Microfluidics and Nanofluidics

, Volume 18, Issue 5–6, pp 807–818 | Cite as

Dynamics of fluid bridges between a rising capillary tube and a substrate

  • Yechun WangEmail author
  • Artur Lutfurakhmanov
  • Iskander S. Akhatov
Research Paper


Micro/nanolithography is an emerging technique to create micro-/nano-features on substrate. New capillary-based lithography method has been developed to overcome the limitations (e.g., the direct contact with the substrate) of existing lithography techniques including dip-pen nanolithography, nano-imprint lithography, and electron-beam lithography. The understanding of the behavior of the liquid bridge formed between a capillary tube and a substrate is essential for the recently developed capillary-based lithography method that is non-invasive to the substrate. A three-dimensional spectral boundary element method has been employed and modified to describe the dynamics of the liquid bridge. Starting with a steady-state liquid bridge shape, the transient bridge deformation is computed as the capillary tube is being lifted away from the substrate. The motion of the three-phase contact line on the substrate is taken into consideration. The computational results are validated with the experimental findings. The influences of the lifting speed of the capillary, liquid properties, and contact line slip conditions on the bridge dynamics are investigated. We conclude by computations that with a higher lifting speed of the capillary tube, the contact line radius on the substrate and the bridge neck radius reduce in a faster manner; a smaller residual droplet tends to form on the substrate if the viscosity ratio (the bridge liquid versus the surrounding medium) is larger or the substrate is more slippery to the fluids.


Liquid bridge Capillary-based deposition Spectral boundary element method 



This work is supported in part by the Department of Energy under award #DE-FG52-08NA28921 and NDSU Advance FORWARD program sponsored by National Science Foundation HRD-0811239. I.S.A. was also supported by the Grants of the Ministry of Education and Science of the Russian Federation (11.G34.31.0040).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Yechun Wang
    • 1
    Email author
  • Artur Lutfurakhmanov
    • 1
  • Iskander S. Akhatov
    • 1
    • 2
  1. 1.Department of Mechanical EngineeringNorth Dakota State UniversityFargoUSA
  2. 2.Center for Micro and Nanoscale Dynamics of Dispersed SystemsBashkir State UniversityUfaRussia

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