Skip to main content
SpringerLink
Log in

Flow regimes of the immiscible liquids within a rectangular microchannel

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Flow regimes of two immiscible liquids at the cross junction within a rectangular microchannel are experimentally investigated. Characteristics of the flow regimes including critical conditions and interfacial deformations are presented. It is found that the occurrence of the tubing regime is favored by increased viscosity of the dispersed phase or reduced cross-sectional aspect ratio, leading to the shrinkage of the flow rate range that could produce droplets. In order to reveal the physical mechanism, the force analysis is carried out based on the tunnel structure formed between the interface and channel side walls within the rectangular cross-section. The reshaping stage and pinch-off stage are mainly driven by the interfacial tension, leading to far larger neck thinning rate compared to the superficial velocity of either phase. The filling stage and squeezing stage are dominated by the pressure drop across the dispersed tip while the role of the shear force becomes more important with increasing tunnel width. The filling period is estimated as t2≈kHwn02/Qd with k = 1.34 and the squeezing period is expressed as t3/Tc = 0.3Cac−1. According to the force analysis, the critical tip velocity under dripping scales with three key parameters, which can be expressed as (utip/U)* ~ QcLtip/wtunnel3.

Graphic abstract

Flow regimes of two immiscible liquids at the cross junction within a rectangular microchannel are experimentally investigated. Distribution maps and critical conditions of four flow regimes are presented. Interfacial deformations during the droplet generation at regimes of squeezing and dripping are compared. Force analysis is carried out based on the different tunnel shape confined by the rectangular cross-section.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

Abbreviations

F P :

Force caused by pressure drop (N)

F τ :

Force caused by shear stress (N)

H :

Height of microchannels (m)

L tip :

Length of dispersed tip (m)

Q d :

Volumetric flow rate of dispersed phase (m3/s)

Q c :

Volumetric flow rate of continuous phase (m3/s)

Q :

Flow rate ratio of two liquid phases (q = Qd/Qc)

q* :

Critical flow rate ratio of tubing

R 1 :

Radii of in-plane curvature (m)

R 2 :

Radii of out-of-plane curvature (m)

T :

Time (s)

t 2 :

Period of stage II (filling stage) (s)

t 3 :

Period of stage III (squeezing stage) (s)

t 4 :

Period of stage IV (pinch-off stage) (s)

T c :

Capillary time (Tc = (ρcW3/σ)1/2) (s)

U :

Superficial velocity of mixed liquids in focusing channel (m/s)

U c :

Superficial velocity of continuous phase (m/s)

U d :

Superficial velocity of dispersed phase (m/s)

u n :

Thinning rate of neck (m/s)

u tip :

Dispersed tip velocity (m/s)

V tip :

Volume of the dispersed tip at the end of filling stage (m3)

W c :

Width of inlet channel of continuous phase (m)

W d :

Width of inlet channel of dispersed phase (m)

W :

Width of focusing channel (m)

w n :

Neck width (m)

w n 0 :

Initial neck width at the beginning of squeezing stage (m)

w tunnel :

Width of tunnel between droplet interface and side walls (m)

x tip :

Dispersed tip position along the x axis (m)

μ :

Viscosity (Pa·s)

ρ :

Density (kg/m3)

σ :

Interfacial tension coefficient (N/m)

δ :

Width ratio of inlet channels (δ = Wd/Wc)

ω :

Aspect ratio of the cross-section of focusing channel (ω = H/W)

λ :

Viscosity ratio of two liquid phases (λ = μd/μc)

ΔP :

Pressure drop across dispersed tip (Pa)

ΔP L :

Laplace pressure jump (Pa)

τ c :

Shear stress exerted by continuous tip (Pa)

τ d :

Viscous stress of dispersed phase (Pa)

Ca :

Capillary number (Ca = μU/σ)

We :

Weber number (We = ρU2W/σ)

d :

Dispersed phase

c :

Continuous phase

n :

Neck

References

  1. Dressler, O.J., Casadevall, I.S.X., deMello, A.J.: Chemical and biological dynamics using droplet-based microfluidics. Annu. Rev. Anal. Chem. 10(1), 1–24 (2017)

    Article  Google Scholar 

  2. Anna, S.L.: Droplets and bubbles in microfluidic devices. Annu. Rev. Fluid Mech. 48(1), 285–309 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Pang, Y., Kim, H., Liu, Z., et al.: A soft microchannel decreases polydispersity of droplet generation. Lab Chip. 14(20), 4029–4034 (2014)

    Article  Google Scholar 

  4. Shang, L., Cheng, Y., Zhao, Y.: Emerging Droplet Microfluidics. Chem Rev. 117(12), 7964–8040 (2017)

    Article  Google Scholar 

  5. Si, T., Li, G., Wu, Q., et al.: Optical droplet vaporization of nanoparticle-loaded stimuli-responsive microbubbles. Appl. Phys. Lett. 108(11), 111109 (2016)

    Article  Google Scholar 

  6. Wang, X., Liu, Z., Pang, Y.: Concentration gradient generation methods based on microfluidic systems. RSC Adv. 7(48), 29966–29984 (2017)

    Article  Google Scholar 

  7. Wang, X., Liu, Z., Pang, Y.: Droplet breakup in an asymmetric bifurcation with two angled branches. Chem. Eng. Sci. 188, 11–17 (2018)

    Article  Google Scholar 

  8. Liu, C., Hu, G., Jiang, X., et al.: Inertial focusing of spherical particles in rectangular microchannels over a wide range of Reynolds numbers. Lab Chip 15(4), 1168–1177 (2015)

    Article  Google Scholar 

  9. Baroud, C.N., Gallaire, F., Dangla, R.: Dynamics of microfluidic droplets. Lab Chip 10(16), 2032–2045 (2010)

    Article  Google Scholar 

  10. Zhu, P., Wang, L.: Passive and active droplet generation with microfluidics: a review. Lab Chip. 17(1), 34–75 (2016)

    Article  Google Scholar 

  11. Um, E., Kim, M., Kim, H., et al.: Phase synchronization of fluid-fluid interfaces as hydrodynamically coupled oscillators. Nat. Commun. 11(1), 5221 (2020)

    Article  Google Scholar 

  12. Wang, N., Semprebon, C., Liu, H., et al.: Modelling double emulsion formation in planar flow-focusing microchannels. J. Fluid Mech. 895, 1 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  13. Salkin, L., Schmit, A., Courbin, L., et al.: Passive breakups of isolated drops and one-dimensional assemblies of drops in microfluidic geometries: experiments and models. Lab Chip. 13(15), 3022–3032 (2013)

    Article  Google Scholar 

  14. Wang, X., Liu, Z., Pang, Y.: Breakup dynamics of droplets in an asymmetric bifurcation by μPIV and theoretical investigations. Chem. Eng. Sci. 197, 258–268 (2019)

    Article  Google Scholar 

  15. Zhang, S., Guivier-Curien, C., Veesler, S., et al.: Prediction of sizes and frequencies of nanoliter-sized droplets in cylindrical T-junction microfluidics. Chem. Eng. Sci. 138, 128–139 (2015)

    Article  Google Scholar 

  16. Pang, Y., Zhou, Q., Wang, X., et al.: Droplets generation under different flow rates in T-junction microchannel with a neck. AIChE J. 66(10), e16290 (2020)

    Article  Google Scholar 

  17. Chen, X., Xue, C., Hu, G.: Confinements regulate capillary instabilities of fluid threads. J. Fluid Mech. 873, 816–834 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yao, C., Liu, Y., Xu, C., et al.: Formation of liquid-liquid slug flow in a microfluidic T-junction: effects of fluid properties and leakage flow. AIChE J. 64(1), 346–357 (2018)

    Article  Google Scholar 

  19. van Steijn, V., Kleijn, C.R., Kreutzer, M.T.: Flows around confined bubbles and their importance in triggering pinch-off. Phys Rev Lett. 103(21), 214501 (2009)

    Article  Google Scholar 

  20. Gupta, A., Sbragaglia, M.: A lattice Boltzmann study of the effects of viscoelasticity on droplet formation in microfluidic cross-junctions. Eur. Phys. J. E 39(1), 1–15 (2016)

    Article  Google Scholar 

  21. Ngo, I.L., Dang, T.D., Byon, C., et al.: A numerical study on the dynamics of droplet formation in a microfluidic double T-junction. Biomicrofluidics 9(2), 024107–024107 (2015)

    Article  Google Scholar 

  22. Che, Z., Nguyen, N.T., Wong, T.N.: Hydrodynamically mediated breakup of droplets in microchannels. Appl. Phys. Lett. 98(5), 54102 (2011)

    Article  Google Scholar 

  23. Rostami, B., Morini, G.L.: Experimental characterization of a micro cross-junction as generator of Newtonian and non-Newtonian droplets in silicone oil flow at low Capillary numbers. Exp. Thermal Fluid Sci. 103, 191–200 (2019)

    Article  Google Scholar 

  24. van Loo, S., Stoukatch, S., Kraft, M., et al.: Droplet formation by squeezing in a microfluidic cross-junction. Microfluid. Nanofluid. 20(10), 146 (2016)

    Article  Google Scholar 

  25. Li, X., He, L., He, Y., et al.: Numerical study of droplet formation in the ordinary and modified T-junctions. Phys. Fluids. 31(8), 82101 (2019)

    Article  Google Scholar 

  26. Liu, H., Zhang, Y.: Droplet formation in a T-shaped microfluidic junction. J. Appl. Phys. 106(3), 34906 (2009)

    Article  MathSciNet  Google Scholar 

  27. Mastiani, M., Seo, S., Jimenez, S.M., et al.: Flow regime mapping of aqueous two-phase system droplets in flow-focusing geometries. Colloids Surf. A 531, 111–120 (2017)

    Article  Google Scholar 

  28. Arias, S., Montlaur, A.: Numerical study and experimental comparison of two-phase flow generation in a T-junction. AIAA J. 55(5), 1565–1574 (2017)

    Article  Google Scholar 

  29. Chen, X., Glawdel, T., Cui, N., et al.: Model of droplet generation in flow focusing generators operating in the squeezing regime. Microfluid. Nanofluid. 18(5–6), 1341–1353 (2014)

    Google Scholar 

  30. Tan, J., Xu, J.H., Li, S.W., et al.: Drop dispenser in a cross-junction microfluidic device: Scaling and mechanism of break-up. Chem. Eng. J. 136(2), 306–311 (2008)

    Article  Google Scholar 

  31. Liu, H., Zhang, Y.: Lattice Boltzmann simulation of droplet generation in a microfluidic cross-junction. Commun. Comput. Phys. 9(5), 1235–1256 (2011)

    Article  MATH  Google Scholar 

  32. Garstecki, P., Fuerstman, M.J., Stone, H.A., et al.: Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of break-up. Lab Chip. 6(3), 437–446 (2006)

    Article  Google Scholar 

  33. Cubaud, T., Mason, T.G.: Capillary threads and viscous droplets in square microchannels. Phys. Fluids 20(5), 53302 (2008)

    Article  MATH  Google Scholar 

  34. Liu, H., Zhang, Y.: Droplet formation in microfluidic cross-junctions. Phys. Fluids. 23(8), 82101 (2011)

    Article  Google Scholar 

  35. Yu, W., Liu, X., Zhao, Y., et al.: Droplet generation hydrodynamics in the microfluidic cross-junction with different junction angles. Chem. Eng. Sci. 203, 259–284 (2019)

    Article  Google Scholar 

  36. Christopher, G.F., Noharuddin, N.N., Taylor, J.A., et al.: Experimental observations of the squeezing-to-dripping transition in T-shaped microfluidic junctions. Phys. Rev. E. 78(3), 36317 (2008)

    Article  Google Scholar 

  37. Du, W., Fu, T., Zhu, C., et al.: Breakup dynamics for high-viscosity droplet formation in a flow-focusing device: Symmetrical and asymmetrical ruptures. AIChE J. 62(1), 325–337 (2016)

    Article  Google Scholar 

  38. Du, W., Fu, T., Duan, Y., et al.: Breakup dynamics for droplet formation in shear-thinning fluids in a flow-focusing device. Chem. Eng. Sci. 176, 66–76 (2018)

    Article  Google Scholar 

  39. Wu, Z., Sundén, B.: Liquid-liquid two-phase flow patterns in ultra-shallow straight and serpentine microchannels. Heat Mass Transf. 55(4), 1095–1108 (2018)

    Article  Google Scholar 

  40. Funfschilling, D., Debas, H., Li, H.Z., et al.: Flow-field dynamics during droplet formation by dripping in hydrodynamic-focusing microfluidics. Phys. Rev. E 80(1 Pt 2), 15301 (2009)

    Article  Google Scholar 

  41. Wu, L., Tsutahara, M., Kim, L.S., et al.: Three-dimensional lattice Boltzmann simulations of droplet formation in a cross-junction microchannel. Int. J. Multiph. Flow 34(9), 852–864 (2008)

    Article  MATH  Google Scholar 

  42. Fu, T., Wu, Y., Ma, Y., et al.: Droplet formation and breakup dynamics in microfluidic flow-focusing devices: from dripping to jetting. Chem. Eng. Sci. 84, 207–217 (2012)

    Article  Google Scholar 

  43. Roumpea, E., Kovalchuk, N., Chinaud, M., et al.: Experimental studies on droplet formation in a flow-focusing microchannel in the presence of surfactants. Chem. Eng. Sci. 195, 507–518 (2019)

    Article  Google Scholar 

  44. Mazutis, L., Griffiths, A.D.: Selective droplet coalescence using microfluidic systems. Lab Chip. 12(10), 1800–1806 (2012)

    Article  Google Scholar 

  45. Peltonen, L., Hirvonen, J., Yliruusi, J.: The behavior of sorbitan surfactants at the water-oil interface: straight-chained hydrocarbons from pentane to dodecane as an oil phase. J Colloid Interface Sci. 240(1), 272–276 (2001)

    Article  Google Scholar 

  46. Wu, Z., Cao, Z., Sunden, B.: Flow patterns and slug scaling of liquid-liquid flow in square microchannels. Int. J. Multiph. Flow 112, 27–39 (2019)

    Article  MathSciNet  Google Scholar 

  47. Chakraborty, I., Ricouvier, J., Yazhgur, P., et al.: Droplet generation at Hele-Shaw microfluidic T-junction. Phys. Fluids. 31(2), 22010 (2019)

    Article  Google Scholar 

  48. Aytouna, M., Paredes, J., Shahidzadeh-Bonn, N., et al.: Drop formation in non-Newtonian fluids. Phys. Rev. Lett. 110(3), 34501 (2013)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  50. Romero, P.A., Abate, A.R.: Flow focusing geometry generates droplets through a plug and squeeze mechanism. Lab Chip 12(24), 5130–5132 (2012)

    Article  Google Scholar 

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

    Article  Google Scholar 

  52. van Steijn, V., Kleijn, C.R., Kreutzer, M.T.: Predictive model for the size of bubbles and droplets created in microfluidic T-junctions. Lab Chip. 10(19), 2513–2518 (2010)

    Article  Google Scholar 

  53. Fuerstman, M.J., Lai, A., Thurlow, M.E., et al.: The pressure drop along rectangular microchannels containing bubbles. Lab Chip. 7(11), 1479–1489 (2007)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 11872083 and 11702007), the China Postdoctoral Science Foundation (Grant 2020M680270), the Beijing Postdoctoral Research Foundation (Grant 2020-ZZ-075), and the Chaoyang District Postdoctoral Research Foundation (Grant 2020ZZ-40).

Author information

Authors and Affiliations

  1. College of Mechanical Engineering and Applied Electronics Technology, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing, 100124, China

    Xiang Wang, Yan Pang, Yilin Ma, Yanlin Ren & Zhaomiao Liu

  2. Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing, 100124, China

    Xiang Wang, Yan Pang & Zhaomiao Liu

Authors
  1. Xiang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yan Pang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yilin Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanlin Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhaomiao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhaomiao Liu.

Additional information

Executive Editor: Mingjiu Ni

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (MP4 10792 KB)

Supplementary file2 (MP4 5175 KB)

Supplementary file3 (MP4 7316 KB)

Supplementary file4 (DOC 552 KB)

Supplementary file5 (MP4 1603 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Pang, Y., Ma, Y. et al. Flow regimes of the immiscible liquids within a rectangular microchannel. Acta Mech. Sin. 37, 1544–1556 (2021). https://doi.org/10.1007/s10409-021-01128-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-021-01128-5

Keywords

Search

Navigation