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Numerical simulation of shear thinning slug flows: the effect of viscosity variation on the shape of Taylor bubbles and wall shear stress

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Abstract

In the present work, the rise of a single Taylor bubble through stagnant shear thinning liquids is numerically investigated. The non-Newtonian liquid rheology is modeled using the well-known Carreau–Yasuda viscosity function and the gas/liquid interface is captured by the volume of fluid method. 2D axisymmetric and 3D numerical results obtained by the finite volume method are strongly validated against available experimental measurements for Newtonian and shear thinning cases. A detailed parametric study is also undertaken in order to delineate and quantify the effect of viscosity variation of the liquid phase on the Taylor bubble rising in vertical tubes. It was shown that the rate of viscosity decline and the overall extent of viscosity variation significantly alter the main features of a slug flow including bubble rise velocity, liquid velocity field, bubble shape, wall shear stress, and the absence/presence of a liquid recirculation zone behind the gas bubble. A detailed account of these effects is provided in the present study.

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References

  1. Dumitrescu DT (1943) Strömung an einer Luftblase im senkrechten Rohr. J Appl Math Mech 23(3):139–149

    MATH  Google Scholar 

  2. Davies R, Taylor G (1950) The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proc R Soc Lond Ser A Math Phys Sci 200:375–390

    Google Scholar 

  3. White E, Beardmore R (1962) The velocity of rise of single cylindrical air bubbles through liquids contained in vertical tubes. Chem Eng Sci 17(5):351–361

    Article  Google Scholar 

  4. Sousa RG, Riethmuller ML, Pinto AMFR, Campos JBLM (2006) Flow around individual Taylor bubbles rising in stagnant polyacrylamide (PAA) solutions. J Nonnewton Fluid Mech 135(1):16–31. https://doi.org/10.1016/j.jnnfm.2005.12.007

    Article  Google Scholar 

  5. Dziubinski M, Fidos H, Sosno M (2004) The flow pattern map of a two-phase non-Newtonian liquid–gas flow in the vertical pipe. Int J Multiph Flow 30(6):551–563. https://doi.org/10.1016/j.ijmultiphaseflow.2004.04.005

    Article  MATH  Google Scholar 

  6. Sousa RG, Riethmuller ML, Pinto AMFR, Campos JBLM (2005) Flow around individual Taylor bubbles rising in stagnant CMC solutions: PIV measurements. Chem Eng Sci 60(7):1859–1873. https://doi.org/10.1016/j.ces.2004.11.035

    Article  Google Scholar 

  7. Sobieszuk P, Cygański P, Pohorecki R (2010) Bubble lengths in the gas–liquid Taylor flow in microchannels. Chem Eng Res Des 88(3):263–269

    Article  Google Scholar 

  8. Luo R, Wang L (2012) Liquid flow pattern around Taylor bubbles in an etched rectangular microchannel. Chem Eng Res Des 90(8):998–1010

    Article  Google Scholar 

  9. Xu B, Cai W, Liu X, Zhang X (2013) Mass transfer behavior of liquid–liquid slug flow in circular cross-section microchannel. Chem Eng Res Des 91(7):1203–1211

    Article  Google Scholar 

  10. Otten L, Fayed AS (1976) Pressure drop and drag reduction in two-phase non-newtonian slug flow. Can J Chem Eng 54(1–2):111–114. https://doi.org/10.1002/cjce.5450540117

    Article  Google Scholar 

  11. Rosehart RG, Rhodes E, Scott DS (1975) Studies of gas → liquid (non-Newtonian) slug flow: void fraction meter, void fraction and slug characteristics. Chem Eng J 10(1):57–64. https://doi.org/10.1016/0300-9467(75)88017-8

    Article  Google Scholar 

  12. Terasaka K, Tsuge H (2003) Gas holdup for slug bubble flow of viscous liquids having a yield stress in bubble columns. Chem Eng Sci 58(2):513–517. https://doi.org/10.1016/S0009-2509(02)00558-4

    Article  Google Scholar 

  13. Niranjan K, Hashim MA, Pandit AB, Davidson JF (1988) Liquid-phase controlled mass transfer from a gas slug. Chem Eng Sci 43(6):1247–1252. https://doi.org/10.1016/0009-2509(88)85096-6

    Article  Google Scholar 

  14. Carew PS, Thomas NH, Johnson AB (1995) A physically based correlation for the effects of power law rheology and inclination on slug bubble rise velocity. Int J Multiph Flow 21(6):1091–1106. https://doi.org/10.1016/0301-9322(95)00047-2

    Article  MATH  Google Scholar 

  15. Sousa RG, Nogueira S, Pinto AMFR, Riethmuller ML, Campos JBLM (2004) Flow in the negative wake of a Taylor bubble rising in viscoelastic carboxymethylcellulose solutions: particle image velocimetry measurements. J Fluid Mech 511:217–236. https://doi.org/10.1017/S0022112004009644

    Article  MATH  Google Scholar 

  16. Kemiha M, Frank X, Poncin S, Li HZ (2006) Origin of the negative wake behind a bubble rising in non-Newtonian fluids. Chem Eng Sci 61(12):4041–4047. https://doi.org/10.1016/j.ces.2006.01.051

    Article  Google Scholar 

  17. Rabenjafimanantsoa AH, Time RW, Paz T (2011) Dynamics of expanding slug flow bubbles in non-Newtonian drilling fluids. Ann Trans Nord Rheol Soc 19:1–8

    Google Scholar 

  18. Sousa RG, Pinto AMFR, Campos JBLM (2007) Interaction between Taylor bubbles rising in stagnant non-Newtonian fluids. Int J Multiph Flow 33(9):970–986. https://doi.org/10.1016/j.ijmultiphaseflow.2007.03.009

    Article  Google Scholar 

  19. Zhao W, Zhang S, Lu M, Shen S, Yun J, Yao K, Xu L, Lin D-Q, Guan Y-X, Yao S-J (2014) Immiscible liquid–liquid slug flow characteristics in the generation of aqueous drops within a rectangular microchannel for preparation of poly (2-hydroxyethylmethacrylate) cryogel beads. Chem Eng Res Des 92(11):2182–2190

    Article  Google Scholar 

  20. Picchi D, Manerba Y, Correra S, Margarone M, Poesio P (2015) Gas/shear-thinning liquid flows through pipes: modeling and experiments. Int J Multiph Flow 73:217–226. https://doi.org/10.1016/j.ijmultiphaseflow.2015.03.005

    Article  Google Scholar 

  21. Taha T, Cui ZF (2006) CFD modelling of slug flow in vertical tubes. Chem Eng Sci 61(2):676–687. https://doi.org/10.1016/j.ces.2005.07.022

    Article  Google Scholar 

  22. Kashid MN, Renken A, Kiwi-Minsker L (2010) CFD modelling of liquid–liquid multiphase microstructured reactor: slug flow generation. Chem Eng Res Des 88(3):362–368

    Article  Google Scholar 

  23. Quan S (2011) Co-current flow effects on a rising Taylor bubble. Int J Multiph Flow 37(8):888–897. https://doi.org/10.1016/j.ijmultiphaseflow.2011.04.004

    Article  Google Scholar 

  24. Araújo JDP, Miranda JM, Pinto AMFR, Campos JBLM (2012) Wide-ranging survey on the laminar flow of individual Taylor bubbles rising through stagnant Newtonian liquids. Int J Multiph Flow 43:131–148. https://doi.org/10.1016/j.ijmultiphaseflow.2012.03.007

    Article  Google Scholar 

  25. Abadie T, Xuereb C, Legendre D, Aubin J (2013) Mixing and recirculation characteristics of gas–liquid Taylor flow in microreactors. Chem Eng Res Des 91(11):2225–2234

    Article  Google Scholar 

  26. Ratkovich N, Majumder S, Bentzen TR (2013) Empirical correlations and CFD simulations of vertical two-phase gas–liquid (Newtonian and non-Newtonian) slug flow compared against experimental data of void fraction. Chem Eng Res Des 91(6):988–998

    Article  Google Scholar 

  27. Araújo JDP, Miranda JM, Campos JBLM (2017) Taylor bubbles rising through flowing non-Newtonian inelastic fluids. J Nonnewton Fluid Mech 245:49–66. https://doi.org/10.1016/j.jnnfm.2017.04.009

    Article  MathSciNet  Google Scholar 

  28. Gopala VR, van Wachem BGM (2008) Volume of fluid methods for immiscible-fluid and free-surface flows. Chem Eng J 141(1–3):204–221. https://doi.org/10.1016/j.cej.2007.12.035

    Article  Google Scholar 

  29. Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225

    Article  Google Scholar 

  30. Tryggvason G, Esmaeeli A, Lu J, Biswas S (2006) Direct numerical simulations of gas/liquid multiphase flows. Fluid Dyn Res 38(9):660–681. https://doi.org/10.1016/j.fluiddyn.2005.08.006

    Article  MathSciNet  MATH  Google Scholar 

  31. Irgens F (2014) Rheology and non-Newtonian fluids. Springer, Berlin

    Book  Google Scholar 

  32. Wallis GB (1969) One-dimensional two-phase flow, 1st edn. McGraw-Hill, New York City, New York, US. ISBN-10: 0070679428

  33. Brown R (1965) The mechanics of large gas bubbles in tubes: I Bubble velocities in stagnant liquids. Can J Chem Eng 43(5):217–223

    Article  Google Scholar 

  34. Youngs DL (1982) Time-dependent multi-material flow with large fluid distortion. In: Morton KW, Baines MJ (eds) Numerical methods for fluid dynamics. Academic Press, New York, NY, USA, pp 273–285

  35. Nogueira S, Riethmuler ML, Campos JBLM, Pinto AMFR (2006) Flow in the nose region and annular film around a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids. Chem Eng Sci 61(2):845–857. https://doi.org/10.1016/j.ces.2005.07.038

    Article  Google Scholar 

  36. Nogueira S, Riethmuller ML, Campos JBLM, Pinto AMFR (2006) Flow patterns in the wake of a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids: an experimental study. Chem Eng Sci 61(22):7199–7212. https://doi.org/10.1016/j.ces.2006.08.002

    Article  Google Scholar 

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Correspondence to A. Ahmadpour.

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Technical Editor: Cezar Negrao, PhD.

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Ahmadpour, A., Amani, E. & Esmaili, M. Numerical simulation of shear thinning slug flows: the effect of viscosity variation on the shape of Taylor bubbles and wall shear stress. J Braz. Soc. Mech. Sci. Eng. 41, 48 (2019). https://doi.org/10.1007/s40430-018-1558-x

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  • DOI: https://doi.org/10.1007/s40430-018-1558-x

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