Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

High-viscosity liquid mixing in a slug-flow micromixer: a numerical study


Mixing of high-viscosity liquids (e.g. glycerol–water solutions) is challenging and costly and often requires employing active mixing methods. Two-phase flow micromixers have attracted attention due to their low cost, simple structure, and high performance. In the present work, we investigate the mixing of similar fluids with viscosities equal to or higher than that of water in a two-phase (gas-liquid) slug-flow micromixer, as an economical passive design. Various cases are studied, in which the liquid samples to be mixed are either water or glycerol–water solution. The performance of the proposed slug-flow micromixer is compared with that of a single-phase micromixer with similar geometrical configuration. We demonstrate that mixing efficiencies higher than 90% are attainable for species with viscosities of about 54% higher than that of water (O(10−3) kg m−1 s−1); a result that is not attainable in the corresponding single-phase micromixer. Moreover, a mixing efficiency of more than 80% is achieved at the outlet of the micromixer for solutions with viscosities of 160% higher than that of water.

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

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


C :

local concentration


Capillary number, dimensionless

D :

Molecular diffusion coefficient

n :

Surface normal vector

p :

Pressure, Pa


Reynolds number, dimensionless

t :

Time, s

U :

Velocity vector, m s−1

x, y :

Coordinates, m

κ :

Surface curvature

α :

Volume fraction

δ :

Dirac function

μ :

Dynamic viscosity, N s m−2

ρ :

Density, kg m−3

σ :

Surface tension coefficient, N m−1

η :

Mixing index

ξ :

Vorticity magnitude, s−1












Steady state


  1. 1.

    Whitesides GM (2006) The origins and the future of microfluidics. Nature. 442:368–373.

  2. 2.

    Taassob A, Kamali R, Bordbar A (2018) Investigation of rarefied gas flow through bended microchannels. Vacuum. 151:197–204.

  3. 3.

    Lee CY, Chang CL, Wang YN, Fu LM (2011) Microfluidic mixing: a review. Int J Mol Sci 12:3263–3287.

  4. 4.

    Suh YK, Kang S (2010) A review on mixing in microfluidics. Micromachines 1(3):82–111

  5. 5.

    Nguyen N-T, Wu Z (2004) Micromixers—a review. J. Micromechanics Microengineering. 15:R1

  6. 6.

    Le The H, Le Thanh H, Dong T, Ta BQ, Tran-Minh N, Karlsen F (2015) An effective passive micromixer with shifted trapezoidal blades using wide Reynolds number range. Chem Eng Res Des 93:1–11

  7. 7.

    Stone HA, Stroock AD, Ajdari A (2004) Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu Rev Fluid Mech 36:381–411

  8. 8.

    A.D. Stroock, S.K.W. Dertinger, A. Ajdari, I. Mezić, H.A. Stone, G.M. Whitesides, Chaotic mixer for microchannels, Science (80-. ). 295 (2002) 647–651

  9. 9.

    Borgohain P, Arumughan J, Dalal A, Natarajan G (2018) Design and performance of a three-dimensional micromixer with curved ribs. Chem Eng Res Des 136:761–775.

  10. 10.

    Bordbar A, Taassob A, Zarnaghsh A, Kamali R (2018) Slug flow in microchannels: numerical simulation and applications. J Ind Eng Chem 62:26–39.

  11. 11.

    Le Teh H, Le Thanh H, Dong T, Ta BQ, Nhut T-M, Karlsen F (2015) An effective passive micromixer with shifted trapezoidal blades using wide Reynolds number range. Chem Eng Res Des 93:1–11.

  12. 12.

    Enders A, Siller IG, Urmann K, Hoffmann MR, Bahnemann J (2019) 3D printed microfluidic mixers—a comparative study on mixing unit performances. Small. 15:1804326

  13. 13.

    He X, Xia T, Gao L, Deng Z, Uzoejinwa BB (2019) Simulation and experimental study of asymmetric split and recombine micromixer with D-shaped sub-channels. Micro Nano Lett 14:293–298

  14. 14.

    Rasouli M, Mehrizi AA, Goharimanesh M, Lashkaripour A, Bazaz SR (2018) Multi-criteria optimization of curved and baffle-embedded micromixers for bio-applications. Chem Eng Process Intensif 132:175–186

  15. 15.

    Mehrdel P, Karimi S, Farré-Lladós J, Casals-Terré J (2018) Novel variable radius spiral–shaped micromixer: from numerical analysis to experimental validation. Micromachines. 9:552

  16. 16.

    Bordbar A, Taassob A, Kamali R (2018) Diffusion and convection mixing of non-Newtonian liquids in an optimized micromixer. Can J Chem Eng 96:1829–1836.

  17. 17.

    Mao X, Juluri BK, Lapsley MI, Stratton ZS, Huang TJ (2010) Milliseconds microfluidic chaotic bubble mixer. Microfluid. Nanofluidics. 8:139–144.

  18. 18.

    Bordbar A, Kamali R, Taassob A (2020) Thermal performance analysis of slug flow in square microchannels. Heat Transf Eng 41:84–100.

  19. 19.

    A. Ufer, M. Mendorf, D.W. Agar, Liquid-Liquid Slug Flow Capillary Microreactor, (2011) 353–360. doi:

  20. 20.

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

  21. 21.

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

  22. 22.

    Günther A, Khan SA, Thalmann M, Trachsel F, Jensen KF (2004) Transport and reaction in microscale segmented gas–liquid flow. Lab Chip 4:278–286

  23. 23.

    Svetlov SD, Abiev RS (2018) Formation mechanisms and lengths of the bubbles and liquid slugs in a coaxial-spherical micro mixer in Taylor flow regime. Chem Eng J 354:269–284

  24. 24.

    Qian J, Li X, Wu Z, Jin Z, Sunden B (2019) A comprehensive review on liquid–liquid two-phase flow in microchannel: flow pattern and mass transfer. Microfluid. Nanofluidics. 23:116

  25. 25.

    Günther A, Jhunjhunwala M, Thalmann M, Schmidt MA, Jensen KF (2005) Micromixing of miscible liquids in segmented gas-liquid flow. Langmuir. 21:1547–1555.

  26. 26.

    Garstecki P, Fuerstman MJ, Fischbach MA, Sia SK, Whitesides GM (2006) Mixing with bubbles: a practical technology for use with portable microfluidic devices. Lab Chip 6:207–212

  27. 27.

    Zhao CX, Middelberg APJ (2011) Two-phase microfluidic flows. Chem Eng Sci 66:1394–1411.

  28. 28.

    Taassob A, Manshadi MKD, Bordbar A, Kamali R (2017) Monodisperse non-Newtonian micro-droplet generation in a co-flow device. J. Brazilian Soc. Mech. Sci. Eng. 39.

  29. 29.

    Cao Z, Wu Z, Sundén B (2018) Dimensionless analysis on liquid-liquid flow patterns and scaling law on slug hydrodynamics in cross-junction microchannels. Chem Eng J 344:604–615.

  30. 30.

    Qian J, Li X, Gao Z, Jin Z (2019) Mixing efficiency analysis on droplet formation process in microchannels by numerical methods. Processes. 7:33

  31. 31.

    Qian JY, Li XJ, Gao ZX, Jin ZJ (2019) Mixing efficiency and pressure drop analysis of liquid-liquid two phases flow in serpentine microchannels. J. Flow Chem. 9:187–197.

  32. 32.

    Yang L, Li S, Liu J, Cheng J (2018) Fluid mixing in droplet-based microfluidics with T junction and convergent–divergent sinusoidal microchannels. Electrophoresis. 39:512–520.

  33. 33.

    Orbay S, Ozcelik A, Lata J, Kaynak M, Wu M, Huang TJ (2017) Mixing high-viscosity fluids via acoustically driven bubbles. J Micromechanics Microengineering 27:0–10.

  34. 34.

    Warnier MJF, De Croon M, Rebrov EV, Schouten JC (2010) Pressure drop of gas–liquid Taylor flow in round micro-capillaries for low to intermediate Reynolds numbers. Microfluid. Nanofluidics 8:33

  35. 35.

    Sontti SG, Atta A (2017) CFD analysis of microfluidic droplet formation in non–Newtonian liquid. Chem Eng J 330:245–261.

  36. 36.

    Cerimovic S, Beigelbeck R, Antlinger H, Schalko J, Jakoby B, Keplinger F (2012) Sensing viscosity and density of glycerol-water mixtures utilizing a suspended plate MEMS resonator. Microsyst Technol 18:1045–1056.

  37. 37.

    Takamura K, Fischer H, Morrow NR (2012) Physical properties of aqueous glycerol solutions. J Pet Sci Eng 98–99:50–60.

  38. 38.

    D’Errico G, Ortona O, Capuano F, Vitagliano V (2004) Diffusion coefficients for the binary system glycerol + water at 25. J Chem Eng Data 49:1665

  39. 39.

    Ait Mouheb N, Malsch D, Montillet A, Solliec C, Henkel T (2012) Numerical and experimental investigations of mixing in T-shaped and cross-shaped micromixers. Chem Eng Sci 68:278–289.

  40. 40.

    A. Afzal, K.Y. Kim (2015) Optimization of pulsatile flow and geometry of a convergent-divergent micromixer, Elsevier B.V. doi:

  41. 41.

    Chen X, Li T, Zeng H, Hu Z, Fu B (2016) Numerical and experimental investigation on micromixers with serpentine microchannels. Int J Heat Mass Transf 98:131–140.

  42. 42.

    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.

  43. 43.

    Salman W, Gavriilidis A, Angeli P (2004) A model for predicting axial mixing during gas-liquid Taylor flow in microchannels at low Bodenstein numbers. Chem Eng J 101:391–396.

  44. 44.

    B.P. Leonard, S. Mokhtari, ULTRA-SHARP nonoscillatory convection schemes for high-speed steady multidimensional flow, (1990)

  45. 45.

    Magnini M, Pulvirenti B, Thome JR (2013) Numerical investigation of the influence of leading and sequential bubbles on slug flow boiling within a microchannel. Int J Therm Sci 71:36–52.

  46. 46.

    Sang L, Hong Y, Wang F (2009) Investigation of viscosity effect on droplet formation in T-shaped microchannels by numerical and analytical methods. Microfluid Nanofluidics 6:621–635.

  47. 47.

    R. Gupta, S.S.Y. Leung, R. Manica, D.F. Fletcher, B.S. Haynes, Three Dimensional Effects in Taylor Flow in Circular Microchannels, La Houille Blanche. (2013) 60–67. doi:

  48. 48.

    Mehdizadeh A, Sherif SA, Lear WE (2011) Numerical simulation of thermofluid characteristics of two-phase slug flow in microchannels. Int J Heat Mass Transf 54:3457–3465

  49. 49.

    Rasouli M, Mehrizi AA, Lashkaripour A (2015) Numerical study on low Reynolds mixing ofT-shaped micro-mixers with obstacles. Transp Phenom Nano Micro Scales 3:68–76.

  50. 50.

    Guo F, Chen B (2009) Numerical study on Taylor bubble formation in a micro-channel T-junction using VOF method. Microgravity Sci Technol 21:51–58.

  51. 51.

    R.W. Fox, A.T. McDonald, Introduction to fluid mechanics, John Wiley&Sons, Inc., New York. (1994)

  52. 52.

    Thulasidas TC, Abraham MA, Cerro RL (1995) Bubble-train flow in capillaries of circular and square cross section. Chem Eng Sci 50:183–199

  53. 53.

    Thulasidas TC, Abraham MA, Cerro RL (1997) Flow patterns in liquid slugs during bubble-train flow inside capillaries. Chem Eng Sci 52:2947–2962.

  54. 54.

    M.T. Kreutzer, W. Wei, F. Kapteijn, J.A. Moulijn, J.J. Heiszwolf, Pressure drop of Taylor flow in capillaries: impact of slug length, in: ASME 2003 1st Int. Conf. Microchannels Minichannels, American Society of Mechanical Engineers Digital Collection, 2003: pp. 519–526

Download references

Author information

Correspondence to Reza Kamali.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bordbar, A., Kheirandish, S., Taassob, A. et al. High-viscosity liquid mixing in a slug-flow micromixer: a numerical study. J Flow Chem (2020).

Download citation


  • Micromixer
  • Two-phase liquid mixer
  • Slug flow
  • Taylor flow
  • Mixing efficiency