Analytical expression for the rotational friction coefficient of DLCA aggregates over the entire Knudsen regime

References

• Bentz, J. A., Tompson, R. V., and Loyalka, S. K. (2001). Measurements of Viscosity, Velocity Slip Coefficients, and Tangential Momentum Accommodation Coefficients Using a Modified Spinning Rotor Gauge. J. Vac. Sci. Technol. A: Vac. Surf. Films, 19(1):317–324.
   Web of Science ®Google Scholar
• Bernal, J. M. G., and Garcia de la Torre, J. (1980). Transport Properties and Hydrodynamic Centers of Rigid Macromolecules with Arbitrary Shapes. Biopolymers, 19(4):751–766.
   Web of Science ®Google Scholar
• 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(3):511–525.
   Web of Science ®Google Scholar
• Brenner, H. (1967). Coupling Between the Translational and Rotational Brownian Motions of Rigid Particles of Arbitrary Shape: II. General Theory. J. Colloid Interface Sci., 23(3):407–436.
   Web of Science ®Google Scholar
• Carrasco, B., and Garcia de la Torre, J. (1999). Improved Hydrodynamic Interaction in Macromolecular Bead Models. J. Chem. Phys., 111(10):4817–4826.
   Web of Science ®Google Scholar
• Chan, P., and Dahneke, B. (1981). Free-Molecule Drag on Straight Chains of Uniform Spheres. J. Appl. Phys., 52(5):3106–3110.
   Web of Science ®Google Scholar
• Cheng, M. T., Xie, G. W., Yang, M., and Shaw, D. (1991). Experimental Characterization of Chain-aggregate Aerosol by Electrooptic Scattering. Aerosol Sci. Technol., 14(1):74–81.
   Web of Science ®Google Scholar
• Colbeck, I., Atkinson, B., and Johar, Y. (1997). The Morphology and Optical Properties of Soot Produced by Different Fuels. J. Aerosol Sci., 28(5):715–723.
   Web of Science ®Google Scholar
• Corson, J., Mulholland, G. W., and Zachariah, M. R. (2017a). Friction Factor for Aerosol Fractal Aggregates ove the Entire Knudsen Range. Phys. Rev. E, 95(1):013103.
   PubMed Web of Science ®Google Scholar
• Corson, J., Mulholland, G. W., and Zachariah, M. R. (2017b). Analytical Expression for the Friction Coefficient of DLCA Aggregates based on Extended Kirkwood–Riseman Theory. Aerosol Sci. Technol., 51(6):766–777.
   Web of Science ®Google Scholar
• Corson, J., Mulholland, G. W., and Zachariah, M. R. (2017c). Calculating the Rotational Friction Coefficient of Fractal Aerosol Particles in the Transition Regime using Extended Kirkwood-Riseman Theory. Phys. Rev. E, 96(1):013110.
   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(2):163–170.
   Google Scholar
• Epstein, P. S. (1924). On the Resistance Experienced by Spheres in Their Motion Through Gases. Phys. Rev., 23(6):710–733.
   Google Scholar
• Garcia de la Torre, J., del Rio Echenique, G., and Ortega, A. (2007). Improved Calculation of Rotational Diffusion and Intrinsic Viscosity of Bead Models for Macromolecules and Nanoparticles. J. Phys. Chem. B, 111(5):955–961.
   PubMed Web of Science ®Google Scholar
• Garcia de la Torre, J., 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(5):2454–2460.
   Web of Science ®Google Scholar
• Halbritter, J. (1974). Torque on a Rotating Ellipsoid in a Rarefied Gas. Zeitschrift fur Naturforschung A, 29(12):1717–1722.
   Google Scholar
• Happel, J., and Brenner, H. (1965). Low Reynolds number Hydrodynamics: with Special Applications to Particulate Media. Prentice Hall, s.l.
   Google Scholar
• Heinson, W. R., Pierce, F., Sorensen, C. M., and Chakrabarti, A. (2014). Crossover from Ballistic to Epstein Diffusion in the Free-molecular Regime. Aerosol Sci. Technol., 48(7):738–746.
   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(6):565–573.
   Web of Science ®Google Scholar
• Koylu, U. O., and Faeth, G. M. (1992). Structure of Overfire Soot in Buoyant Turbulent Diffusion Flames at Long Residence Times. Combust. Flame, 89(2):140–156.
   Web of Science ®Google Scholar
• Larriba, C., and Hogan, C. J. Jr. (2013). Ion Mobilities in Diatomic Gases: Measurement Versus Prediction with Non-specular Scattering Models. J. Phys. Chem. A, 117(19):3887–3901.
   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 (1958–1988), 29(11):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(9):1550–1557.
   Web of Science ®Google Scholar
• Li, M., Mulholland, G. W., and Zachariah, M. R. (2012). The Effect of Orientation on the Mobility and dynamic Shape Factor of Charged Axially Symmetric Particles in an Electric Field. Aerosol Sci. Technol., 46(9):1035–1044.
   Web of Science ®Google Scholar
• Li, M., Mulholland, G. W., and Zachariah, M. R. (2014). Rotational Diffusion Coefficient (or Rotational Mobility) of a Nanorod in the Free-molecular Regime. Aerosol Sci. Technol., 48(2):139–141.
   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(2):022112.
   Web of Science ®Google Scholar
• Li, M., Mulholland, G. W., and Zachariah, M. R. (2016). The Effect of Alignment on the Electric Mobility of Soot. Aerosol Sci. Technol., 50(10):1003–1016.
   Web of Science ®Google Scholar
• Loyalka, S. K. (1992). Motion of a Sphere in a Gas: Numerical Solution of the Linearized Boltzmann Equation. Phys. Fluids A: Fluid Dyn., 4(5):1049–1056.
   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(3):242–259.
   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(8):3786–3789.
   Web of Science ®Google Scholar
• Melas, A. D., Isella, L., Konstandopoulos, A. G., and Drossinos, Y. (2015). A Methodology to Calculate the Friction Coefficient in the Transition Regime: Application to Straight Chains. J. Aerosol Sci., 82:40–50.
   Web of Science ®Google Scholar
• Mountain, R. D., Mulholland, G. W., and Baum, H. (1986). Simulation of Aerosol Agglomeration in the Free Molecular and Continuum Flow Regimes. J. Colloid Interface Sci., 114(1):67–81.
   Web of Science ®Google Scholar
• Mulholland, G. W., Hagwood, C. R., Li, M., and Zachariah, M. R. (2016). Effect of Particle Rotation on the Drift Velocity for Nonspherical Aerosol Particles. J. Aerosol Sci., 101:65–76.
   Web of Science ®Google Scholar
• Ortega, A., and Garcia de la Torre, J. (2003). Hydrodynamic Properties of Rodlike and Disklike Particles in Dilute Solution. J. Chem. Phys., 119(18):9914–9919.
   Web of Science ®Google Scholar
• Rotne, J., and Prager, S. (1969). Variational Treatment of Hydrodynamic Interaction in Polymers. J. Chem. Phys., 50(11):4831–4837.
   Web of Science ®Google Scholar
• Shrivastav, V., Nahin, M., Hogan, C. J., and Larriba-Andaluz, C. (2017). Benchmark Comparison for a Multi-Processing Ion Mobility Calculator in the Free Molecular Regime. J. Am. Soc. Mass Spectrom., 28:1540–1551.
   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
• Tekasakul, P., Bentz, J. A., Tompson, R. V., and Loyalka, S. K. (1996). The Spinning Rotor Gauge: Measurements of Viscosity, Velocity Slip Coefficients, and Tangential Momentum Accommodation Coefficients. J. Vac. Sci. Technol. A: Vac. Surf. Films, 14(5):2946–2952.
   Web of Science ®Google Scholar
• Weiss, R. E., Kapustin, V. N., and Hobbs, P. V. (1992). Chain-Aggregate Aerosols in Smoke from the Kuwait Oil Fires. J. Geophys. Res.: Atmospheres, 97(D13):14527–14531.
   Web of Science ®Google Scholar
• Williams, M. M. R., and Loyalka, S. K. (1991). Aerosol Science: Theory and Practice: With Special Applications to the Nuclear Industry. Pergamon Press, Oxford.
   Google Scholar
• Yamakawa, H. (1970). Transport Properties of Polymer Chains in Dilute Solution: Hydrodynamic Interaction. J. Chem. Phys., 53(1):436–443.
   Web of Science ®Google Scholar
• Zhang, C., Thajudeen, T., Larriba, C., Schwartzentruber, T. E., and Hogan, C. J., Jr. (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(10):1065–1078.
   Web of Science ®Google Scholar