973a . Slip Correction Factors for Nonspherical Bodies - I: Introduction and Continuum Flow . J. Aerosol Sci. , 4 : 139 – 145 .
   Google Scholar
• Dahneke , B. E. 1973b . Slip Correction Factors for Nonspherical Bodies - II: Free Molecular Flow . J. Aerosol Sci. , 4 : 147 – 161 .
   Google Scholar
• Dahneke , B. E. 1973c . Slip Correction Factors for Nonspherical Bodies - III: The Form of the General Law . J. Aerosol Sci. , 4 : 163 – 170 .
   Google Scholar
• Dahneke , B. E. 1982 . Viscous Resistance of Straight-Chain Aggregates of Uniform Spheres . Aerosol Sci. Technol. , 1 : 179 – 185 .
   Web of Science ®Google Scholar
• Davies , C. N. 1945 . Definitive Equations for the Fluid Resistance of Spheres . Proc. Phys. Soc. , 57 : 259 – 270 .
   Google Scholar
• Douglas , J. F. , Zhou , H. X. and Hubbard , J. B. 1994 . Hydrodynamic Friction and the Capacitance of Arbitrarily-Shaped Objects . Phys. Rev. E , 49 ( 6 ) : 5319 – 5337 .
   Web of Science ®Google Scholar
• Eglin , J. M. 1923 . The Coefficients of Viscosity and Slip of Carbon Dioxide by the Oil Drop Method and the Law of Motion of an Oil Drop in Carbon Dioxide, Oxygen, and Helium, at Low Pressures . Phys. Rev. , 22 : 161 – 170 .
   Google Scholar
• Epstein , P. S. 1924 . On the Resistance Experienced by Spheres in Their Motion through Gases . Phys. Rev. , 23 : 710 – 733 .
   Google Scholar
• Fernandez de la Mora , J. 2002 . Free-Molecule Mobility of Polyhedra and Other Convex Hard-Bodies . J. Aerosol Sci. , 33 ( 3 ) : 477 – 489 .
   Web of Science ®Google Scholar
• Filippov , A. V. 2000 . Drag and Torque on Clusters of N-Arbitrary Spheres at Low Reynolds Number . J. Colloid Interface Sci. , 229 ( 1 ) : 184 – 195 .
   PubMed Web of Science ®Google Scholar
• Filippov , A. V. and Rosner , D. E. 2000 . Energy Transfer between an Aerosol Particle and Gas at High Temperature Ratios in the Knudsen Transition Regime . Int. J. Heat Mass Transfer , 43 : 127 – 138 .
   Web of Science ®Google Scholar
• Filippov , A. V. , Zurita , M. and Rosner , D. E. 2000 . Fractal-Like Aggregates: Relation between Morphology and Physical Properties . J. Colloid Interface Sci. , 229 ( 1 ) : 261 – 273 .
   PubMed Web of Science ®Google Scholar
• Fuchs , N. A. and Stechkina , I. B. 1962 . Resistance of a Gaseous Medium to the Motion of a Spherical Particle of a Size Comparable to the Mean Free Path of the Gas Molecules . Trans. Faraday Soc. , 58 : 1949 – 1952 .
   Google Scholar
• Gallis , M. A. , Rader , D. J. and Torczynski , J. R. 2002 . Calculations of the Near-Wall Thermophoretic Force in Rarefied Gas Flow . Phys. Fluids , 14 : 1518692
   Web of Science ®Google Scholar
• Gao , D. , Zhang , C. and Schwartzentruber , T. E. 2011 . Particle Simulations of Planetary Probe Flows Employing Automated Mesh Refinement . J. Spacecraft Rockets , 48 ( 3 ) : 397 – 405 .
   Web of Science ®Google Scholar
• Garcia-Ybarra , P. L. , Castillo , J. L. and Rosner , D. E. 2006 . Drag on a Large Spherical Aggregate with Self-Similar Structure: An Asymptotic Analysis . J. Aerosol Sci. , 37 ( 3 ) : 413 – 428 .
   Web of Science ®Google Scholar
• Given , J. A. , Hubbard , J. B. and Douglas , J. F. 1997 . A First-Passage Algorithm for the Hydrodynamic Friction and Diffusion-Limited Reaction Rate of Macromolecules . J. Chem. Phys. , 106 ( 9 ) : 3761 – 3771 .
   Web of Science ®Google Scholar
• Gmachowski , L. 2010 . Mobility Radius of Fractal Aggregates Growing in the Slip Regime . J. Aerosol Sci. , 41 ( 12 ) : 1152 – 1158 .
   Web of Science ®Google Scholar
• Gopalakrishnan , R. , Thajudeen , T. and Hogan , C. J. 2011 . Collision Limited Reaction Rates for Arbitrarily Shaped Particles across the Entire Diffusive Knudsen Number Range . J. Chem. Phys. , 135 : 054302
   PubMed Web of Science ®Google Scholar
• Gopinath , A. and Koch , D. L. 1999 . Hydrodynamic Interactions between Two Equal Spheres in a Highly Rarefied Gas . Phys. Fluids , 11 ( 9 ) : 2772 – 2787 .
   Web of Science ®Google Scholar
• Hadjiconstantinou , N. G. , Garcia , A. L. , Bazant , M. Z. and He , G. 2003 . Statistical Error in Particle Simulations of Hydrodynamic Phenomena . J. Comput. Phys. , 187 : 274 – 297 .
   Web of Science ®Google Scholar
• Hirschfelder , J. O. , Curtiss , C. F. and Bird , R. B. 1954 . Molecular Theory of Gases and Liquids , New York : Wiley .
   Google Scholar
• Hogan , C. J. and Fernandez de la Mora , J. 2011 . Ion Mobility Measurements of Non-Denatured 12–150 kDa Proteins and Protein Multimers by Tandem Differential Mobility Analysis – Mass Spectrometry (DMA-MS) . J. Am. Soc. Mass. Spectrom. , 22 : 158 – 172 .
   PubMed Web of Science ®Google Scholar
• Hogan , C. J. , Ruotolo , B. T. , Robinson , C. V. and Fernandez de la Mora , J. 2011 . Tandem Differential Mobility Analysis-Mass Spectrometry Reveals Partial Collapse of the GroEL Complex . J. Phys. Chem. B , 115 : 3614 – 4621 .
   PubMed Web of Science ®Google Scholar
• Hubbard , J. B. and Douglas , J. F. 1993 . Hydrodynamic Friction of Arbitrarily Shaped Brownian Particles . Phys. Rev. E , 47 ( 5 ) : R2983 – R2986 .
   Web of Science ®Google Scholar
• Isella , L. and Drossinos , Y. 2011 . On the Friction Coefficient of Straight-Chain Aggregates . J. Colloid Interface Sci. , 356 ( 2 ) : 505 – 512 .
   PubMed Web of Science ®Google Scholar
• Kim , J. H. , Mulholland , G. W. , Kukuck , S. R. and Pui , D. Y. H. 2005 . Slip Correction Measurements of Certified PSL Nanoparticles using a Nanometer Differential Mobility Analyzer (Nano-DMA) for Knudsen Number from 0.5 to 83 . J. Res. Nat. Inst. Stand. Technol. , 110 ( 1 ) : 31 – 54 .
   PubMed Web of Science ®Google Scholar
• Kim , S. H. , Mulholland , G. W. and Zachariah , M. R. 2007 . Understanding Ion-Mobility and Transport Properties of Aerosol Nanowires . J. Aerosol Sci. , 38 ( 8 ) : 823 – 842 .
   Web of Science ®Google Scholar
• Kirkwood , J. G. and Riseman , J. 1948 . The Intrinsic Viscosities and Diffusion Constants of Flexible Macromolecules in Solution . J. Chem. Phys. , 16 : 565 – 573 .
   Web of Science ®Google Scholar
• Ku , B. K. and Fernandez de la Mora , J. 2009 . Relation between Electrical Mobility, Mass, and Size for Nanodrops 1–6.5 nm in Diameter in Air . Aerosol Sci. Technol. , 43 ( 3 ) : 241 – 249 .
   Web of Science ®Google Scholar
• Lall , A. A. and Friedlander , S. K. 2006 . On-Line Measurement of Ultrafine Aggregate Surface Area and Volume Distributions by Electrical Mobility Analysis: 1. Theoretical Analysis . J. Aerosol Sci. , 37 ( 3 ) : 260 – 271 .
   Web of Science ®Google Scholar
• Larriba , C. , Hogan , C. J. , Attoui , M. , Borrajo , R. , Fernandez-Garcia , J. and Fernandez de la Mora , J. 2011 . The Mobility-Volume Relationship below 3.0 nm Examined by Tandem Mobility-Mass Measurement . Aerosol Sci. Technol. , 45 : 453 – 467 .
   Web of Science ®Google Scholar
• Li , Z. and Wang , H. 2003 . Drag Force, Diffusion Coefficient, and Electric Mobility of Small Particles. I. Theory Applicable to the Free-Molecule Regime . Phys. Rev. E , 68 : 061206
   Web of Science ®Google Scholar
• Loyalka , S. K. and Griffin , J. L. 1994 . Rotation of Non-Spherical Axisymmetric Particles in the Slip Regime . J. Aerosol Sci. , 25 : 509 – 525 .
   Web of Science ®Google Scholar
• Mackowski , D. W. 2006 . Monte Carlo Simulation of Hydrodynamic Drag and Thermophoresis of Fractal Aggregates of Spheres in the Free-Molecule Flow Regime . J. Aerosol Sci. , 37 : 242 – 259 .
   Web of Science ®Google Scholar
• Mason , E. A. and McDaniel , E. W. 1988 . Transport Properties of Ions in Gases , New York : Wiley .
   Google Scholar
• Meakin , P. , Donn , B. and Mulholland , G. W. 1989 . Collisions between Point Masses and Fractal Aggregates . Langmuir , 5 ( 2 ) : 510 – 518 .
   Web of Science ®Google Scholar
• Millikan , R. A. 1923 . The General Law of Fall of a Small Spherical Body through a Gas, and Its Bearing upon the Nature of Molecular Reflection from Surfaces . Phys. Rev. , 22 : 1 – 23 .
   Google Scholar
• Moshfegh , A. , Shams , M. , Ahmadi , G. and Ebrahimi , R. 2010 . A New Expression for Spherical Aerosol Drag in Slip Flow Regime . J. Aerosol Sci. , 41 ( 4 ) : 384 – 400 .
   Web of Science ®Google Scholar
• Nakamura , R. and Hidaka , Y. 1998 . Free Molecular Gas Drag on Fluffy Aggregates . Astron. Astrophys. , 340 ( 2 ) : 329 – 334 .
   Web of Science ®Google Scholar
• Nakamura , R. , Kitada , Y. and Mukai , T. 1994 . Gas Drag Forces on Fractal Aggregates . Planet. Space Sci. , 42 ( 9 ) : 721 – 726 .
   Web of Science ®Google Scholar
• Northrup , S. H. , Allison , S. A. and McCammon , J. A. 1984 . Brownian Dynamics Simulation of Diffusion-Influenced Bimolecular Reactions . J. Chem. Phys. , 80 ( 4 ) : 1517 – 1526 .
   Web of Science ®Google Scholar
• Northrup , S. H. , Curvin , M. S. , Allison , S. A. and McCammon , J. A. 1986 . Optimization of Brownian Dynamics Methods for Diffusion-Influenced Rate-Constant Calculations . J. Chem. Phys. , 84 ( 4 ) : 2196 – 2203 .
   Web of Science ®Google Scholar
• Park , K. , Dutcher , D. , Emery , M. , Pagels , J. , Sakurai , H. and Scheckman , J. 2008 . Tandem Measurements of Aerosol Properties – A Review of Mobility Techniques with Extensions . Aerosol Sci. Technol. , 42 ( 10 ) : 801 – 816 .
   Web of Science ®Google Scholar
• Peters , M. H. 1999 . Fokker-Planck Equation and the Grand Molecular Friction Tensor for Coupled Rotational and Translational Motions of Structured Brownian Particles near Structured Surfaces . J. Chem. Phys. , 110 ( 1 ) : 528 – 538 .
   Web of Science ®Google Scholar
• Phillips , W. F. 1975 . Drag on a Small Sphere Moving through a Gas . Phys. Fluids , 18 : 1089 – 1093 .
   Web of Science ®Google Scholar
• Pich , J. 1969 . The Drag of a Cylinder in the Transition Region . J. Colloid Interface Sci. , 29 : 91 – 96 .
   Web of Science ®Google Scholar
• Pierce , F. , Sorensen , C. M. and Chakrabarti , A. 2006 . Computer Simulation of Diffusion-Limited Cluster-Cluster Aggregation with an Epstein Drag Force . Phys. Rev. E , 74 ( 2 ) : 021411
   Web of Science ®Google Scholar
• Prasanth , P. S. and Kakkassery , J. K. 2006 . Direct Simulation Monte Carlo (DSMC): A Numerical Method for Transition-Regime Flows – A Review . J. Indian Inst. Sci. , 86 : 169 – 192 .
   Google Scholar
• Rader , D. J. 1990 . Momentum Slip Correction Factor for Small Particles in 9 Common Gases . J. Aerosol Sci. , 21 : 161 – 168 .
   Web of Science ®Google Scholar
• Ramanathan , S. , Koch , D. L. and Bhiladvala , R. B. 2010 . Noncontinuum Drag Force on a Nanowire Vibrating Normal to a Wall: Simulations and Theory . Phys. Fluids , 22 ( 10 ) : 103101
   Web of Science ®Google Scholar
• Rogak , S. N. , Baltensperger , U. and Flagan , R. C. 1991 . Measurement of Mass-Transfer to Agglomerate Aerosols . Aerosol Sci. Technol. , 14 ( 4 ) : 447 – 458 .
   Web of Science ®Google Scholar
• Rogak , S. N. , Flagan , R. C. and Nguyen , H. V. 1993 . The Mobility and Structure of Aerosol Agglomerates . Aerosol Sci. Technol. , 18 ( 1 ) : 25 – 47 .
   Web of Science ®Google Scholar
• Scheckman , J. H. , McMurry , P. H. and Pratsinis , S. E. 2009 . Rapid Characterization of Agglomerate Aerosols by In Situ Mass-Mobility Measurements . Langmuir , 25 ( 14 ) : 8248 – 8254 .
   PubMed Web of Science ®Google Scholar
• Shvartsburg , A. A. and Jarrold , M. F. 1996 . An Exact Hard-Spheres Scattering Model for the Mobilities of Polyatomic Ions . Chem. Phys. Lett. , 261 ( 1–2 ) : 86 – 91 .
   Web of Science ®Google Scholar
• Shvartsburg , A. A. , Mashkevich , S. V. , Baker , E. S. and Smith , R. D. 2007 . Optimization of Algorithms for Ion Mobility Calculations . J. Phys. Chem. A , 111 ( 10 ) : 2002 – 2010 .
   PubMed Web of Science ®Google Scholar
• Sorensen , C. M. 2011 . The Mobility of Fractal Aggregates: A Review . Aerosol Sci. Technol. , 45 ( 7 ) : 765 – 779 .
   Web of Science ®Google Scholar
• Sorensen , C. M. and Wang , G. M. 2000 . Note on the Correction for Diffusion and Drag in the Slip Regime . Aerosol Sci. Technol. , 33 ( 4 ) : 353 – 356 .
   Web of Science ®Google Scholar
• Takata , S. , Sone , Y. and Aoki , K. 1993 . Numerical Analyses of a Uniform Flow of a Rarefied Gas Past a Sphere on the Basis of the Boltzmann Equation for Hard-Sphere Molecules . Phys. Fluids A – Fluid Dyn. , 5 ( 3 ) : 716 – 737 .
   Web of Science ®Google Scholar
• Tammet , H. 1995 . Size and Mobility of Nanometer Particles, Clusters and Ions . J. Aerosol Sci. , 26 ( 3 ) : 459 – 475 .
   Web of Science ®Google Scholar
• Tandon , P. and Rosner , D. E. 1995 . Translational Brownian Diffusion Coefficient of Large (Multiparticle) Suspended Aggregates . Ind. Eng. Chem. Res. , 34 ( 10 ) : 3265 – 3277 .
   Web of Science ®Google Scholar
• Vainshtein , P. and Shapiro , M. 2005 . Mobility of Permeable Fractal Agglomerates in Slip Regime . J. Colloid Interface Sci. , 284 ( 2 ) : 501 – 509 .
   PubMed Web of Science ®Google Scholar
• Volkov , A. N. 2011 . Transitional Flow of a Rarefied Gas over a Spinning Sphere . J. Fluid Mech. , 683 : 320 – 345 .
   Web of Science ®Google Scholar
• Wang , G. M. and Sorensen , C. M. 1999 . Diffusive Mobility of Fractal Aggregates over the Entire Knudsen Number Range . Phys. Rev. E , 60 ( 3 ) : 3036 – 3044 .
   Web of Science ®Google Scholar
• Wang , G. M. and Sorensen , C. M. 2001 . Aggregation Kernel Homogeneity for Fractal Aggregate Aerosols in the Slip Regime . Aerosol Sci. Technol. , 34 ( 3 ) : 297 – 306 .
   Web of Science ®Google Scholar
• Wang , J. , Shin , W. G. , Mertler , M. , Sachweh , B. , Fissan , H. and Pui , D. Y. H. 2010 . Measurement of Nanoparticle Agglomerates by Combined Measurement of Electrical Mobility and Unipolar Charging Properties . Aerosol Sci. Technol. , 44 ( 2 ) : 97 – 108 .
   Web of Science ®Google Scholar
• Weber , A. P. , Baltensperger , U. , Gaggeler , H. W. and Schmidt-Ott , A. 1996 . In Situ Characterization and Structure Modification of Agglomerated Aerosol Particles . J. Aerosol Sci. , 27 ( 6 ) : 915 – 929 .
   Web of Science ®Google Scholar
• Zhang , C. and Schwartzentruber , T. E. 2011 . “ Robust Cut-Cell Algorithms for DSMC Implementations Employing Multi-Level Cartesian Grids ” . In Proceedings of the 42nd AIAA Thermophysics Conference , 598 – 619 . Red Hook , NY : Curran Associates .
   Google Scholar
• Zhou , H. X. , Szabo , A. , Douglas , J. F. and Hubbard , J. B. 1994 . A Brownian Dynamics Algorithm for Calculating the Hydrodynamic Friction and the Electrostatic Capacitance of an Arbitrarily-Shaped Object . J. Chem. Phys. , 100 ( 5 ) : 3821 – 3826 .
   Web of Science ®Google Scholar