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
Dumitrescu DT (1943) Strömung an einer Luftblase im senkrechten Rohr. J Appl Math Mech 23(3):139–149
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
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
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
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
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
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
Luo R, Wang L (2012) Liquid flow pattern around Taylor bubbles in an etched rectangular microchannel. Chem Eng Res Des 90(8):998–1010
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225
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
Irgens F (2014) Rheology and non-Newtonian fluids. Springer, Berlin
Wallis GB (1969) One-dimensional two-phase flow, 1st edn. McGraw-Hill, New York City, New York, US. ISBN-10: 0070679428
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
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
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
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
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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