Microfluidics and Nanofluidics

, Volume 18, Issue 5–6, pp 911–917 | Cite as

Capillary focusing close to a topographic step: shape and instability of confined liquid filaments

  • Michael Hein
  • Shahriar AfkhamiEmail author
  • Ralf Seemann
  • Lou Kondic
Research Paper


Step-emulsification is a microfluidic technique for droplet generation which relies on the abrupt decrease of confinement of a liquid filament surrounded by a continuous phase. A striking feature of this geometry is the transition between two distinct droplet breakup regimes, the “step-regime” and “jet-regime,” at a critical capillary number. In the step-regime, small and monodisperse droplets break off from the filament directly at a topographic step, while in the jet-regime a jet protrudes into the larger channel region and large plug-like droplets are produced. We characterize the breakup behavior as a function of the filament geometry and the capillary number and present experimental results on the shape and evolution of the filament for a wide range of capillary numbers in the jet-regime. We compare the experimental results with numerical simulations. Assumptions based on the smallness of the depth of the microfluidic channel allow us to reduce the governing equations to the Hele-Shaw problem with surface tension. The full nonlinear equations are then solved numerically using a volume-of-fluid-based algorithm. The computational framework also captures the transition between both regimes, offering a deeper understanding of the underlying breakup mechanism .


Drops and bubbles Step-emulsification Capillary focusing Hele-Shaw flow Volume-of-fluid 



Authors gratefully acknowledge Dr. Jean-Baptiste Fleury (Saarland University) for helpful discussions and the DFG-GRK1276 for financial support. This work was partially supported by the NSF Grant Nos. DMS-1320037 (S.A.) and CBET-1235710 (L.K.).

Supplementary material

Supplementary material 1 (avi 1124 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Michael Hein
    • 1
  • Shahriar Afkhami
    • 2
    Email author
  • Ralf Seemann
    • 1
    • 3
  • Lou Kondic
    • 2
  1. 1.Experimental PhysicsSaarland UniversitySaarbrückenGermany
  2. 2.Department of Mathematical SciencesNew Jersey Institute of TechnologyNewarkUSA
  3. 3.Max Planck Institute for Dynamics and Self-OrganizationGöttingenGermany

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