Skip to main content Accessibility help

Shear lift forces on nanocylinders in the free molecule regime

  • Shuang Luo (a1) (a2), Jun Wang (a1), Song Yu (a1), Guodong Xia (a1) and Zhigang Li (a2)...


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.


Corresponding author

Email address for correspondence:


Hide All
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), 537547.
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, 6387.
Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation Monte Carlo of Gas Flows. Oxford University Press.
Bird, R. B., Hirschfelder, J. O. & Curtiss, C. F. 1954 Molecular Theory of Gases and Liquids. Wiley.
Britz, D. A. & Khlobystov, A. N. 2006 Noncovalent interactions of molecules with single walled carbon nanotubes. Chem. Soc. Rev. 35 (7), 637659.
Bretherton, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284304.
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.
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, 118.
Cox, R. G. 1971 The motion of long slender bodies in a viscous fluid. Part 2. Shear flow. J. Fluid Mech. 45, 625657.
Dong, R. Y. & Cao, B. Y. 2014 Anomalous orientations of a rigid carbon nanotube in a sheared fluid. Sci. Rep. 4, 6120.
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), 8871988724.
Fan, F. G. & Ahmadi, G. 2000 Wall deposition of small ellipsoids from turbulent air flows: a Brownian dynamics simulation. J. Aerosol Sci. 31 (10), 12051229.
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), 97115.
Feng, Y. & Kleinstreuer, C. 2013 Analysis of non-spherical particle transport in complex internal shear flows. Phys. Fluids 25 (9), 091904.
Garcia-Ybarra, P. & Rosner, D. E. 1989 Thermophoretic properties of nonspherical particles and large molecules. AIChE J. 35 (1), 139147.
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, 5979.
Girifalco, L. A., Hodak, M. & Lee, R. S. 2000 Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential. Phys. Rev. B 62 (19), 13104.
Harper, E. Y. & Chang, I. D. 1968 Maximum dissipation resulting from lift in a slow viscous shear flow. J. Fluid Mech. 33, 209225.
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, 847860.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161179.
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), 277287.
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, 4248.
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.
Kleinstreuer, C., Zhang, Z. & Donohue, J. F. 2008a Targeted drug-aerosol delivery in the human respiratory system. Annu. Rev. Biomed. Engng 10, 195220.
Kleinstreuer, C., Zhang, Z. & Li, Z. 2008b Modeling airflow and particle transport/deposition in pulmonary airways. Respir. Physiol. Neurobiol. 163 (1–3), 128138.
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.
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), 650664.
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), 2073820747.
Leal, L. G. 1980 Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12 (1), 435476.
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.
Li, Z. & Wang, H. 2003b Drag force, diffusion coefficient, and electric mobility of small particles. Part II. Application. Phys. Rev. E 68 (6), 061207.
Li, Z. & Wang, H. 2004 Thermophoretic force and velocity of nanoparticles in the free molecule regime. Phys. Rev. E 70 (2), 021205.
Li, Z. & Wang, H. 2005 Gas–nanoparticle scattering: a molecular view of momentum accommodation function. Phys. Rev. Lett. 95 (1), 014502.
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.
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), 80658074.
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), 15231530.
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.
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.
Loth, E. 2008 Lift of a spherical particle subject to vorticity and/or spin. AIAA J. 46 (4), 801809.
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, 443454.
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, 345359.
Massoudi, M. 2002 On the importance of material frame-indifference and lift forces in multiphase flows. Chem. Engng Sci. 57 (17), 36873701.
McLaughlin, J. B. 1989 Aerosol particle deposition in numerically simulated channel flow. Phys. Fluids A 1 (7), 12111224.
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), 123.
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), 242246.
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), 883890.
Saffman, P. G. T. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385400.
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, 118.
Wang, J. & Li, Z. 2011 Thermophoretic force on micro-and nanoparticles in dilute binary gas mixtures. Phys. Rev. E 84 (2), 021201.
Wang, J. & Li, Z. 2012 Negative thermophoresis of nanoparticles in the free molecular regime. Phys. Rev. E 86 (1), 011201.
Wang, J., Luo, S. & Xia, G. 2017 Thermophoretic force on nanocylinders in the free molecule regime. Phys. Rev. E 95 (3), 033101.
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).
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), 103109.
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), 23112319.
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.
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.
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), 34893498.
Zhang, Y., Li, S., Yan, W. & Yao, Q. 2012 Nanoparticle transport and deposition in boundary layer of stagnation-point premixed flames. Powder Technol. 227, 2434.
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), 18.
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.
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), 1122.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Shear lift forces on nanocylinders in the free molecule regime

  • Shuang Luo (a1) (a2), Jun Wang (a1), Song Yu (a1), Guodong Xia (a1) and Zhigang Li (a2)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.