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Quantum effects on thermal vibration of single-walled carbon nanotubes conveying fluid

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Abstract

In this paper, we investigate the microfluid induced vibration of a nanotube in thermal environment. Attention is focused on a special case that the law of energy equipartition is unreliable unless the quantum effect is taken into account. A nonlocal Euler—Bernoulli beam model is used to model the transverse vibration of a single-walled nanotube (SWCNT). Results reveal that the root of mean squared (RMS) amplitude of thermal vibration of the fluid-conveying SWCNT predicted from the quantum theory is lower than that predicted from the law of energy equipartition. The quantum effect on the thermal vibration of the fluid-conveying SWCNT is more significant for the cases of higher-order modes, lower flow velocity, lower temperature, and lower fluid density.

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References

  1. D. Cai, J.M. Mataraza, Z.H. Qin, et al., Highly efficient molecular delivery into mammalian cells using carbon nanotube spearing, Nat. Methods 2 (2005) 449–454.

    Article  Google Scholar 

  2. G. Pastorin, W. Wu, S. Wieckowski, et al., Double functionalisation of carbon nanotubes for multimodal drug delivery, Chem. Commun. 11 (2006) 1182–1184.

    Article  Google Scholar 

  3. J. Yoon, C.Q. Ru, A. Mioduchowski, Vibration and instability of carbon nanotubes conveying fluid, Compos. Sci. Technol. 65 (2005) 1326–1336.

    Article  Google Scholar 

  4. J. Yoon, C.Q. Ru, A. Mioduchowski, Flow-induced flutter instability of cantilever carbon nanotubes, Int. J. Solids Struct. 43 (2006) 3337–3349.

    Article  MATH  Google Scholar 

  5. L. Wang, Q. Ni, On vibration and instability of carbon nanotubes conveying fluid, Comput. Mater. Sci. 43 (2008) 399–402.

    Article  Google Scholar 

  6. C.D. Reddy, C. Lu, S. Rajendran, et al., Free vibration analysis of fluid-conveying single-walled carbon nanotubes, Appl. Phys. Lett. 90 (2007) 133122.

    Article  Google Scholar 

  7. W.J. Chang, H.L. Lee, Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model, Phys. Lett. A 373 (2009) 982–985.

    Article  MATH  Google Scholar 

  8. Y. Yan, X.Q. He, L.X. Zhang, et al., Dynamic behavior of triple-walled carbon nanotubes conveying fluid, J. Sound Vib. 319 (2009) 1003–1018.

    Article  Google Scholar 

  9. T. Natsuki, Q.Q. Ni, M. Endo, Wave propagation in single-and double-walled carbon nanotubes filled with fluids, J. Appl. Phys. 101 (2007) 034319.

    Article  Google Scholar 

  10. Y. Li, B. Fang, J. Zhang, et al., Vibration analysis of fluid-conveying nanotubes embedded in an elastic medium considering surface effects, Theor. Appl. Mech. Lett. 2 (2012) 031011.

    Article  Google Scholar 

  11. S. Govindjee, J.L. Sackman, On the use of continuum mechanics to estimate the properties of nanotubes, Solid State Commun. 110 (1999) 227–230.

    Article  Google Scholar 

  12. A.C. Eringen, Nonlocal polar elastic continua, Int. J. Eng. Sci. 10 (1972) 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  13. H.L. Lee, W.J. Chang, Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory, J. Appl. Phys. 103 (2008) 024302.

    Article  Google Scholar 

  14. L. Wang, Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small length scale, Comput. Mater. Sci. 45 (2009) 584–588.

    Article  Google Scholar 

  15. H.L. Lee, W.J. Chang, Vibration analysis of fluid-conveying double-walled carbon nanotubes based on nonlocal elastic theory, J. Phys.: Condens. Matter 21 (2009) 115302.

    Google Scholar 

  16. L. Wang, W. Guo, H. Hu, Flexural wave dispersion in multi-walled carbon nanotubes conveying fluids, Acta Mech. Solida Sin. 22 (2009) 623–629.

    Article  Google Scholar 

  17. Y.W. Zhang, T.Z. Yang, J. Zang, et al., Terahertz wave propagation in a nanotube conveying fluid taking into account surface effect, Materials 6 (2013) 2393–2399.

    Article  Google Scholar 

  18. J. Zang, B. Fang, Y.W. Zhang, et al., Longitudinal wave propagation in a piezoelectric nanoplate considering surface effects and nonlocal elasticity theory, Phys. E 63 (2014) 147–150.

    Article  Google Scholar 

  19. R. Ansari, R. Gholami, S. Sahmani, et al., Dynamic stability analysis of embedded multi-walled carbon nanotubes in the thermal environment, Acta Mech. Solida Sin. 28 (2015) 659–667.

    Article  Google Scholar 

  20. L. Wang, Vibration analysis of fluid-conveying nanotubes with consideration of surface effects, Phys. E 43 (2010) 437–439.

    Article  Google Scholar 

  21. L. Wang, Surface effect on buckling configuration of nanobeams containing internal flowing fluid: a nonlinear analysis, Phys. E 44 (2012) 808–812.

    Article  Google Scholar 

  22. L. Wang, Y. Hong, H. Dai, et al., Natural frequency and stability tuning of cantilevered CNTs conveying fluid in magnetic field, Acta Mech. Solida Sin. 29 (2016) 567–576.

    Article  Google Scholar 

  23. M.M.J. Treacy, T.W. Ebbesen, J.M. Gibson, Exceptionally high Young’s modulus observed for individual carbon nanotubes, Nature 381 (1996) 678–680.

    Article  Google Scholar 

  24. A. Krishnan, E. Dujardin, T.W. Ebbesen, et al., Young’s modulus of single-walled nanotubes, Phys. Rev. B 58 (1998) 14013.

    Article  Google Scholar 

  25. L. Wang, H. Hu, W. Guo, Thermal vibration of carbon nanotubes predicted by beam models and molecular dynamics, Proc. R. Soc. A 466 (2010) 2325–2340.

    Article  MathSciNet  MATH  Google Scholar 

  26. J. Hone, B. Batligg, Z. Benes, et al., Quantized phonon spectrum of single-walled carbon nanotube, Science 289 (2000) 1730–1733.

    Article  Google Scholar 

  27. J. Zimmermann, P. Pavone, G. Cuniberti, Vibrational modes and low-temperature thermal properties of graphene and carbon nanotubes: minimal force-constant model, Phys. Rev. B 78 (2008) 045410.

    Article  Google Scholar 

  28. C.Y. Li, T.W. Chou, Quantized molecular structural mechanics modeling for studying the specific heat of single-walled carbon nanotubes, Phys. Rev. B 71 (2005) 075409.

    Article  Google Scholar 

  29. J.S. Wang, Quantum thermal transport from classical molecular dynamics, Phys. Rev. Lett. 99 (2007) 160601.

    Article  Google Scholar 

  30. A.V. Savin, Y.A. Kosevich, A. Cantarero, Semiquantum molecular dynamics simulation of thermal properties and heat transport in low-dimensional nanostructures, Phys. Rev. B 86 (2012) 064305.

    Article  Google Scholar 

  31. L. Wang, H. Hu, Thermal vibration of single-walled carbon nanotubes with quantum effects, Proc. R. Soc. A 470 (2014) 20140087.

    Article  Google Scholar 

  32. L. Wang, H. Hu, Thermal vibration of a rectangular single-layered graphene sheet with quantum effects, J. Appl. Phys. 115 (2014) 233515.

    Article  Google Scholar 

  33. R. Liu, L. Wang, Thermal vibration of a single-walled carbon nanotube predicted by semiquantum molecular dynamics, Phys. Chem. Chem. Phys. 17 (2015) 5194–5201.

    Article  Google Scholar 

  34. T. Xiao, J. Liu, H. Xiong, Effects of different functionalization schemes on the interfacial strength of carbon nanotube polyethylene composite, Acta Mech. Solida Sin. 28 (2015) 277–284.

    Article  Google Scholar 

  35. S. Sharma, R. Chandra, P. Kumar, et al., Molecular dynamics simulation of polymer/carbon nanotube composites, Acta Mech. Solida Sin. 28 (2015) 409–419.

    Article  Google Scholar 

  36. Z. Zhang, Y. Liu, H. Zhao, et al., Acoustic nanowave absorption through clustered carbon nanotubes conveying fluid, Acta Mech. Solida Sin. 29 (2016) 257–270.

    Article  Google Scholar 

  37. W.H. Duan, C.M. Wang, Y.Y. Zhang, Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics, J. Appl. Phys. 101 (2007) 24305–24307.

    Article  Google Scholar 

  38. Q. Wang, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, J. Appl. Phys. 98 (2005) 124301.

    Article  Google Scholar 

Download references

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Correspondence to Tian-Zhi Yang.

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Zhang, YW., Zhou, L., Fang, B. et al. Quantum effects on thermal vibration of single-walled carbon nanotubes conveying fluid. Acta Mech. Solida Sin. 30, 550–556 (2017). https://doi.org/10.1016/j.camss.2017.07.007

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  • DOI: https://doi.org/10.1016/j.camss.2017.07.007

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