Microfluidics and Nanofluidics

, Volume 18, Issue 5–6, pp 897–910 | Cite as

Effect of random surface topography on the gaseous flow in microtubes with an extended slip model

  • Han Yan
  • Wen-Ming ZhangEmail author
  • Zhi-Ke Peng
  • Guang Meng
Research Paper


The gas slip flow in microtubes is studied incorporating the effect of three-dimensional (3D) random surface topography as characterized by the fractal geometry. The modified two-variable Weierstrass-Mandelbrot function is utilized to describe the multi-scale self-affine roughness. An extended first-order slip model suitable for random rough surfaces is proposed to characterize the gas–solid interactions at the wall. The flow field in microtubes is numerically analyzed by solving the 3D Navier–Stokes (N–S) equation with the extended slip model. The effect of rarefication, compressibility, roughness height and fractal dimension are investigated and discussed. The results indicate that the effect of surface roughness increases with the increasing rarefication effect. The increase in the fractal dimension makes the Poiseuille number more sensitive to the Mach number. In addition, the 3D surface topography has a significant effect on the tangential momentum accommodation coefficient.


Microtubes An extended slip model 3D fractal surface topography Flow characteristics TMAC 



The authors gratefully acknowledge supports provided by the National Science Foundation of China under Grant No. 11322215, National Program for Support of Top-notch Young Professionals, and the Fok Ying Tung Education Foundation under Grand No. 141050.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Han Yan
    • 1
  • Wen-Ming Zhang
    • 1
    Email author
  • Zhi-Ke Peng
    • 1
  • Guang Meng
    • 1
  1. 1.State Key Laboratory of Mechanical System and Vibration, School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiChina

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