Microfluidics and Nanofluidics

, Volume 18, Issue 4, pp 695–708 | Cite as

Modeling capillary forces for large displacements

  • Massimo MastrangeliEmail author
  • Gari Arutinov
  • Edsger C. P. Smits
  • Pierre Lambert
Research Paper


Originally applied to the accurate, passive positioning of submillimetric devices, recent works proved capillary self-alignment as effective also for larger components and relatively large initial offsets. In this paper, we describe an analytic quasi-static model of 1D capillary restoring forces that generalizes existing geometrical models and extends the validity to large displacements from equilibrium. The piece-wise nature of the model accounts for contact line unpinning singularities ensuing from large perturbations of the liquid meniscus and dewetting of the bounding surfaces. The superior accuracy of the generalized model across the extended displacement range, and particularly beyond the elastic regime as compared to purely elastic models, is supported by finite element simulations and recent experimental evidence. Limits of the model are discussed in relation to the aspect ratio of the meniscus, contact angle hysteresis, tilting and self-alignment dynamics.


Contact Angle Contact Line Capillary Force Liquid Bridge Contact Angle Hysteresis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research has been funded by the Interuniversity Attraction Poles Program (IAP 7/38 MicroMAST) initiated by the Belgian Science Policy Office.

Supplementary material

Supplementary material 1 (wmv 8379 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Massimo Mastrangeli
    • 1
    Email author
  • Gari Arutinov
    • 2
    • 3
  • Edsger C. P. Smits
    • 2
  • Pierre Lambert
    • 1
  1. 1.Department of Bio, Electro And Mechanical Systems (BEAMS), École Polytechnique de BruxellesUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Holst Center/TNOEindhovenThe Netherlands
  3. 3.Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

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