Skip to main content

The effect of weak-inertia on droplet formation phenomena in T-junction microchannel


We present droplet formation in a T-junction microfluidic device in five different regimes of squeezing, dripping, transition, jetting and parallel. Droplet is created as a result of interaction of two immiscible liquids. Effects of Capillary number (Ca) and Reynolds number (Re) are investigated which changes the regime of droplet formation and creates rotational flow inside droplet, respectively. Simulations were done with the open source code Gerris using volume of fluid method and adaptive mesh refinement techniques in order to track interface properly. Two kinds of jetting regimes, i.e., stable and unstable, were simulated in this work. For higher Re number the parallel regime is observed so Re number is limited to 25. This study shows that the results of Re > 1 have some differences compared with those of Re < 1. Using the effect of inertial forces, transition regime is limited to a range of Ca number. Simulations indicate that new vortices are created due to effect of inertial forces at a moment after droplet detachment, while it is fully creeping flow for Re < 1. The vortices which have appeared at the tail of droplet will become weaker with time. Also, at the downstream, two rotational flows were observed in droplet for both Re > 1 and Re < 1 which are due to wall shear stresses. Droplets with rotational flow can increase diffusivity, which is motivation of this work.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13


C :

Tracer for multi-fluid interface

\( \tilde{c} \) :

Spatial filter

D :

Deformation tensor

L :

Droplet length

m :

Local normal to the interface

n :

Normal vector at the interface

p :


Q :

Flow rate ratio = \( {\raise0.7ex\hbox{${Q_{c} }$} \!\mathord{\left/ {\vphantom {{Q_{c} } {Q_{d} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${Q_{d} }$}} \)

R :

Radius of curvature of interface

u :

Velocity vector


Channel width

x :

Position vector

κ :

Radius of curvature of the interface

μ :

Dynamic viscosity

λ :

Viscosity ratio = \( {\raise0.7ex\hbox{${\mu_{d} }$} \!\mathord{\left/ {\vphantom {{\mu_{d} } {\mu_{c} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\mu_{c} }$}} \)

θ :


ρ :



Gradient of parameters


Difference operator


Bond number = gravitational/interfacial forces


Capillary number = \( {\raise0.7ex\hbox{${u_{c} \mu_{c} }$} \!\mathord{\left/ {\vphantom {{u_{c} \mu_{c} } \gamma }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\gamma $}} \)


Reynolds number of the continuous phase = \( {\raise0.7ex\hbox{${u_{\text{c}} \rho_{\text{c}} {\text{w}}}$} \!\mathord{\left/ {\vphantom {{u_{\text{c}} \rho_{\text{c}} {\text{w}}} {\mu_{\text{c}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\mu_{\text{c}} }$}} \)

Red :

Reynolds number of the dispersed phase = \( {\raise0.7ex\hbox{${u_{\text{d}} \rho_{\text{d}} {\text{w}}}$} \!\mathord{\left/ {\vphantom {{u_{\text{d}} \rho_{\text{d}} {\text{w}}} {\mu_{\text{d}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\mu_{\text{d}} }$}} \)

α :

Determine volume fraction

δ :

Dirac delta function

σ :

Surface tension

γ :

Interfacial tension = |σ c  − σ d |


Continuous phase


Dispersed phase




  1. Tabeling P (2010) Introduction to microfluidics. Oxford University Press, Oxford

    Google Scholar 

  2. Thorsen T, Roberts RW, Arnold FH, Quake SR (2001) Dynamic pattern formation in a vesicle-generating microfluidic device. Phys Rev Lett 86:4163

    ADS  Article  Google Scholar 

  3. 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 6:437–446

    Article  Google Scholar 

  4. van Steijn V, Kreutzer MT, Kleijn CR (2007) μ-PIV study of the formation of segmented flow in microfluidic T-junctions. Chem Eng Sci 62:7505–7514

    Article  Google Scholar 

  5. Li X-B, Li F-C, Yang J-C, Kinoshita H, Oishi M, Oshima M (2012) Study on the mechanism of droplet formation in T-junction microchannel. Chem Eng Sci 69:340–351

    Article  Google Scholar 

  6. Oishi M, Kinoshita H, Fujii T, Oshima M (2009) Confocal micro-PIV measurement of droplet formation in a T-shaped micro-junction. J Phys Conf Ser 147:012061

  7. Xu J, Li S, Tan J, Luo G (2008) Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping. Microfluid Nanofluid 5:711–717

    Article  Google Scholar 

  8. Yeom S, Lee SY (2011) Size prediction of drops formed by dripping at a micro T-junction in liquid–liquid mixing. Exp Therm Fluid Sci 35:387–394

    Article  Google Scholar 

  9. van Steijn V, Kleijn CR, Kreutzer MT (2010) Predictive model for the size of bubbles and droplets created in microfluidic T-junctions. Lab Chip 10:2513–2518

    Article  Google Scholar 

  10. De Menech M, Garstecki P, Jousse F, Stone H (2008) Transition from squeezing to dripping in a microfluidic T-shaped junction. J Fluid Mech 595:141–161

    ADS  MATH  Google Scholar 

  11. Gupta A, Kumar R (2010) Effect of geometry on droplet formation in the squeezing regime in a microfluidic T-junction. Microfluid Nanofluid 8:799–812

    Article  Google Scholar 

  12. Wang W, Liu Z, Jin Y, Cheng Y (2011) LBM simulation of droplet formation in micro-channels. Chem Eng J 173:828–836

    Article  Google Scholar 

  13. Yang H, Zhou Q, Fan L-S (2013) Three-dimensional numerical study on droplet formation and cell encapsulation process in a micro T-junction. Chem Eng Sci 87:100–110

    Article  Google Scholar 

  14. Sivasamy J, Wong T-N, Nguyen N-T, Kao LT-H (2011) An investigation on the mechanism of droplet formation in a microfluidic T-junction. Microfluid Nanofluid 11:1–10

    Article  Google Scholar 

  15. Yan Y, Guo D, Wen S (2012) Numerical simulation of junction point pressure during droplet formation in a microfluidic T-junction. Chem Eng Sci 84:591–601

    Article  Google Scholar 

  16. Bashir S, Rees JM, Zimmerman WB (2014) Investigation of pressure profile evolution during confined microdroplet formation using a two-phase level set method. Int J Multiph Flow 60:40–49

    Article  Google Scholar 

  17. Popinet S (2009) An accurate adaptive solver for surface-tension-driven interfacial flows. J Comput Phys 228:5838–5866

    ADS  MathSciNet  Article  MATH  Google Scholar 

  18. Popinet S (2003) Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J Comput Phys 190:572–600

    ADS  MathSciNet  Article  MATH  Google Scholar 

  19. Chen X, Yang V (2014) Thickness-based adaptive mesh refinement methods for multi-phase flow simulations with thin regions. J Comput Phys 269:22–39

    ADS  MathSciNet  Article  Google Scholar 

  20. Chen X, Ma D, Yang V, Popinet S (2013) High-fidelity simulations of impinging jet atomization. At Sprays 23:1079–1101

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Milad Azarmanesh.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Azarmanesh, M., Farhadi, M. The effect of weak-inertia on droplet formation phenomena in T-junction microchannel. Meccanica 51, 819–834 (2016).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Droplet formation
  • T-junction
  • Reynolds number
  • Microchannel
  • VOF