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A Novel Slip Correction Factor for Spherical Aerosol Particles
Abstract:A 3D simulation study for an incompressible slip flow around a spherical aerosol particle was performed. The full Navier-Stokes equations were solved and the velocity jump at the gas-particle interface was treated numerically by imposition of the slip boundary condition. Analytical solution to the Stokesian slip flow past a spherical particle was used as a benchmark for code verification, and excellent agreement was achieved. The Simulation results showed that in addition to the Knudsen number, the Reynolds number affects the slip correction factor. Thus, the Cunningham-based slip corrections must be augmented by the inclusion of the effect of Reynolds number for application to Lagrangian tracking of fine particles. A new expression for the slip correction factor as a function of both Knudsen number and Reynolds number was developed.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060691Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3157
 S.A. Schaaf, and P.L. Chambre, Flow of rarefied gases, Princeton University Press, 1961.
 M. Gad-el-Hak, "The fluid mechanics of microdevicesÔÇöthe freeman scholar lecture," J. of Fluids Engineering., vol. 121, pp. 5-33, 1999.
 C.T. Crowe, Multiphase Flow Handbook, 1rd Edition. Taylor and Francis, Florida, 2006.
 J.H. Kim, G.W. Mulholland, S.R. Kukuck and D.Y.H. Pui, "Slip correction measurements of certified PSL nanoparticles using a nanometer differential mobility analyzer (Nano-DMA) for Knudsen number from 0.5 to 8," J. Res. Natl. Inst. Stand. Technol., vol. 110, pp. 31-54, 2005.
 E. Cunningham, "On the velocity of steady fall of spherical particles through fluid medium (Published Conference Proceedings style)," in Proc. Royal Soc. (London) A, vol. 83, pp. 357-365, 1910.
 R.A. Millikan, "The isolation of an ion, a precision measurement of its charge, and the correction of stokes's law." Science, vol. 32, pp. 436- 448, 1910.
 M. Knudsen and S. Weber, Ann. D. Phys., vol. 36, p. 981, 1911.
 W.C. Hinds, Aerosol Technology, Properties Behavior, and Measurement of Airborne Particles, 2nd ed. John Wiley and Sons, New York, 1998.
 R.A. Millikan, "The general law of fall of a small spherical body through a gas, and its bearing upon the nature of molecular reflection from surfaces," Physical Review, vol. 22, pp. 1-23, 1923.
 R.A. Millikan, The Electron: Its Isolation and Measurement and The Determination of some of Its Properties, University of Chicago Press, 8th Ed, 1963.
 M.D. Allen and O.G. Raabe, "Slip correction measurements of spherical solid aerosol particles in an improved Millikan apparatus." J. Aerosol Sci. Tech., vol. 4, p. 269, 1985.
 D.J. Rader, "Momentum slip correction factor for small particles in nine common gases," J. Aerosol Sci., vol. 21, pp. 161-168, 1990.
 D.K. Hutchins, M.H. Harper and R.L. Felder, J. Aerosol Sci. Tech., vol. 22, p. 202, 1995.
 M.D. Allen, and O.G. Raabe, "Re-evaluation of millikan's oil drop data for the motion of small particles in air," J. Aerosol Sci., vol. 13, p. 537, 1982.
 C.N. Davies, "Definite equations for the fluid resistance of spheres (Published Conference Proceedings style)," in Proc. Phys. Soc., vol. 57, p. 18, 1945.
 R.W. Barber and D.R. Emerson, "Analytic solution of low Reynolds number slip flow past a sphere (Report style)," Centre for Microfluidics, Department of Computational Science and Engineering, CLRC Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, 2001a.
 R.W. Barber and D.R. Emerson, "Numerical simulation of low Reynolds number slip flow past a confined microsphere (Published Conference Proceedings style)," in 23rd International Symposium on Rarefied Gas Dynamics, Whistler, Canada, pp. 20-25, 2002a.
 H-C. F. Liu, A. Beskok, N. Gatsonis and G.E. Karniadakis, "Flow past a microsphere in a pipe: effects of rarefaction," Micro-Electro-Mechanical Systems (MEMS). ASME, DSC-Vol. 66, pp. 445-452, 1998.
 J.K. Fremerey, "Spinning rotor vacuum gauges," J. Vacuum, vol. 32, pp. 685-690, 1982.
 G. Reich, "Spinning rotor viscosity gauge: A transfer standard for the laboratory or an accurate gauge for vacuum process control," J. Vacuum Science and Technology, vol. 20, pp. 1148-1152, 1982.
 A. Li, G. Ahmadi, R.G. Bayer and M.A. Gaynes, "Aerosol particle deposition in an obstructed turbulent duct flow," J. Aerosol Sci., vol. 25, pp. 91-112, 1994.
 M. Soltani, G. Ahmadi, H. Ounis and B. McLaughlin, "Direct simulation of charged particle deposition in a turbulent flow," Int. J. Multiphase flow, vol. 24, pp. 77-92, 1998.
 S. Dhaniyala, P.O. Wennberg, R.C. Flagan, D.W. Fahey, M.J. Northway, R.S. Gao and T.P. Bui, "Stratospheric aerosol sampling: effect of a blunt-body housing on inlet sampling characteristics," J. Aerosol Sci. and Technology, vol. 38, pp. 1080-1090, 2004.
 T.M. Peters and D. Leith, "Particle deposition in industrial duct bends," Ann. occup. Hyg., pp. 1-8, 2004.
 Z. Zhang, C. Kleinstreuer, J.F. Donohue and C.S. Kim, "Comparison of micro- and nano-size particle depositions in a human upper airway model," J. Aerosol Sci., vol. 36, pp. 211-233, 2005.
 X. Wang, A. Gidwani, S.L. Girshick, and P.H. McMurry, "Aerodynamic focusing of nanoparticles: II. Numerical simulation of particle motion through aerodynamic lenses," J. Aerosol Science and Technology, vol. 39, pp. 624-636, 2005.
 F.M. White, Viscous Fluid Flow. New York: Mc-Graw Hill, 2006, P. 47.
 B.P. Leonard, "Adjusted quadratic upstream algorithms for transient incompressible convection (Published Conference Proceedings style)," A Collection of Technical Papers. AIAA Computational Fluid Dynamics Conference, AIAA Paper 79-1469, 1979.
 R.W. Davis, J. Noye and C. Fletcher, Finite Difference Methods for Fluid Flow, Computational Techniques and Applications, Eds., Elsevier, pp. 51-69, 1984.
 C.J. Freitas, R.L. Street, A.N. Findikakis, and J.R. Koseff, "Numerical simulation of three-dimensional flow in a cavity," Int. J. Numerical Methods Fluids, vol. 5, pp. 561-575, 1985.
 W. Ji and P.K. Wang, "Numerical simulation of three-dimensional unsteady viscous flow past fixed hexagonal ice crystals in the airÔÇö Preliminary results," Atmos. Res., vol. 25, pp. 539-557, 1990.
 B.P. Leonard and S. Mokhtari, "ULTRA-SHARP Nonoscillatory convection schemes for high-speed steady multidimensional flow (Report style)," NASA Lewis Research Center, NASA TM 1-2568 (ICOMP-90-12), 1990.
 W. Ji and P.K. Wang, "Numerical simulation of three-dimensional unsteady viscous flow past finite cylinders in an unbounded fluid at low intermediate Reynolds numbers," Theor. Comput. Fluid Dyn., vol. 3, pp. 43-59, 1991.
 J.M. Weiss, J.P. Maruszewski and W.A. Smith, "Implicit solution of the Navier-Stokes equations on unstructured meshes (Published Conference Proceedings style)," 13th AIAA CFD Conference, Snowmass, CO, Technical Report AIAA-97-2103, 1997.
 S. Giors, F. Subba and R. Zanino, "Navier-Stokes modeling of a Gaede pump stage in the viscous and transitional flow regimes using slip-flow boundary conditions," J. Vac. Sci. Technol. A, vol. 23, No. 2, pp. 336- 346, 2005.
 V. Jain and C.X. Lin, "Numerical modeling of three-dimensional compressible gas flow in microchannels," J. Micromech. Microeng., vol. 16, pp. 292-302, 2006.
 E.O.B. Ogedengbe, G.F. Naterer and M.A. Rosen, "Slip-Flow irreversibility of dissipative kinetic and internal energy exchange in microchannels," J. Micromech. Microeng., vol. 16, pp. 2167-2176, 2006.
 F.M. White, Viscous Fluid Flow. New York: Mc-Graw Hill, 2006, P. 175.
 H.P Kavehpour, M. Faghri and Y. Asako, "Effects of compressibility and rarefaction on gaseous flows in microchannels," Numerical Heat Transfer, Part A: Applications, vol. 32, pp. 677 - 696, 1997.
 G. Zuppardi, D. Paterna and A. Rega "Quantifying the effects of rarefaction in high velocity, slip-flow regime (Published Conference Proceedings style)," in Rarefied Gas Dynamics: 25-th International Symposium, Russia, Novosibirsk, 2007.
 R.W. Barber and D.R. Emerson, "A numerical study of low Reynolds number slip flow in the hydrodynamic development region of circular and parallel plate ducts (Report style)," Centre for Microfluidics, Department of Computational Science and Engineering, CLRC Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, 2002b.