Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-29T02:31:03.577Z Has data issue: false hasContentIssue false
  • English
  • Français

Shear lift forces on nanocylinders in the free molecule regime

Published online by Cambridge University Press:  08 May 2018

Shuang Luo ,
Jun Wang Open the ORCID record for Jun Wang [Opens in a new window] ,
Song Yu ,
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 Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
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
Song Yu
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]
Get access Rights & Permissions [Opens in a new window]

Abstract

In the present paper, analytical formulae for the shear lift forces on nanocylinders moving in linear shear flows in the free molecule regime are derived on the basis of the gas kinetic theory. The model takes into account the intermolecular interactions between the nanocylinders and gas molecules, i.e., the non-rigid-body effect. It is shown that the resulting formulae are consistent with the previous theory in the limit of rigid-body collisions. The lift forces acting on carbon nanotubes and long-chain $n$ -alkanes are evaluated as examples. It is found that the non-rigid-body effect is of great importance for small nanocylinders at low temperatures.

JFM classification

Rarefied Gas Flow: Kinetic theory Multiphase and Particle-laden Flows: Particle/fluid flow Rarefied Gas Flow: Rarefied Gas Flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , pp. 392 - 410
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, M. D. & Raabe, O. G. 1982 Re-evaluation of Millikan’s oil drop data for the motion of small particles in air. J. Aerosol. Sci. 13 (6), 537–547.CrossRefGoogle Scholar
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 Monte Carlo of Gas Flows. Oxford University Press.CrossRefGoogle Scholar
Bird, R. B., Hirschfelder, J. O. & Curtiss, C. F. 1954 Molecular Theory of Gases and Liquids. Wiley.Google Scholar
Britz, D. A. & Khlobystov, A. N. 2006 Noncovalent interactions of molecules with single walled carbon nanotubes. Chem. Soc. Rev. 35 (7), 637–659.Google Scholar
Bretherton, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284–304.Google 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
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.Google Scholar
Cox, R. G. 1971 The motion of long slender bodies in a viscous fluid. Part 2. Shear flow. J. Fluid Mech. 45, 625–657.Google Scholar
Dong, R. Y. & Cao, B. Y. 2014 Anomalous orientations of a rigid carbon nanotube in a sheared fluid. Sci. Rep. 4, 6120.CrossRefGoogle Scholar
Dong, R. Y. & Cao, B. Y. 2015 Superhigh-speed unidirectional rotation of a carbon nanotube in a sheared fluid and its decoupled dynamics. RSC Adv. 5 (108), 88719–88724.Google Scholar
Fan, F. G. & Ahmadi, G. 2000 Wall deposition of small ellipsoids from turbulent air flows: a Brownian dynamics simulation. J. Aerosol Sci. 31 (10), 1205–1229.CrossRefGoogle Scholar
Fan, F. G., Soltani, M., Ahmadi, G. & Hart, S. C. 1997 Flow-induced resuspension of rigid-link fibers from surfaces. Aerosol Sci. Technol. 27 (2), 97–115.CrossRefGoogle Scholar
Feng, Y. & Kleinstreuer, C. 2013 Analysis of non-spherical particle transport in complex internal shear flows. Phys. Fluids 25 (9), 091904.CrossRefGoogle Scholar
Garcia-Ybarra, P. & Rosner, D. E. 1989 Thermophoretic properties of nonspherical particles and large molecules. AIChE J. 35 (1), 139–147.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.Google Scholar
Harper, E. Y. & Chang, I. D. 1968 Maximum dissipation resulting from lift in a slow viscous shear flow. J. Fluid Mech. 33, 209–225.CrossRefGoogle Scholar
Högberg, S. M., Åkerstedt, H. O., Lundström, T. S & Freund, J. B. 2010 Respiratory deposition of fibers in the non-inertial regime: development and application of a semi-analytical model. Aerosol Sci. Technol. 44, 847–860.CrossRefGoogle Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161–179.Google Scholar
Ji, C., Dames, E., Wang, Y. L., Wang, H. & Egolfopoulos, F. N. 2010 Propagation and extinction of premixed C5 –C12 n-alkane flames. Combust. Flame 157 (2), 277–287.CrossRefGoogle Scholar
Jung, H., Han, K., Mulholland, G. W., Pui, D. Y. & Kim, J. H. 2013 Effect of the surface energy of particle materials on the accommodation of gas molecules to the particle surfaces. J. Aerosol. Sci. 65, 42–48.CrossRefGoogle Scholar
Kleinstreuer, C. & Feng, Y. 2013 Computational analysis of non-spherical particle transport and deposition in shear flow with application to lung aerosol dynamics: a review. J. Biomech. Engng 135 (2), 021008.Google Scholar
Kleinstreuer, C., Zhang, Z. & Donohue, J. F. 2008a Targeted drug-aerosol delivery in the human respiratory system. Annu. Rev. Biomed. Engng 10, 195–220.Google Scholar
Kleinstreuer, C., Zhang, Z. & Li, Z. 2008b Modeling airflow and particle transport/deposition in pulmonary airways. Respir. Physiol. Neurobiol. 163 (1–3), 128–138.Google Scholar
Kröger, M. & Hütter, M. 2006a Unifying kinetic approach to phoretic forces and torques onto moving and rotating convex particles. J. Chem. Phys. 125 (4), 044105.Google ScholarPubMed
Kröger, M. & Hütter, M. 2006b Symbolic computation of the phoretic acceleration of convex particles suspended in a non-uniform gas. Comput. Phys. Commun. 175 (10), 650–664.Google Scholar
Laiho, P., Mustonen, K., Ohno, Y., Maruyama, S. & Kauppinen, E. I. 2017 Dry and direct deposition of aerosol-synthesized single-walled carbon nanotubes by thermophoresis. ACS Appl. Mater. Interfaces 9 (24), 20738–20747.Google Scholar
Leal, L. G. 1980 Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12 (1), 435–476.Google Scholar
Li, Z. & Wang, H. 2003a Drag force, diffusion coefficient, and electric mobility of small particles. Part I. Theory applicable to the free-molecule regime. Phys. Rev. E 68 (2), 061206.Google Scholar
Li, Z. & Wang, H. 2003b Drag force, diffusion coefficient, and electric mobility of small particles. Part II. Application. Phys. Rev. E 68 (6), 061207.Google Scholar
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, C., Li, Z. & Wang, H. 2016a Drag force and transport property of a small cylinder in free molecule flow: a gas-kinetic theory analysis. Phys. Rev. E 94 (2), 023102.Google Scholar
Liu, C., McGivern, W. S., Manion, J. A. & Wang, H. 2016b Theory and experiment of binary diffusion coefficient of n-alkanes in dilute gases. J. Phys. Chem. A 120 (41), 8065–8074.Google Scholar
Liu, C., Zhao, R., Xu, R., Egolfopoulos, F. N. & Wang, H. 2017 Binary diffusion coefficients and non-premixed flames extinction of long-chain alkanes. Proc. Combust. Inst. 36 (1), 1523–1530.CrossRefGoogle Scholar
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.Google 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
Loth, E. 2008 Lift of a spherical particle subject to vorticity and/or spin. AIAA J. 46 (4), 801–809.Google Scholar
Luo, S., Wang, J., Xia, G. & Li, Z. 2016a Lift force on nanoparticles in shear flows of dilute gases: negative or positive? J. Fluid Mech. 795, 443–454.CrossRefGoogle Scholar
Luo, S., Wang, J., Xia, G. & Li, Z. 2016b Lift force on spherical nanoparticles in shear flows of rarefied binary gas mixtures. J. Fluid Mech. 809, 345–359.Google Scholar
Massoudi, M. 2002 On the importance of material frame-indifference and lift forces in multiphase flows. Chem. Engng Sci. 57 (17), 3687–3701.Google Scholar
McLaughlin, J. B. 1989 Aerosol particle deposition in numerically simulated channel flow. Phys. Fluids A 1 (7), 1211–1224.CrossRefGoogle 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), 1–23.CrossRefGoogle Scholar
Okada, Y., Nishiumi, K., Ueno, S., Kawabata, T. & Kudoh, S. 2011 Accuracy of nanoparticle diameters measured with a differential mobility analyzer in free-molecule regime. Earozoru Kenkyu 26 (3), 242–246.Google Scholar
Prabha, S. K. & Sathian, S. P. 2012 Determination of accommodation coefficients of a gas mixture in a nanochannel with molecular dynamics. Microfluid Nanofluid 13 (6), 883–890.Google Scholar
Saffman, P. G. T. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400.Google Scholar
Tian, L., Ahmadi, G., Wang, Z. & Hopke, P. K. 2012 Transport and deposition of ellipsoidal fibers in low Reynolds number flows. J. Aerosol. Sci. 45, 1–18.Google 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.Google Scholar
Wang, J., Luo, S. & Xia, G. 2017 Thermophoretic force on nanocylinders in the free molecule regime. Phys. Rev. E 95 (3), 033101.Google Scholar
Wang, J., Yu, S., Luo, S., Xia, G. D. & Zong, L. X. 2018 Lift forces on an axial symmetry particle rotating in a linear shear flow of a rarefied gas. Phys. Fluids (submitted).Google Scholar
Watanabe, Y., Yamaguchi, H., Hashinokuchi, M., Sawabe, K., Maruyama, S., Matsumoto, Y. & Shobatake, K. 2006 Energy transfer in hyperthermal Xe–graphite surface scattering. Eur. Phys. J. D 38 (1), 103–109.Google Scholar
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.Google Scholar
Yamaguchi, H., Matsuda, Y. & Niimi, T. 2017 Molecular dynamics study on characteristics of energy and tangential momentum accommodation coefficients. Phys. Rev. E 96 (1), 013116.Google Scholar
Yang, L., Bian, J. J. & Wang, G. F. 2017 Impact of atomic-scale surface morphology on the size-dependent yield stress of gold nanoparticles. J. Phys. D: Appl. Phys. 50, 245302.Google Scholar
Yin, C., Rosendahl, L., Kær, S. K. & Sørensen, H. 2003 Modelling the motion of cylindrical particles in a nonuniform flow. Chem. Engng Sci. 58 (15), 3489–3498.CrossRefGoogle Scholar
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
Zhao, B., Zhang, Y., Li, X., Yang, X. & Huang, D. 2004 Comparison of indoor aerosol particle concentration and deposition in different ventilated rooms by numerical method. Build. Environ. 39 (1), 1–8.Google 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
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 (1–2), 11–22.Google Scholar