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

Abstract

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 .

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Acknowledgments

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.).

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Correspondence to Shahriar Afkhami.

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Hein, M., Afkhami, S., Seemann, R. et al. Capillary focusing close to a topographic step: shape and instability of confined liquid filaments. Microfluid Nanofluid 18, 911–917 (2015). https://doi.org/10.1007/s10404-014-1481-0

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Keywords

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