Skip to main content
SpringerLink
Log in

Hydrodynamics of gas–liquid Taylor flow in rectangular microchannels

  • Research Paper
  • Published:
Microfluidics and Nanofluidics Aims and scope Submit manuscript

Abstract

The effect of fluid properties and operating conditions on the generation of gas–liquid Taylor flow in microchannels has been investigated experimentally and numerically. Visualisation experiments and 2D numerical simulations have been performed to study bubble and slug lengths, liquid film hold-up and bubble velocities. The results show that the bubble and slug lengths increase as a function of the gas and liquid flow rate ratios. The bubble and slug lengths follow the model developed by Garstecki et al. (Lab chip 6:437–446, 2006) and van Steijn et al. (Chem Eng Sci 62:7505–7514, 2007), however, the model coefficients appear to be dependent on the liquid properties and flow conditions in some cases. The ratio of the bubble velocity to superficial two-phase velocity is close to unity, which confirms a thin liquid film under the assumption of a stagnant liquid film. Numerical simulations confirm the hypothesis of a stagnant liquid film and provide information on the thickness of the liquid film.

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
Fig. 11
Fig. 12

Similar content being viewed by others

Abbreviations

A :

Cross-section area (m2)

C :

Color function (VOF) (−)

d :

Diameter (m)

f :

Break-up frequency (s−1)

\(\mathbf{F_\sigma}\) :

Capillary force (Pa/m)

k :

Constant (−)

\(l_{1,\infty}\) :

norms in the spurious currents evaluation (m/s)

L :

Length (m)

m :

Constant (−)

\(\mathbf{n}\) :

Normal to the interface (−)

P :

Pressure (Pa)

Q :

Flow rate (m3/s)

r :

Radius (m)

U :

Velocity (m/s)

W :

Dimensionless velocity (−)

w :

Width (m)

x, y :

Axis in 2D simulations (−)

α:

Volume fraction (−)

β1,2 :

Constant (−)

δ:

Liquid film thickness (m)

δ I :

Dirac distribution (interface) (−)

\(\varepsilon\) :

Fraction of area (−)

λ1,2 :

Constant (−)

μ:

Dynamic viscosity (Pa . s)

ρ:

Density (kg/m3)

σ:

Surface tension (N/m)

\(\varvec{\Upsigma}\) :

Viscous stress tensor (Pa)

B:

Bubble

ch:

Channel

G:

Gas phase (air)

h:

Hydraulic

in:

Gas inlet

L:

Liquid phase

S:

Slug

SC:

Spurious currents

TP:

Two-phase

Bo TP :

Bond number \( Bo \;=\; {\frac{(\rho_{\rm{L}} - \rho_{\rm{G}}) d_{\rm h}^2 g}{\sigma}} \)

Ca TP :

Capillary number \( Ca \;=\; {\frac{\mu_{\rm L} U_{\rm TP}} {\sigma}} \)

Re TP :

Reynolds number \( Re \;=\; {\frac{\rho_{\rm L} U_{\rm TP} d_{\rm h}}{\mu_{\rm L}}} \)

We TP :

Weber number \( We \;=\; {\frac{\rho_{\rm L} U_{\rm TP}^2 d_{\rm h}}{\sigma}} \)

References

  • Akbar MK, Plummer DA, Ghiaasiaan SM (2003) On gas–liquid two-phase flow regimes in microchannels. Int J Multiph Flow 29:855–865

    Article  MATH  Google Scholar 

  • Aussillous P, Quéré D (2000) Quick deposition of a fluid on the wall of a tube. Phys Fluids 12(10):2367

    Article  Google Scholar 

  • Bonometti T, Magnaudet J (2007) An interface-capturing method for incompressible two-phase flows. Validation and application to bubble dynamics. Int J Multiph Flow 33:109–133

    Google Scholar 

  • Brackbill J, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comput Phys 100:335–354

    Article  MATH  MathSciNet  Google Scholar 

  • Bretherton FP (1961) The motion of long bubbles in tubes. J Fluid Mech 10:166

    Article  MATH  MathSciNet  Google Scholar 

  • de Lózar A, Juel A, Hazel AL (2008) The steady propagation of an air finger into a rectangular tube. J Fluid Mech 614:173–195

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Dupont J-B, Legendre D (2010) Numerical simulation of static and sliding drop with contact angle hysteresis. J Comput Phys 229:2453–2478

    Article  MATH  MathSciNet  Google Scholar 

  • Fouilland TS, Fletcher DF, Haynes BS (2010) Film and slug behaviour in intermittent slugannular microchannel flows. Chem Eng Sci 65:5344–5355

    Article  Google Scholar 

  • Francois MM, Cummins SJ, Dendy ED, Kothe DB, Sicilian JM, Williams MW (2006) A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J Comput Phys 213:141–173

    Article  MATH  Google Scholar 

  • 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 

  • Giavedoni MD, Saita FA (1997) The axisymmetric and plane cases of a gas phase steadily displacing a Newtonian liquid—a simultaneous solution of the governing equations. Phys Fluids 9(8):2428

    Article  Google Scholar 

  • Guillot P, Colin A (2005) Stability of parallel flows in a microchannel after a T junction. Phys Rev E 72:066301

    Google Scholar 

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

    Article  Google Scholar 

  • Gupta R, Fletcher DF, Haynes BS (2009) On the CFD modelling of Taylor flow in microchannels. Chem Eng Sci 64:2941–2950

    Article  Google Scholar 

  • Gupta R, Fletcher DF, Haynes BS (2010) CFD modelling of heat and mass transfer in the Taylor flow regime. Chem Eng Sci 65:2094–2107

    Article  Google Scholar 

  • Han Y, Shikazono N (2009a) Measurement of the liquid film thickness in micro tube slug flow. Int J Heat Fluid Fl 35:842–853

    Article  Google Scholar 

  • Han Y, Shikazono N (2009b) Measurement of the liquid film thickness in micro square channel. Int J Multiph Flow 30:896–903

    Article  Google Scholar 

  • Haverkamp V, Ehrfeld W, Gebauer K, Hessel V, Lowe H, Richter T, Wille C (1999) The potential of micromixers for contacting of disperse liquid phases. Fresen J Anal Chem 364:617–624

    Article  Google Scholar 

  • Hazel AL, Heil M (2002) The steady propagation of a semi infinite bubble into a tube of elliptical or rectangular cross-section. J Fluid Mech 470:91–114

    Article  MATH  Google Scholar 

  • Kreutzer MT, Kapteijn F, Moulijn JA, Heiszwolf JJ (2005a) Multiphase monolith reactors: chemical reaction engineering of segmented flow in microchannels. Chem Eng Sci 60:5895–5916

    Article  Google Scholar 

  • Kreutzer MT, Kapteijn F, Moulijn JA, Heiszwolf JJ (2005b) Inertial and interfacial effects on pressure drop of Taylor flow in capillaries. AIChE J 51:2428–2440

    Article  Google Scholar 

  • Lafaurie B, Nardone C, Scardovelli R, Zaleski S, Zanetti G (1994) Modelling merging and fragmentation in multiphase flow with SURFER. J Comput Phys 113:134–147

    Article  MATH  MathSciNet  Google Scholar 

  • Leclerc A, Philippe R, Houzelot V, Schweich D, de Bellefon C (2010) Gas–liquid Taylor flow in square microchannels: New inlet geometries and interfacial area tuning. Chem Eng J 165:290–300

    Article  Google Scholar 

  • Leung SSY, Liu Y, Fletcher DF, Haynes BS (2010) Heat transfer in well-characterised Taylor flow. Chem Eng Sci. doi:10.1016/j.ces.2010.09.014

  • Liu D, Wang S (2008) Hydrodynamics of Taylor flow in noncircular capillaries. Chem Eng Process 47:2098–2106

    Article  Google Scholar 

  • Pohorecki R, Kula K (2008) A simple mechanism of bubble and slug formation in Taylor flow in microchannels. Chem Eng Res Des 86:997–1001

    Article  Google Scholar 

  • Qian D, Lawal A (2006) Numerical study on gas and liquid slugs for Taylor flow in a T-junction microchannel. Chem Eng Sci 61:7609–7625

    Google Scholar 

  • Renardy Y, Renardy M (2002) PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method. J Comput Phys 183:400–421

    Article  MATH  MathSciNet  Google Scholar 

  • Sarrazin F, Bonometti T, Loubière K, Prat L, Gourdon C, Magnaudet J (2006) Experimental and numerical study of droplets hydrodynamics in microchannels. AIChE J 52:4061–4070

    Article  Google Scholar 

  • Scardovelli R, Zaleski S (1999) Direct numerical simulation of free-surface and interfacial flow. Annu Rev Fluid Mech 31:567–303

    Article  MathSciNet  Google Scholar 

  • Sobieszuk P, Cyganski P, Pohorecki R (2008) Volumetric liquid side mass transfer coefficient in a gas–liquid microreactor. Chem Process Eng 29:651–661

    Google Scholar 

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

    Article  Google Scholar 

  • Taha T, Cui ZF (2006) CFD modelling of slug flow inside square capillaries. Chem Eng Sci 61:665–675

    Article  Google Scholar 

  • Taylor GI (1961) Deposition of a viscous fluid on the wall of a tube. J Fluid Mech 10:161–165

    Article  MATH  Google Scholar 

  • Triplett KA, Ghiaasiaan SM, Abdel-Khalik SI, Sadowsli DL (1999) Gas–liquid two-phase flow in microchannels. Part i: two-phase flow patterns. Int J Multiph Flow 25:377–394

    Article  MATH  Google Scholar 

  • Völkel N (2009) Design and characterization of gas–liquid microreactors, PhD Thesis, Institut National Polytechnique de Toulouse, France

  • Waelchli S, von Rohr PR (2006) Two-phase flow characteristics in gas–liquid microreactors. Int J Multiph Flow 32:791–806

    Article  MATH  Google Scholar 

  • Wong H, Radke CJ, Morris S (1995) The motion of long bubbles in polygonal capillaries Part 1:Thin films. J Fluid Mech 292:71–94

    Article  MATH  Google Scholar 

  • Yue J, Chen G, Yuan Q, Luo L, Gonthier Y (2007) Hydrodynamics and mass transfer characteristics in gas–liquid flow through a rectangular microchannel. Chem Eng Sci 62:2096–2108

    Article  Google Scholar 

  • Yue J, Luo L, Gonthier Y, Chen G, Yuan Q (2008) An experimental investigation of gas–liquid two-phase flow in single microchannel contactors. Chem Eng Sci 63:4189–4202

    Article  Google Scholar 

  • Yun J, Lei Q, Zhang S, Shen S, Yao K (2010) Slug flow characteristics of gas-miscible liquids in a rectangular microchannel with cross and T-shaped junctions. Chem Eng Sci 65:5256–5263

    Article  Google Scholar 

Download references

Acknowledgments

This work was financed by the French “Agence Nationale de la Recherche” in the framework of the project MIGALI no. ANR-09-BLAN-0381-01. We also acknowledge the support for this project from the CNRS research federation FERMaT, such as the CALMIP project for providing computational resources.

Author information

Authors and Affiliations

  1. Institut de Mécanique des Fluides CNRS/INPT/UPS, University of Toulouse, Allée du Prof. Camille Soula, 31400, Toulouse, France

    Thomas Abadie & Dominique Legendre

  2. Laboratoire de Génie Chimique CNRS/INPT/UPS, University of Toulouse, 4 Allée Emile Monso, BP 84-234, 31030, Toulouse, France

    Thomas Abadie, Joëlle Aubin & Catherine Xuereb

Authors
  1. Thomas Abadie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joëlle Aubin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dominique Legendre
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Catherine Xuereb
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joëlle Aubin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abadie, T., Aubin, J., Legendre, D. et al. Hydrodynamics of gas–liquid Taylor flow in rectangular microchannels. Microfluid Nanofluid 12, 355–369 (2012). https://doi.org/10.1007/s10404-011-0880-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10404-011-0880-8

Keywords

Search

Navigation