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Lift force on nanoparticles in shear flows of dilute gases: negative or positive?

Published online by Cambridge University Press:  18 April 2016

Shuang Luo ,
Jun Wang ,
Guodong Xia  and
Zhigang Li
Shuang Luo
Affiliation:
Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Ministry of Education, College of Environmental and Energy Engineering, Beijing University of Technology, Beijing 100124, PR China
Jun Wang*
Affiliation:
Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Ministry of Education, College of Environmental and Energy Engineering, Beijing University of Technology, Beijing 100124, PR China
Guodong Xia
Affiliation:
Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Ministry of Education, College of Environmental and Energy Engineering, Beijing University of Technology, Beijing 100124, PR China
Zhigang Li
Affiliation:
Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
*
†Email address for correspondence: [email protected]
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Abstract

We theoretically investigate the lift force on spherical nanoparticles in a shear flow of a dilute gas, wherein the non-rigid-body collision between the particle and the gas molecules is considered. The analytical formula of the lift force is derived based on the gas kinetic theory. In the limit of rigid-body collision, the formula is consistent with the theoretical results in the literature (Liu & Bogy, Phys. Fluids, vol. 20, 2008, 107102), which predicts that the lift force is in the opposite direction to the fluid velocity gradient (negative lift force). However, by taking into account gas–particle intermolecular interactions, the direction of the lift force on the nanoparticle is found to be dependent on temperature, i.e. both positive and negative lift forces exist in a certain temperature range. An explanation for the direction change of the lift force is given based on the analysis of the scattering angle under non-rigid-body particle–molecule collisions.

JFM classification

Rarefied Gas Flow: Kinetic theory Multiphase and Particle-laden Flows: Particle/fluid flow Rarefied Gas Flow: Rarefied Gas Flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 443 - 454
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Copyright
© 2016 Cambridge University Press 

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References

Asmolov, E. S. 1999 The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. J. Fluid Mech. 381, 63–87.CrossRefGoogle Scholar
Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon.CrossRefGoogle Scholar
Bretherton, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284–304.CrossRefGoogle Scholar
Busnaina, A., Taylor, J. & Kashkoush, I. 1993 Measurement of the adhesion and removal forces of submicrometer particles on silicon substrates. J. Adhes. Sci. Technol. 7 (5), 441–455.CrossRefGoogle Scholar
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases. Cambridge University Press.Google Scholar
Chen, X. & Xu, D. Y. 2002 Thermophoresis of a near-wall particle at great Knudsen numbers. J. Aerosol Sci. 36, 39–47.Google Scholar
Cherukat, P. & McLaughlin, J. B. 1994 The inertial lift on a rigid sphere in a linear shear flow field near a flat wall. J. Fluid Mech. 263, 1–18.CrossRefGoogle Scholar
Dandy, D. S. & Dwyer, H. A. 1990 A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer. J. Fluid Mech. 216, 381–410.CrossRefGoogle Scholar
Everett, D. H. & Powl, J. C. 1976 Adsorption in slit-like and cylindrical micropores in the Henry’s law region: a model for the microporosity of carbons. J. Chem. Soc. Faraday Trans. 1 72, 619–636.CrossRefGoogle Scholar
Gavze, E. & Shapiro, M. 1998 Motion of inertial spheroidal particles in a shear flow near a solid wall with special application to aerosol transport in microgravity. J. Fluid Mech. 371, 59–79.CrossRefGoogle Scholar
Girifalco, L. A., Hodak, M. & Lee, R. S. 2000 Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential. Phys. Rev. B 62 (19), 13104–13110.CrossRefGoogle Scholar
Gombosi, T. I. 1994 Gaskinetic Theory. Cambridge University Press.CrossRefGoogle Scholar
Hamaker, H. C. 1937 The London–van der Waals attraction between spherical particles. Physica 4 (10), 1058–1072.CrossRefGoogle Scholar
Hirschfelder, J. O., Curtiss, C. F., Bird, R. B. & Mayer, M. G. 1954 Molecular Theory of Gases and Liquids. Wiley.Google Scholar
Ivchenko, I. N., Loyalka, S. K. & Tompson, R. V. Jr. 2007 Analytical Methods for Problems of Molecular Transport, vol. 83. Springer Science & Business Media.CrossRefGoogle Scholar
Kaufman, S. L., Skogen, J. W., Dorman, F. D., Zarrin, F. & Lewis, K. C. 1996 Macromolecule analysis based on electrophoretic mobility in air: globular proteins. Analyt. Chem. 68 (11), 1895–1904.CrossRefGoogle ScholarPubMed
Khrapak, S. A. 2013 Electron and ion thermal forces in complex (dusty) plasmas. Phys. Plasmas 20 (1), 013703.CrossRefGoogle Scholar
Khrapak, S. A. 2014 Accurate transport cross sections for the Lennard-Jones potential. Eur. Phys. J. D 68 (10), 1–6.CrossRefGoogle Scholar
Kim, S. U. & Monroe, C. W. 2014 High-accuracy calculations of sixteen collision integrals for Lennard-Jones (12–6) gases and their interpolation to parameterize neon, argon, and krypton. J. Comput. Phys. 273, 358–373.CrossRefGoogle Scholar
Kleinstreuer, C., Zhang, Z. & Donohue, J. F. 2008 Targeted drug-aerosol delivery in the human respiratory system. Annu. Rev. Biomed. Engng 10, 195–220.CrossRefGoogle ScholarPubMed
Knudsen, M. 1950 The Kinetic Theory of Gases: Some Modern Aspects. Metheun & Company.Google Scholar
Kröger, M. & Hütter, M. 2006 Unifying kinetic approach to phoretic forces and torques onto moving and rotating convex particles. J. Chem. Phys. 125 (4), 044105.Google ScholarPubMed
Li, Z. 2009 Critical particle size where the Stokes–Einstein relation breaks down. Phys. Rev. E 80 (6), 061204.CrossRefGoogle ScholarPubMed
Li, Z. & Wang, H. 2003a Drag force, diffusion coefficient, and electric mobility of small particles. I. Theory applicable to the free-molecule regime. Phys. Rev. E 68 (6), 061206.Google Scholar
Li, Z. & Wang, H. 2003b Drag force, diffusion coefficient, and electric mobility of small particles. II. Application. Phys. Rev. E 68 (6), 061207.Google ScholarPubMed
Li, Z. & Wang, H. 2004 Thermophoretic force and velocity of nanoparticles in the free molecule regime. Phys. Rev. E 70 (2), 021205.Google ScholarPubMed
Li, Z. & Wang, H. 2005 Gas–nanoparticle scattering: a molecular view of momentum accommodation function. Phys. Rev. Lett. 95 (1), 014502.CrossRefGoogle ScholarPubMed
Liu, N. & Bogy, D. B. 2008 Forces on a rotating particle in a shear flow of a highly rarefied gas. Phys. Fluids 20 (10), 107102.CrossRefGoogle Scholar
Liu, N. & Bogy, D. B. 2009 Forces on a spherical particle with an arbitrary axis of rotation in a weak shear flow of a highly rarefied gas. Phys. Fluids 21 (4), 047102.CrossRefGoogle Scholar
Mädler, L. & Friedlander, S. K. 2007 Transport of nanoparticles in gases: overview and recent advances. Aerosol Air Qual. Res. 7 (3), 304–342.CrossRefGoogle Scholar
McLaughlin, J. B. 1991 Inertial migration of a small sphere in linear shear flows. J. Fluid Mech. 224, 261–274.CrossRefGoogle Scholar
Merzkirch, W. & Bracht, K. 1978 The erosion of dust by a shock wave in air: initial stages with laminar flow. Intl J. Multiphase Flow 4 (1), 89–95.CrossRefGoogle Scholar
de la Mora, J. F., De Juan, L., Liedtke, K. & Schmidt-Ott, A. 2003 Mass and size determination of nanometer particles by means of mobility analysis and focused impaction. J. Aerosol Sci. 34 (1), 79–98.CrossRefGoogle Scholar
Poiseuille, J. L. M. 1836 Observations of blood flow. Ann. Sci. Nat. Strie. 5 (2), 111–115.Google Scholar
Rouquerol, F., Rouquerol, J. & Sing, K. 1999 Adsorption by Powders and Porous Solids: Principles, Methodology and Applications. Academic.Google Scholar
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447–459.CrossRefGoogle Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400.CrossRefGoogle Scholar
Salmanzadeh, M., Zahedi, G., Ahmadi, Gh., Marr, D. R. & Glauser, M. 2012 Computational modeling of effects of thermal plume adjacent to the body on the indoor airflow and particle transport. J. Aerosol Sci. 53, 29–39.CrossRefGoogle Scholar
Seville, J. P. K., Tüzün, U. & Clift, R. 1997 Processing of Particulate Solids, vol. 9. Island Press.CrossRefGoogle Scholar
Wang, J. & Li, Z. 2011 Thermophoretic force on micro- and nanoparticles in dilute binary gas mixtures. Phys. Rev. E 84 (2), 021201.CrossRefGoogle ScholarPubMed
Wang, J. & Li, Z. 2012 Negative thermophoresis of nanoparticles in the free molecular regime. Phys. Rev. E 86 (1), 011201.CrossRefGoogle ScholarPubMed
Wong, R. Y., Liu, C., Wang, J., Chao, C. Y. & Li, Z. 2012 Evaluation of the drag force on single-walled carbon nanotubes in rarefied gases. J. Nanosci. Nanotechnol. 12 (3), 2311–2319.CrossRefGoogle ScholarPubMed
Zhang, Y., Li, S., Yan, W. & Yao, Q. 2012 Nanoparticle transport and deposition in boundary layer of stagnation-point premixed flames. Powder Technol. 227, 24–34.CrossRefGoogle Scholar
Zheng, X. & Silber-Li, Z. 2009 The influence of Saffman lift force on nanoparticle concentration distribution near a wall. Appl. Phys. Lett. 95 (12), 124105.CrossRefGoogle Scholar
Zhou, J. & Papautsky, I. 2013 Fundamentals of inertial focusing in microchannels. Lab on a Chip 13 (6), 1121–1132.CrossRefGoogle ScholarPubMed
Zou, X.-Y., Cheng, H., Zhang, C.-L. & Zhao, Y.-Z. 2007 Effects of the Magnus and Saffman forces on the saltation trajectories of sand grain. Geomorphology 90 (1), 11–22.CrossRefGoogle Scholar