The vertically upward Taylor flow in a small square channel (side length 2 mm) is one of the guiding measures within the priority program “Transport Processes at Fluidic Interfaces” (SPP 1506) of the German Research Foundation (DFG). This paper presents the results of coordinated experiments and three-dimensional numerical simulations (with three different academic computer codes) for typical local flow parameters (bubble shape, thickness of the liquid film, and velocity profiles) in different cutting planes (lateral and diagonal) for a specific co-current Taylor flow. For most quantities, the differences between the three simulation results and also between the numerical and experimental results are below a few percent. The experimental and computational results consistently show interesting three-dimensional flow effects in the rear part of the liquid film. There, a local back flow of liquid occurs in the fixed frame of reference which leads to a temporary reversal of the direction of the wall shear stress during the passage of a Taylor bubble. Notably, the axial positions of the region with local backflow and those of the minimum vertical velocity differ in the lateral and the diagonal liquid films. By a thorough analysis of the fully resolved simulation results, this previously unknown phenomenon is explained in detail and, moreover, approximate criteria for its occurrence in practical applications are given. It is the different magnitude of the velocity in the lateral film and in the corner region which leads to azimuthal pressure differences in the lateral and diagonal liquid films and causes a slight deviation of the bubble from the rotational symmetry. This deviation is opposite in the front and rear parts of the bubble and has the mentioned significant effects on the local flow field in the rear part of the liquid film.
REFERENCES
1.
S.
Osher
and R. P.
Fedkiw
, Level Set Methods and Dynamic Implicit Surfaces
(Springer
, Berlin, London
, 2003
).2.
G.
Tryggvason
, R.
Scardovelli
, and S.
Zaleski
, Direct Numerical Simulations of Gas-Liquid Multiphase Flows
(Cambridge University Press
, Cambridge
, 2011
).3.
A.
Prosperetti
and G.
Tryggvason
, Computational Methods for Multiphase Flow
(Cambridge University Press
, Cambridge
, 2007
).4.
S.
Groß
and A.
Reusken
, Numerical Methods for Two-Phase Incompressible Flows
(Springer
, Heidelberg
, 2011
).5.
M.
Wörner
, “Numerical modeling of multiphase flows in microfluidics and micro process engineering: A review of methods and applications
,” Microfluid. Nanofluid.
12
, 841
(2012
).6.
M.
Suo
and P.
Griffith
, “Two-phase flow in capillary tubes
,” J. Basic Eng.
86
, 576
(1964
).7.
D. T.
Dumitrescu
, “Strömung an einer luftblase im senkrechten Rohr
,” Z. Angew. Math. Mech.
23
, 139
(1943
).8.
R. M.
Davies
and G.
Taylor
, “The mechanics of large bubbles rising through extended liquids and through liquids in tubes
,” Proc. R. Soc. A
200
, 375
(1950
).9.
K.
Jähnisch
, M.
Baerns
, V.
Hessel
, W.
Ehrfeld
, V.
Haverkamp
, H.
Löwe
, C.
Wille
, and A.
Guber
, “Direct fluorination of toluene using elemental fluorine in gas/liquid microreactors
,” J. Fluorine Chem.
105
, 117
(2000
).10.
M.
Al-Rawashdeh
, J.
Zalucky
, C.
Muller
, T. A.
Nijhuis
, V.
Hessel
, and J. C.
Schouten
, “Phenylacetylene hydrogenation over [Rh(NBD)(PPh3)2]BF4 catalyst in a numbered-up microchannels reactor
,” Ind. Eng. Chem. Res.
52
, 11516
(2013
).11.
M. T.
Kreutzer
, F.
Kapteijn
, J. A.
Moulijn
, and J. J.
Heiszwolf
, “Multiphase monolith reactors: Chemical reaction engineering of segmented flow in microchannels
,” Chem. Eng. Sci.
60
, 5895
(2005
).12.
A.
Günther
and K. F.
Jensen
, “Multiphase microfluidics: From flow characteristics to chemical and materials synthesis
,” Lab Chip
6
, 1487
(2006
).13.
J. I.
Park
, A.
Saffari
, S.
Kumar
, A.
Günther
, and E.
Kumacheva
, “Microfluidic synthesis of polymer and inorganic particulate materials
,” Annu. Rev. Mater. Res.
40
, 415
(2010
).14.
J. M.
Köhler
, S. N.
Li
, and A.
Knauer
, “Why is micro segmented flow particularly promising for the synthesis of nanomaterials?
,” Chem. Eng. Technol.
36
, 887
(2013
).15.
J.
El-Ali
, S.
Gaudet
, A.
Günther
, P. K.
Sorger
, and K. F.
Jensen
, “Cell stimulus and lysis in a microfluidic device with segmented gas-liquid flow
,” Anal. Chem.
77
, 3629
(2005
).16.
T. C.
Thulasidas
, M. A.
Abraham
, and R. L.
Cerro
, “Bubble-train flow in capillaries of circular and square cross-section
,” Chem. Eng. Sci.
50
, 183
(1995
).17.
T. C.
Thulasidas
, M. A.
Abraham
, and R. L.
Cerro
, “Flow patterns in liquid slugs during bubble-train flow inside capillaries
,” Chem. Eng. Sci.
52
, 2947
(1997
).18.
T.
Cubaud
and C. M.
Ho
, “Transport of bubbles in square microchannels
,” Phys. Fluids
16
, 4575
(2004
).19.
H.
Liu
, C. O.
Vandu
, and R.
Krishna
, “Hydrodynamics of Taylor flow in vertical capillaries: Flow regimes, bubble rise velocity, liquid slug length, and pressure drop
,” Ind. Eng. Chem. Res.
44
, 4884
(2005
).20.
D. M.
Fries
, F.
Trachsel
, and P. R.
von Rohr
, “Segmented gas-liquid flow characterization in rectangular microchannels
,” Int. J. Multiphase Flow
34
, 1108
(2008
).21.
M. J. F.
Warnier
, E.
Rebrov
, M. H. J. M.
De Croon
, V.
Hessel
, and J. C.
Schouten
, “Gas hold-up and liquid film thickness in Taylor flow in rectangular microchannels
,” Chem. Eng. J.
135
, S153
(2008
).22.
Y.
Han
and N.
Shikazono
, “Measurement of liquid film thickness in micro square channel
,” Int. J. Multiphase Flow
35
, 896
(2009
).23.
S.
Haase
and T.
Bauer
, “New method for simultaneous measurement of hydrodynamics and reaction rates in a mini-channel with Taylor flow
,” Chem. Eng. J.
65
, 176
–177
(2011
).24.
M.
Roudet
, K.
Loubiere
, C.
Gourdon
, and M.
Cabassud
, “Hydrodynamic and mass transfer in inertial gas-liquid flow regimes through straight and meandering millimetric square channels
,” Chem. Eng. Sci.
66
, 2974
(2011
).25.
P.
Zaloha
, J.
Kristal
, V.
Jiricny
, N.
Volkel
, C.
Xuereb
, and J.
Aubin
, “Characteristics of liquid slugs in gas-liquid Taylor flow in microchannels
,” Chem. Eng. Sci.
68
, 640
(2012
).26.
T.
Abadie
, J.
Aubin
, D.
Legendre
, and C.
Xuereb
, “Hydrodynamics of gas-liquid Taylor flow in rectangular microchannels
,” Microfluid. Nanofluid.
12
, 355
(2012
).27.
S.
Boden
, T.
dos Santos Rolo
, T.
Baumbach
, and U.
Hampel
, “Synchrotron radiation microtomography of Taylor bubbles in capillary two-phase flow
,” Exp. Fluids
55
, 1
(2014
).28.
B. E.
Ghidersa
, M.
Wörner
, and D. G.
Cacuci
, “Exploring the flow of immiscible fluids in a square vertical mini-channel by direct numerical simulation
,” Chem. Eng. J.
101
, 285
(2004
).29.
T.
Taha
and Z. F.
Cui
, “CFD modelling of slug flow inside square capillaries
,” Chem. Eng. Sci.
61
, 665
(2006
).30.
M.
Wörner
, B.
Ghidersa
, and A.
Onea
, “A model for the residence time distribution of bubble-train flow in a square mini-channel based on direct numerical simulation results
,” Int. J. Heat Fluid Flow
28
, 83
(2007
).31.
D. S.
Liu
and S. D.
Wang
, “Hydrodynamics of Taylor flow in noncircular capillaries
,” Chem. Eng. Process.
47
, 2098
(2008
).32.
M. C.
Öztaskin
, M.
Wörner
, and H. S.
Soyhan
, “Numerical investigation of the stability of bubble train flow in a square minichannel
,” Phys. Fluids
21
, 042108
(2009
).33.
A.
Onea
, M.
Wörner
, and D. G.
Cacuci
, “A qualitative computational study of mass transfer in upward bubble train flow through square and rectangular mini-channels
,” Chem. Eng. Sci.
64
, 1416
(2009
).34.
S.
Kececi
, M.
Wörner
, A.
Onea
, and H. S.
Soyhan
, “Recirculation time and liquid slug mass transfer in co-current upward and downward Taylor flow
,” Catal. Today
147
, S125
(2009
).35.
O.
Keskin
, M.
Wörner
, H. S.
Soyhan
, T.
Bauer
, O.
Deutschmann
, and R.
Lange
, “Viscous co-current downward Taylor flow in a square mini-channel
,” AIChE J.
56
, 1693
(2010
).36.
M.
Wörner
, “Computational study on scaling of co-current downward Taylor flow in small square channels of three different sizes
,” J. Chem. Eng. Jpn.
46
, 335
(2013
).37.
H.
Marschall
, S.
Boden
, C.
Lehrenfeld
, C. J. D.
Falconi
, U.
Hampel
, A.
Reusken
, M.
Wörner
, and D.
Bothe
, “Validation of interface capturing and tracking techniques with different surface tension treatments against a Taylor bubble benchmark problem
,” Comput. Fluids
102
, 336
(2014
).38.
P.
Angeli
and A.
Gavriilidis
, “Hydrodynamics of Taylor flow in small channels: A review
,” Proc. Inst. Mech. Eng., Part C
222
, 737
(2008
).39.
R.
Gupta
, D. F.
Fletcher
, and B. S.
Haynes
, “Taylor flow in microchannels: A review of experimental and computational work
,” J. Comput. Multiphase Flows
2
, 1
(2010
).40.
P.
Sobieszuk
, J.
Aubin
, and R.
Pohorecki
, “Hydrodynamics and mass transfer in gas-liquid flows in microreactors
,” Chem. Eng. Technol.
35
, 1346
(2012
).41.
V.
Talimi
, Y. S.
Muzychka
, and S.
Kocabiyik
, “A review on numerical studies of slug flow hydrodynamics and heat transfer in microtubes and microchannels
,” Int. J. Multiphase Flow
39
, 88
(2012
).42.
S.
Aland
, C.
Lehrenfeld
, H.
Marschall
, C.
Meyer
, and S.
Weller
, “Accuracy of two-phase flow simulations: The Taylor flow benchmark
,” PAMM
13
, 595
(2013
).43.
S.
Aland
, S.
Boden
, A.
Hahn
, F.
Klingbeil
, M.
Weismann
, and S.
Weller
, “Quantitative comparison of Taylor flow simulations based on sharp-interface and diffuse-interface models
,” Int. J. Numer. Methods Fluids
73
, 344
(2013
).44.
C.
Meyer
, M.
Hoffmann
, and M.
Schlüter
, “Micro-PIV analysis of gas–liquid Taylor flow in a vertical oriented square shaped fluidic channel
,” Int. J. Multiphase Flow
67
, 140
(2014
).45.
S. P.
Quan
, “Co-current flow effects on a rising Taylor bubble
,” Int. J. Multiphase Flow
37
, 888
(2011
).46.
M.
Rieber
, “Numerische modellierung der dynamik freier grenzflächen in zweiphasenströmungen
,” Fortschrittberichte VDI/7, VDI-Verlag,2003
.47.
R. B.
DeBar
, “Fundamentals of the KRAKEN code. [Eulerian hydrodynamics code for compressible nonviscous flow of several fluids in two-dimensional (axially symmetric) region]
,” Technical Report UCID-17366 Lawrence Livermore Lab. CA
, 1974
.48.
C. W.
Hirt
and B. D.
Nichols
, “Volume of fluid (VOF) method for the dynamics of free boundaries
,” J. Comput. Phys.
39
, 201
(1981
).49.
W. J.
Rider
and D. B.
Kothe
, “Reconstructing volume tracking
,” J. Comput. Phys.
141
, 112
(1998
).50.
D.
Bothe
, M.
Kröger
, and H.-J.
Warnecke
, “A VOF-based conservative method for the simulation of reactive mass transfer from rising bubbles
,” Fluid Dyn. Mater. Process.
7
, 303
(2011
).51.
D.
Bothe
and S.
Fleckenstein
, “A volume-of-fluid-based method for mass transfer processes at fluid particles
,” Chem. Eng. Sci.
101
, 283
(2013
).52.
C.
Gotaas
, P.
Havelka
, H. A.
Jakobsen
, H. F.
Svendsen
, M.
Hase
, N.
Roth
, and B.
Weigand
, “Effect of viscosity on droplet-droplet collision outcome: Experimental study and numerical comparison
,” Phys. Fluids
19
, 102106
(2007
).53.
C.
Focke
and D.
Bothe
, “Direct numerical simulation of binary off-center collisions of shear thinning droplets at high Weber numbers
,” Phys. Fluids
24
, 073105
(2012
).54.
C.
Albert
, H.
Raach
, and D.
Bothe
, “Influence of surface tension models on the hydrodynamics of wavy laminar falling films in volume of fluid-simulations
,” Int. J. Multiphase Flow
43
, 66
(2012
).55.
W.
Sabisch
, “Dreidimensionale numerische simulation der dynamik von aufsteigenden einzelblasen und blasenschwärmen mit einer volume-of-fluid-methode
,” Ph.D. thesis,University Karlsruhe
, 2000
.56.
S.
Groß
and A.
Reusken
, “Finite element discretization error analysis of a surface tension force in two-phase incompressible flows
,” SIAM J. Numer. Anal.
45
, 1679
(2007
).57.
S.
Groß
, J.
Peters
, V.
Reichelt
, and A.
Reusken
, The DROPS package for numerical simulations of incompressible flows using parallel adaptive multigrid techniques,RWTH Aachen University
, 2002
, IGPM Report No. 211.58.
E.
Bertakis
, S.
Gross
, J.
Grande
, O.
Fortmeier
, A.
Reusken
, and A.
Pfennig
, “Validated simulation of droplet sedimentation with finite-element and level-set methods
,” Chem. Eng. Sci.
65
, 2037
(2010
).59.
M.
Wörner
, B.
Ghidersa
, and A.
Shahab
, Numerical Study of Bubble Train Flow in a Square Vertical Mini-Channel: Influence of the Length of the Flow Unit Cell
(Proc. 5th Int. Conf. Multiphase Flow ICMF-2004, Yokohama, Japan
, 2004
).60.
M. R.
Ozgu
, J. C.
Chen
, and A. H.
Stenning
, “Local liquid film thickness around Taylor bubbles
,” J. Heat Transfer
95
, 425
(1973
).61.
L. W.
Schwartz
, H. M.
Princen
, and A. D.
Kiss
, “On the motion of bubbles in capillary tubes
,” J. Fluid Mech.
172
, 259
(1986
).62.
E.
Klaseboer
, R.
Gupta
, and R.
Manica
, “An extended Bretherton model for long Taylor bubbles at moderate capillary numbers
,” Phys. Fluids
26
, 032107
(2014
).63.
W. B.
Kolb
and R. L.
Cerro
, “Coating the inside of a capillary of square cross section
,” Chem. Eng. Sci.
46
, 2181
(1991
).64.
A. L.
Hazel
and M.
Heil
, “The steady propagation of a semi-infinite bubble into a tube of elliptical or rectangular cross-section
,” J. Fluid Mech.
470
, 91
(2002
).65.
G. I.
Taylor
, “Deposition of a viscous fluid on the wall of a tube
,” J. Fluid Mech.
10
, 161
(1961
).66.
B. G.
Cox
, “An experimental investigation of the streamlines in viscous fluid expelled from a tube
,” J. Fluid Mech.
20
, 193
(1964
).67.
R. S.
Abiev
, “Bubbles velocity Taylor circulation rate and mass transfer model for slug flow in milli- and microchannels
,” Chem. Eng. J.
227
, 66
(2013
).68.
B. K. H.
Yen
, A.
Günther
, M. A.
Schmidt
, K. F.
Jensen
, and M. G.
Bawendi
, “A microfabricated gas-liquid segmented flow reactor for high-temperature synthesis: The case of CdSe quantum dots
,” Angew. Chem., Int. Ed.
44
, 5447
(2005
).69.
J.
Hua
, L. E.
Erickson
, T.-Y.
Yiin
, and L. A.
Glasgow
, “A review of the effects of shear and interfacial phenomena on cell viability
,” Crit. Rev. Biotechnol.
13
, 305
(1993
).70.
M.
Mercier
, C.
Fonade
, and C.
Lafforgue-Delorme
, “How slug flow can enhance the ultrafiltration flux in mineral tubular membranes
,” J. Membr. Sci.
128
, 103
(1997
).71.
N.
Ratkovich
, C. C. V.
Chan
, P. R.
Berube
, and I.
Nopens
, “Experimental study and CFD modelling of a two-phase slug flow for an airlift tubular membrane
,” Chem. Eng. Sci.
64
, 3576
(2009
).72.
T.
Taha
and Z. F.
Cui
, “CFD modelling of slug flow in vertical tubes
,” Chem. Eng. Sci.
61
, 676
(2006
).73.
R. A. S.
Brown
and G. W.
Govier
, “Mechanics of large gas bubbles in tubes: II. Prediction of voidage in verticle gas-liquid flow
,” Can. J. Chem. Eng.
43
, 224
(1965
).74.
R. S.
Abiev
, “Simulation of the slug flow of a gas-liquid system in capillaries
,” Theor. Found. Chem. Eng.
42
, 105
(2008
).75.
P.
Aussillous
and D.
Quere
, “Quick deposition of a fluid on the wall of a tube
,” Phys. Fluids
12
, 2367
(2000
).© 2016 AIP Publishing LLC.
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