Towards chip prototyping: a model for droplet formation at both T and X-junctions in dripping regime

  • Axel Vansteene
  • Jean-Philippe Jasmin
  • Siméon Cavadias
  • Clarisse MarietEmail author
  • Gérard Cote
Research Paper


Segmented flows in both T and X-junction glass microchannels are investigated. The effective pressure domain of use of the microchips are compared for two chemical systems. After studying the flow patterns and current empirical equations proposed in the literature, a new empirical equation is validated for both T and X-junctions allowing the prediction of not only the domain of use of the microchip in terms of flow rates knowing the viscosities of the two phases but also the droplets diameter, volume, spacing, and specific interfacial area. Specific interfacial area could be optimized using the model within our specific microsystems, and a maximum of 10,000 m−1 is determined. Ensuing the definition of the model, several insights in the way to optimize segmented flows for different purposes are discussed, i.e., for the production of monodisperse populations of droplets and mass transfer optimization.


Solvent extraction Microfluidics Lab-on-chip Hydrodynamics Modelling Uranium Europium 

List of symbols

(αlag, αfill, β)

Parameters defined in Glawdel et al. (Eq. 11) and Chen et al. (Eq. 12) comprehensive models

\(\bar {\beta }\)

Parameter defined in Sessoms et al. (Eq. 14) for the velocity of the unconfined droplets

(χ1, χ2, χ3)

Fitting parameters of our empirical equation


Capillary number


Modified capillary number


N,N′-Dimethyl N,N′-dibutyl tetradecylmalonamide


Droplet generation frequency (Hz)


Focalized flux-junction


Frame per second (s−1)


Channel height (m)


Distance between the inlet of the dispersed phase and the orifice in FF-junctions


Internal diameter (m)


Length of a microchannel (m)


Diameter/Length of the droplet/plug (m)




Pressure (Pa)


Polyether ether ketone


Flow-rate (m3 s−1)


Surface (m2)


Spacing between consecutive droplets (m)


Specific interfacial area (m−1)




Average superficial velocity (m s−1)


Velocity (m s−1)




Channel width (m)


Cross junction


Height-to-width ratio of the junction/aspect ratio h/w


Variation of inlet pressure (Pa)


Relative error (%)


Dynamic viscosity (Pa s)


Viscosity ratio ηdc


Dispersed-to-continuous channel width ratio wd/wc


Interfacial tension (N m−1)


Flow-rate ratio Qd/Qc



Continuous phase


Outlet microchannel


Dispersed phase




Maximum value


Average value


Minimum value


Orifice in FF-junctions


Related to the droplet or plug


Targeted value







This work was supported by the French Alternative Energies and Atomic Energy Commission. We would like to thank Amar Basu (Electrical and Computer Engineering, Wayne State University, Michigan) for providing us the DMV software we used to acquire droplets shapes and velocities.

Supplementary material

10404_2018_2080_MOESM1_ESM.docx (614 kb)
Supplementary material 1 (DOCX 614 KB)


  1. Ahmed B, Barrow D, Wirth T (2006) Enhancement of reaction rates by segmented fluid flow in capillary scale reactors. Adv Synth Catal 348(9):1043–1048CrossRefGoogle Scholar
  2. Anna SL (2016) Droplets and bubbles in microfluidic devices. Annu Rev Fluid Mech 48(1):285–309MathSciNetCrossRefzbMATHGoogle Scholar
  3. Aota A, Nonaka M, Hibara A, Kitamori T (2007) Countercurrent laminar microflow for highly efficient solvent extraction. Angew Chem Int Ed Engl 46(6):878–880CrossRefGoogle Scholar
  4. Assmann N, Ładosz A, Rudolf von Rohr P (2013) Continuous micro liquid–liquid extraction. Chem Eng Technol 36(6):921–936CrossRefGoogle Scholar
  5. Baret JC, Kleinschmidt F, El Harrak A, Griffiths AD (2009) Kinetic aspects of emulsion stabilization by surfactants: a microfluidic analysis. Langmuir 25(11):6088–6093CrossRefGoogle Scholar
  6. Basu AS (2013) Droplet morphometry and velocimetry (DMV): a video processing software for time-resolved, label-free tracking of droplet parameters. Lab Chip 13(10):1892–1901CrossRefGoogle Scholar
  7. Boyd-Moss M, Baratchi S, Di Venere M, Khoshmanesh K (2016) Self-contained microfluidic systems: a review. Lab Chip 16(17):3177–3192CrossRefGoogle Scholar
  8. Burns JR, Ramshaw C (2001) The intensification of rapid reactions in multiphase systems using slug flow in capillaries. Lab Chip 1(1):10–15CrossRefGoogle Scholar
  9. Chen X, Glawdel T, Cui N, Ren CL (2014) Model of droplet generation in flow focusing generators operating in the squeezing regime. Microfluid Nanofluid 18(5–6):1341–1353Google Scholar
  10. Chong ZZ, Tan SH, Ganan-Calvo AM, Tor SB et al (2015) Active droplet generation in microfluidics. Lab Chip 16(1):35–58CrossRefGoogle Scholar
  11. Chong ZZ, Tor SB, Gañán-Calvo AM, Chong ZJ et al. (2016) Automated droplet measurement (ADM): an enhanced video processing software for rapid droplet measurements. Microfluid Nanofluid 20(4):66CrossRefGoogle Scholar
  12. Christopher GF, Anna SL (2007) Microfluidic methods for generating continuous droplet streams. J Phys D Appl Phys 40(19):R319–R336CrossRefGoogle Scholar
  13. Cubaud T, Mason TG (2008) Capillary threads and viscous droplets in square microchannels. Phys Fluids 20(5):053302CrossRefzbMATHGoogle Scholar
  14. Dreyfus R, Tabeling P, Willaime H (2003) Ordered and disordered patterns in two-phase flows in microchannels. Phys Rev Lett 90(14):144505CrossRefGoogle Scholar
  15. Fries DM, Voitl T, von Rohr PR (2008) Liquid extraction of vanillin in rectangular microreactors. Chem Eng Technol 31(8):1182–1187CrossRefGoogle Scholar
  16. Fu T, Wu Y, Ma Y, Li HZ (2012) Droplet formation and breakup dynamics in microfluidic flow-focusing devices: from dripping to jetting. Chem Eng Sci 84:207–217CrossRefGoogle Scholar
  17. Garstecki P, Stone HA, Whitesides GM (2005) Mechanism for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions. Phys Rev Lett 94(16):164501CrossRefGoogle Scholar
  18. Garstecki P, Fuerstman MJ, Stone HA, Whitesides GM (2006) Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of break-up. Lab Chip 6(3):437–446CrossRefGoogle Scholar
  19. Glawdel T, Elbuken C, Ren CL (2012a) Droplet formation in microfluidic T-junction generators operating in the transitional regime. I. Experimental observations. Phys Rev E Stat Nonlinear Soft Matter Phys 85(1 Pt 2):016322CrossRefGoogle Scholar
  20. Glawdel T, Elbuken C, Ren CL (2012b) Droplet formation in microfluidic T-junction generators operating in the transitional regime. II. Modeling. Phys Rev E Stat Nonlinear Soft Matter Phys 85(1 Pt 2):016323CrossRefGoogle Scholar
  21. Gupta A, Kumar R (2009) Effect of geometry on droplet formation in the squeezing regime in a microfluidic T-junction. Microfluid Nanofluid 8(6):799–812CrossRefGoogle Scholar
  22. Gupta A, Kumar R (2010) Flow regime transition at high capillary numbers in a microfluidic T-junction: viscosity contrast and geometry effect. Phys Fluids 22(12):122001CrossRefGoogle Scholar
  23. Gupta A, Murshed SMS, Kumar R (2009) Droplet formation and stability of flows in a microfluidic T-junction. Appl Phys Lett 94(16):164107CrossRefGoogle Scholar
  24. Gupta A, Matharoo HS, Makkar D, Kumar R (2014) Droplet formation via squeezing mechanism in a microfluidic flow-focusing device. Comput Fluids 100:218–226CrossRefGoogle Scholar
  25. Hatakeyama T, Chen DL, Ismagilov RF (2006) Microgram-scale testing of reaction conditions in solution using nanoliter plugs in microfluidics with detection by MALDI-MS. J Am Chem Soc 128(8):2518–2519CrossRefGoogle Scholar
  26. Hellé G, Mariet C, Cote G (2014) Liquid–liquid microflow patterns and mass transfer of radionuclides in the systems Eu(III)/HNO3/DMDBTDMA and U(VI)/HCl/Aliquat® 336. Microfluid Nanofluid 17(6):1113–1128CrossRefGoogle Scholar
  27. Hessel V, Angeli P, Graviilidis A, Löwe H (2005) Gas–liquid and gas–liquid–solid microstructured reactors: contacting principles and applications. Ind Eng Chem Res 44:9750–9769CrossRefGoogle Scholar
  28. Kashid MN, Renken A, Kiwi-Minsker L (2011) Influence of flow regime on mass transfer in different types of microchannels. Ind Eng Chem Res 50(11):6906–6914CrossRefGoogle Scholar
  29. Kole S, Bikkina P (2017) A parametric study on the application of microfluidics for emulsion characterization. J Petrol Sci Eng 158:152–159CrossRefGoogle Scholar
  30. Kralj JG, Sahoo HR, Jensen KF (2007) Integrated continuous microfluidic liquid–liquid extraction. Lab Chip 7(2):256–263CrossRefGoogle Scholar
  31. Liu H, Zhang Y (2009) Droplet formation in a T-shaped microfluidic junction. J Appl Phys 106(3):034906MathSciNetCrossRefGoogle Scholar
  32. Liu H, Zhang Y (2011) Droplet formation in microfluidic cross-junctions. Phys Fluids 23(8):082101CrossRefGoogle Scholar
  33. Nie Z, Seo M, Xu S, Lewis PC et al (2008) Emulsification in a microfluidic flow-focusing device: effect of the viscosities of the liquids. Microfluid Nanofluid 5(5):585–594CrossRefGoogle Scholar
  34. Nunes JK, Tsai SS, Wan J, Stone HA (2013) Dripping and jetting in microfluidic multiphase flows applied to particle and fiber synthesis. J Phys D Appl Phys 46(11):114002CrossRefGoogle Scholar
  35. Romero PA, Abate AR (2012) Flow focusing geometry generates droplets through a plug and squeeze mechanism. Lab Chip 12(24):5130–5132CrossRefGoogle Scholar
  36. Sen N, Darekar M, Singh KK, Mukhopadhyay S et al (2014) Solvent extraction and stripping studies in microchannels with TBP nitric acid system. Solvent Extr Ion Exch 32(3):281–300CrossRefGoogle Scholar
  37. Sessoms DA, Belloul M, Engl W, Roche M et al (2009) Droplet motion in microfluidic networks: Hydrodynamic interactions and pressure-drop measurements. Phys Rev E Stat Nonlinear Soft Matter Phys 80(1 Pt 2):016317CrossRefGoogle Scholar
  38. Shui L, Eijkel JC, van den Berg A (2007) Multiphase flow in microfluidic systems—control and applications of droplets and interfaces. Adv Colloid Interface Sci 133(1):35–49CrossRefGoogle Scholar
  39. Song H, Tice JD, Ismagilov RF (2003) A microfluidic system for controlling reaction networks in time. Angew Chem Int Ed Engl 42(7):767–772CrossRefGoogle Scholar
  40. Song H, Chen DL, Ismagilov RF (2006) Reactions in droplets in microfluidic channels. Angew Chem Int Ed Engl 45(44):7336–7356CrossRefGoogle Scholar
  41. Tice JD, Lyon AD, Ismagilov RF (2004) Effects of viscosity on droplet formation and mixing in microfluidic channels. Anal Chim Acta 507(1):73–77CrossRefGoogle Scholar
  42. Umbanhowar PB, Prasad V, Weitz DA (2000) Monodisperse emulsion generation via drop break off in a coflowing stream. Langmuir 16:347–351CrossRefGoogle Scholar
  43. Utada AS, Fernandez-Nieves A, Stone HA, Weitz DA (2007) Dripping to jetting transitions in coflowing liquid streams. Phys Rev Lett 99(9):094502CrossRefGoogle Scholar
  44. van Steijn V, Kleijn CR, Kreutzer MT (2010) Predictive model for the size of bubbles and droplets created in microfluidic T-junctions. Lab Chip 10(19):2513–2518CrossRefGoogle Scholar
  45. van Loo S, Stoukatch S, Kraft M, Gilet T (2016) Droplet formation by squeezing in a microfluidic cross-junction. Microfluid Nanofluid 20(10):146CrossRefGoogle Scholar
  46. Wegener M, Paul N, Kraume M (2014) Fluid dynamics and mass transfer at single droplets in liquid/liquid systems. Int J Heat Mass Transf 71:475–495CrossRefGoogle Scholar
  47. Xu JH, Li SW, Tan J, Wang YJ et al (2006a) Controllable preparation of monodisperse O/W and W/O emulsions in the same microfluidic device. Am Chem Soc 22:7243–7246Google Scholar
  48. Xu JH, Li SW, Tan J, Wang YJ et al (2006b) Preparation of highly monodisperse droplet in a T-junction microfluidic device. AIChE J 52(9):3005–3010CrossRefGoogle Scholar
  49. Xu JH, Luo GS, Li SW, Chen GG (2006c) Shear force induced monodisperse droplet formation in a microfluidic device by controlling wetting properties. Lab Chip 6(1):131–136CrossRefGoogle Scholar
  50. Xu JH, Li SW, Tan J, Luo GS (2008) Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping. Microfluid Nanofluid 5(6):711–717CrossRefGoogle Scholar
  51. Zheng B, Ismagilov RF (2005) A microfluidic approach for screening submicroliter volumes against multiple reagents by using preformed arrays of nanoliter plugs in a three-phase liquid/liquid/gas flow. Angew Chem Int Ed 44(17):2520–2523CrossRefGoogle Scholar
  52. Zhu P, Wang L (2016) Passive and active droplet generation with microfluidics: a review. Lab Chip 17(1):34–75CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Den-Service d’Etudes Analytiques et de Réactivité des Surfaces (SEARS), CEAUniversité Paris-SaclayGif-sur-YvetteFrance
  2. 2.Institut de Recherche de Chimie Paris, Chimie ParisTech-CNRSPSL Research UniversityParisFrance
  3. 3.UPMC-Univ Paris 06ParisFrance

Personalised recommendations