Analytical expression for the friction coefficient of DLCA aggregates based on extended Kirkwood–Riseman theory

References

• Bhatnagar, P. L., Gross, E. P., and Krook, M. (1954). A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems. Phys. Rev., 94:511–525.
   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
• Chen, Z.-Y., Deutch, J. M., and Meakin, P. (1984). Translational Friction Coefficient of Diffusion Limited Aggregates. J. Chem. Phys., 80:2982–2983.
   Web of Science ®Google Scholar
• Corson, J., Mulholland, G. W., and Zachariah, M. R. (2017). Friction Factor for Aerosol Fractal Aggregates over the Entire Knudsen Range. Phys. Rev. E., 95:013103.
   PubMed Web of Science ®Google Scholar
• Dahneke, B. E. (1973). Slip Correction Factors for Nonspherical Bodies—III The Form of the General Law. J. Aerosol Sci., 4:163–170.
   Google Scholar
• de la Torre, J. G., and Rodes, V. (1983). Effects from Bead Size and Hydrodynamic Interactions on the Translational and Rotational Coefficients of Macromolecular Bead Models. J. Chem. Phys., 79:2454–2460.
   Web of Science ®Google Scholar
• Eggersdorfer, M. L., Grohn, A. J., and Sorensen, C. M. (2012). Mass-Mobility Characterization of Flame-Made ZrO2 Aerosols: Primary Particle Diameter and Extent of Aggregation. J. Colloid Interf. Sci., 387:12–23.
   PubMed Web of Science ®Google Scholar
• Epstein, P. S. (1924). On the Resistance Experienced by Spheres in their Motion Through Gases. Phys. Rev., 23:710–733.
   Google Scholar
• Happel, J., and Brenner, H. (1965). Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media. Prentice Hall, Englewood Cliffs, NJ.
   Google Scholar
• Hubbard, J. B., and Douglas, J. F. (1993). Hydrodynamic Friction of Arbitrarily Shaped Brownian Particles. Phys. Rev. E., 47:R2983–R2986.
   PubMed 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
• Lall, A. A., and Friedlander, S. K. (2006). On-line Measurement of Ultrafine Aggregate Surface Area and Volume Distributions by Electrical Mobility Analysis: I. Theoretical Analysis. J. Aerosol Sci., 37:260–271.
   Web of Science ®Google Scholar
• Lattuada, M., Wu, H., and Morbidelli, M. (2003). Hydrodynamic Radius of Fractal Clusters. J. Colloid Interf. Sci., 268:96–105.
   PubMed Web of Science ®Google Scholar
• Law, W. S., and Loyalka, S. K. (1986). Motion of a Sphere in a Rarefied Gas. II. Role of Temperature Variation in the Knudsen Layer. Phys. Fluids, 29:3886–3888.
   Web of Science ®Google Scholar
• Lea, K. C., and Loyalka, S. K. (1982). Motion of a Sphere in a Rarefied Gas. Phys. Fluids, 25:1550–1557.
   Web of Science ®Google Scholar
• Li, M., Mulholland, G. W., and Zachariah, M. R. (2014). Understanding the Mobility of Nonspherical Particles in the Free Molecular Regime. Phys. Rev. E., 89:022112.
   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
• Mansfield, M. L., Douglas, J. F., and Garboczi, E. J. (2001). Intrinsic Viscosity and the Electrical Polarizability of Arbitrarily Shaped Objects. Phys. Rev. E, 64(6):061401.
   Web of Science ®Google Scholar
• Meakin, P., Bertram, D., and Mullholland, G. W. (1989). Collisions Between Point Masses and Fractal Aggregates. Langmuir, 5:510–518.
   Web of Science ®Google Scholar
• Meakin, P., Chen, Z.-Y., and Deutch, J. M. (1985). The Translational Friction Coefficient and Time Dependent Cluster Size Distribution of Three Dimensional Cluster–Cluster Aggregation. J. Chem. Phys., 82:3786–3789.
   Web of Science ®Google Scholar
• Meakin, P., and Deutch, J. M. (1987). Properties of the Fractal Measure Describing the Hydrodynamic Force Distributions for Fractal Aggregates Moving in a Quiescent Fluid. J. Chem. Phys., 86(8):4648–4656.
   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
• Rogak, S. N., Flagan, R. C., and Nguyen, H. V. (1993). The Mobility and Structure of Aerosol Agglomerates. Aerosol Sci. Technol. 18:25–47.
   Web of Science ®Google Scholar
• Rotne, J., and Prager, S. (1969). Variational Treatment of Hydrodynamic Interaction in Polymers. J. Chem. Phys., 50:4831–4837.
   Web of Science ®Google Scholar
• Shin, W. G., Mulholland, G. W., Kim, S. C., Wang, J., Emery, M. S., and Pui, D. Y. (2009). Friction Coefficient and Mass of Silver Agglomerates in the Transition Regime. J. Aerosol Sci., 40:573–587.
   Web of Science ®Google Scholar
• Shin, W. G., Mulholland, G. W., and Pui, D. Y. (2010). Determination of Volume, Scaling Exponents, and Particle Alignment of Nanoparticle Agglomerates using Tandem Differential Mobility Analyzers. J. Aerosol Sci., 41:665–681.
   Web of Science ®Google Scholar
• Sone, Y., and Aoki, K. (1977). Slightly Rarefied Gas Flow Over a Specularly Reflecting Body. Phys. Fluids, 20:571–576.
   Web of Science ®Google Scholar
• Sorensen, C. M. (2011). The Mobility of Fractal Aggregates: A Review. Aerosol Sci. Technol., 45:765–779.
   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., 33:353–356.
   Web of Science ®Google Scholar
• Swanson, E., Teller, D. C., and de Haen, C. (1980). Creeping Flow Translational Resistance of Rigid Assemblies of Spheres. J. Chem. Phys., 72:1623–1628.
   Web of Science ®Google Scholar
• Takata, S., Sone, Y., and Aoki, K. (1993). Numerical Analysis 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., 5:716–737.
   Web of Science ®Google Scholar
• Yamakawa, H. (1970). Transport Properties of Polymer Chains in Dilute Solution: Hydrodynamic Interaction. J. Chem. Phys., 53:436–443.
   Web of Science ®Google Scholar
• Zhang, C., Thajudeen, T., Larriba, C., Schwartzentruber, T. E., and Hogan Jr., C. J. (2012). Determination of the Scalar Friction Factor for Nonspherical Particles and Aggregates Across the Entire Knudsen Number Range by Direct Simulation Monte Carlo (DSMC). Aerosol Sci. Technol., 46:1065–1078.
   Web of Science ®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., 100:3821–3826.
   Web of Science ®Google Scholar