Polymeric droplets are widely employed in fields such as chemical, biomedical, and materials engineering. However, the study of polymeric droplet formation is still insufficient due to the complex elasticity. In this work, the effect of fluid elasticity on the flow patterns for polymeric droplet formation in cross-junction microchannels is investigated by means of finite-volume direct numerical simulations. The volume of fluid method with cell-based adaptive mesh refinement technique is used to capture the interface. Additionally, the rheological behavior of polymeric fluids is described using the exponential Phan-Thien–Tanner constitutive model. The simulated flow behaviors are highly consistent with the experimental observations. The results indicate that three typical flow patterns of dripping, jetting, and threading flows are obtained at different fluid elasticities (denoted by the Weissenberg number Wi) and viscosities (denoted by the Capillary number Ca). Meanwhile, the elastic effect is found to be greater in the dripping flow, significantly reducing the axial tensile stress. It is demonstrated that changes in the stretched state of polymer macromolecules with the same Wi at different Ca lead to variations in the strength of elastic action, which, in turn, affects the extension length and the pinch-off time of droplets. Finally, a relationship equation between the extension length and time of the polymer fluid is established. This present study aims to provide important insight into the preparation of polymeric droplets in microchannels.
REFERENCES
1.
K. F.
Jensen
, “
Flow chemistry—Microreaction technology comes of age
,” AIChE J.
63
, 858
–869
(2017
).2.
Z.
Liu
,
M.
Yang
,
Z.
Dong
,
C.
Yao
, and
G.
Chen
, “
Cavitation behavior and mixing performance of antisolvent precipitation process in an ultrasonic micromixer
,” AIChE J.
69
(7
), e18080
(2023
).3.
L.
Sang
,
J.
Tu
,
H.
Cheng
,
G.
Luo
, and
J.
Zhang
, “
Hydrodynamics and mass transfer of gas–liquid flow in micropacked bed reactors with metal foam packing
,” AIChE J.
66
, e16803
(2019
).4.
J.
Zhang
,
A. R.
Teixeira
,
L. T.
Kögl
,
L.
Yang
, and
K. F.
Jensen
, “
Hydrodynamics of gas-liquid flow in micropacked beds: Pressure drop, liquid holdup, and two-phase model
,” AIChE J.
63
, 4694
–4704
(2017
).5.
A.-E.
Nieuwelink
,
J. C.
Vollenbroek
,
R. M.
Tiggelaar
,
J. G.
Bomer
,
A.
van den Berg
,
M.
Odijk
, and
B. M.
Weckhuysen
, “
High-throughput activity screening and sorting of single catalyst particles with a droplet microreactor using dielectrophoresis
,” Nat. Catal.
4
, 1070
–1079
(2021
).6.
Y.
Zhang
,
H.
Chen
,
X.
Zhao
,
X.
Ma
,
L.
Huang
,
Y.
Qiu
,
J.
Wei
, and
N.
Hao
, “
Acoustofluidic bubble-driven micromixers for the rational engineering of multifunctional ZnO nanoarray
,” Chem. Eng. J.
450
, 138273
(2022
).7.
S.
Sart
,
G.
Ronteix
,
S.
Jain
,
G.
Amselem
, and
C. N.
Baroud
, “
Cell culture in microfluidic droplets
,” Chem. Rev.
122
, 7061
–7096
(2022
).8.
M.
Li
,
T.
Boulafentis
,
A.
Stathoulopoulos
,
Z.
Liu
, and
S.
Balabani
, “
Flows inside polymer microfluidic droplets: Role of elasticity
,” Chem. Eng. Sci.
278
, 118887
(2023
).9.
M.
Sattari-Najafabadi
,
M. N.
Esfahany
,
Z.
Wu
, and
B.
Sundén
, “
The effect of the size of square microchannels on hydrodynamics and mass transfer during liquid-liquid slug flow
,” AIChE J.
63
, 5019
–5028
(2017
).10.
W.
Liu
,
B.
Xie
,
C.
Zhang
,
X.
Duan
, and
J.
Zhang
, “
Nature and characteristics of gas–liquid flow regimes in a micro‐packed bed reactor
,” AIChE J.
69
, e18004
(2023
).11.
Z.
Nisar
,
T.
Hayat
,
K.
Muhammad
,
B.
Ahmed
, and
A.
Aziz
, “
Significance of Joule heating for radiative peristaltic flow of couple stress magnetic nanofluid
,” J. Magn. Magn. Mater.
581
, 170951
(2023
).12.
Z.
Nisar
,
T.
Hayat
,
B.
Ahmed
, and
A.
Alsaedi
, “
Analysis of nonlinear radiative peristaltic transport of hyperbolic tangent nanomaterial with chemical reaction
,” Int. J. Mod. Phys. B
2023
, 2450215
.13.
X.
Pu
,
G.
Li
,
Y.
Song
,
M.
Shang
, and
Y.
Su
, “
Droplet coalescence phenomena during liquid–liquid heterogeneous reactions in microreactors
,” Ind. Eng. Chem. Res.
56
, 12316
–12325
(2017
).14.
G. F.
Christopher
,
N. N.
Noharuddin
,
J. A.
Taylor
, and
S. L.
Anna
, “
Experimental observations of the squeezing-to-dripping transition in T-shaped microfluidic junctions
,” Phys. Rev. E
78
, 036317
(2008
).15.
T.
Fu
,
Y.
Wu
,
Y.
Ma
, and
H. Z.
Li
, “
Droplet formation and breakup dynamics in microfluidic flow-focusing devices: From dripping to jetting
,” Chem. Eng. Sci.
84
, 207
–217
(2012
).16.
T.
Cubaud
and
T. G.
Mason
, “
Capillary threads and viscous droplets in square microchannels
,” Phys. Fluids
20
, 053302
(2008
).17.
Z.
Cao
,
Z.
Wu
, and
B.
Sundén
, “
Dimensionless analysis on liquid-liquid flow patterns and scaling law on slug hydrodynamics in cross-junction microchannels
,” Chem. Eng. J.
344
, 604
–615
(2018
).18.
Y.
Dong
,
C.
Zhu
,
Y.
Ma
, and
T.
Fu
, “
Distribution of liquid-liquid two-phase flow and droplet dynamics in asymmetric parallel microchannels
,” Chem. Eng. J.
441
, 136027
(2022
).19.
T.
Kurniawan
,
M.
Sahebdivani
,
D.
Zaremba
,
S.
Blonski
,
P.
Garstecki
,
V.
van Steijn
, and
P. M.
Korczyk
, “
Formation of droplets in microfluidic cross-junctions at small capillary numbers: Breakdown of the classical squeezing regime
,” Chem. Eng. J.
474
, 145601
(2023
).20.
M. P.
Boruah
,
A.
Sarker
,
P. R.
Randive
,
S.
Pati
, and
K. C.
Sahu
, “
Tuning of regimes during two-phase flow through a cross-junction
,” Phys. Fluids
33
, 122101
(2021
).21.
R. X.
Lu
,
Z. Y.
Guo
,
P.
Yu
, and
Y.
Sui
, “
Transient deformation of a viscoelastic capsule in a cross-slot microchannel: Effects of inertia and membrane viscosity
,” J. Fluid Mech.
962
, A26
(2023
).22.
J.
Mandal
and
S.
Sarkar
, “
Morphology and kinematics of a train of power-law droplets in a corrugated microchannel
,” Chem. Eng. Sci.
274
, 118691
(2023
).23.
Z.
Nisar
,
B.
Ahmed
,
H. A.
Ghazwani
,
K.
Muhammad
,
M.
Hussien
, and
A.
Aziz
, “
Numerical study for bioconvection peristaltic flow of Sisko nanofluid with Joule heating and thermal radiation
,” Heliyon
9
, e22505
(2023
).24.
S.
Van der Graaf
,
T.
Nisisako
,
C. G.
Schroen
,
R. G.
van der Sman
, and
R. M.
Boom
, “
Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel
,” Langmuir
22
, 4144
–4152
(2006
).25.
H.
Liu
and
Y.
Zhang
, “
Droplet formation in microfluidic cross-junctions
,” Phys. Fluids
23
, 082101
(2011
).26.
M.
Nekouei
and
S. A.
Vanapalli
, “
Volume-of-fluid simulations in microfluidic T-junction devices: Influence of viscosity ratio on droplet size
,” Phys. Fluids
29
, 032007
(2017
).27.
J.
Yin
and
S.
Kuhn
, “
Numerical simulation of droplet formation in a microfluidic T-junction using a dynamic contact angle model
,” Chem. Eng. Sci.
261
, 117874
(2022
).28.
Z.
Nisar
,
T.
Hayat
,
A.
Alsaedi
, and
B.
Ahmad
, “
Mathematical modeling for peristalsis of couple stress nanofluid
,” Math. Methods Appl. Sci.
46
, 11683
–11701
(2022
).29.
Z.
Nisar
,
T.
Hayat
,
A.
Alsaedi
, and
S.
Momani
, “
Mathematical modelling for peristaltic flow of fourth‐grade nanoliquid with entropy generation
,” Z. Angew. Math. Mech.
104
, e202300034
(2023
).30.
H.
Yasmin
and
Z.
Nisar
, “
Mathematical analysis of mixed convective peristaltic flow for chemically reactive Casson nanofluid
,” Mathematics
11
, 2673
(2023
).31.
M.
Qiu
,
Y.
Wang
,
M.
Shang
, and
Y.
Su
, “
Understanding differential microemulsion polymerization in continuous slug flow through kinetic Monte Carlo simulation
,” Chem. Eng. J.
475
, 146363
(2023
).32.
Y.
Wu
,
S.
Wang
,
Z.
Liu
, and
Y.
Cheng
, “
Developing thermodynamically stable core–shell and Janus droplets to co-encapsulate hydrophilic and hydrophobic actives
,” Chem. Eng. Sci.
284
, 119469
(2024
).33.
A. P.
Udepurkar
,
W.
Dermaut
,
C.
Clasen
, and
S.
Kuhn
, “
Continuous generation of cross-linked polymer nanoparticles employing an ultrasonic microreactor
,” Ultrason. Sonochem.
101
, 106666
(2023
).34.
T.
Fu
,
L.
Wei
,
C.
Zhu
, and
Y.
Ma
, “
Flow patterns of liquid–liquid two-phase flow in non-Newtonian fluids in rectangular microchannels
,” Chem. Eng. Process.
91
, 114
–120
(2015
).35.
W.
Du
,
T.
Fu
,
Q.
Zhang
,
C.
Zhu
,
Y.
Ma
, and
H. Z.
Li
, “
Self-similar breakup of viscoelastic thread for droplet formation in flow-focusing devices
,” AIChE J.
63
, 5196
–5206
(2017
).36.
X.
Liu
,
S.
Jiang
,
C.
Zhu
,
Y.
Ma
, and
T.
Fu
, “
Formation of viscoelastic droplets in a step‐emulsification microdevice
,” AIChE J.
68
, e17780
(2022
).37.
L.
Sheng
,
L.
Ma
,
Y.
Chen
,
J.
Deng
, and
G.
Luo
, “
A comprehensive study of droplet formation in a capillary embedded step T-junction: From squeezing to jetting
,” Chem. Eng. J.
427
, 132067
(2022
).38.
Q.
Ba
,
W.
Yuan
, and
M.
Mei
, “
On the effects of fluid elasticity and gas holdup on Taylor bubble rising dynamics in viscoelastic media
,” Phys. Fluids
35
, 023106
(2023
).39.
W.
Yuan
,
M.
Zhang
,
B. C.
Khoo
, and
N.
Phan-Thien
, “
Dynamics and deformation of a three-dimensional bubble rising in viscoelastic fluids
,” J. Non-Newtonian Fluid Mech.
285
, 104408
(2020
).40.
W.
Yuan
,
M.
Zhang
,
B. C.
Khoo
, and
N.
Phan-Thien
, “
On peculiar behaviours at critical volumes of a three-dimensional bubble rising in viscoelastic fluids
,” J. Non-Newtonian Fluid Mech.
293
, 104568
(2021
).41.
C. L.
Ong
and
J. R.
Thome
, “
Macro-to-microchannel transition in two-phase flow: Part 1 – Two-phase flow patterns and film thickness measurements
,” Exp. Therm. Fluid Sci.
35
, 37
–47
(2011
).42.
F.
Xu
,
L.
Yang
,
Z.
Liu
, and
G.
Chen
, “
Numerical investigation on the hydrodynamics of Taylor flow in ultrasonically oscillating microreactors
,” Chem. Eng. Sci.
235
, 116477
(2021
).43.
N.
Phan-Thien
and
R. I.
Tanner
, “
A new constitutive equation derived from network theory
,” J. Non-Newtonian Fluid Mech.
2
, 353
–365
(1977
).44.
R. J.
Gordon
and
W. R.
Schowalter
, “
Anisotropic fluid theory: A different approach to the dumbbell theory of dilute polymer solutions
,” Trans. Soc. Rheol.
16
, 79
–97
(1972
).45.
N.
Phan-Thien
, “
A nonlinear network viscoelastic model
,” J. Rheol.
22
, 259
–283
(1978
).46.
R.
Michael
, “
Mathematical analysis of viscoelastic flows
,” Annu. Rev. Fluid Mech.
21
, 21
–36
(1989
).47.
M. A.
Alves
,
P. J.
Oliveira
, and
F. T.
Pinho
, “
Numerical methods for viscoelastic fluid flows
,” Annu. Rev. Fluid Mech.
53
, 509
–541
(2021
).48.
F.
Habla
,
H.
Marschall
,
O.
Hinrichsen
,
L.
Dietsche
,
H.
Jasak
, and
J. L.
Favero
, “
Numerical simulation of viscoelastic two-phase flows using openFOAM®
,” Chem. Eng. Sci.
66
, 5487
–5496
(2011
).49.
M.
Zhang
,
E.
Yang
,
J.
Zeng
,
J.
Ji
,
F.
Tian
, and
L.
Li
, “
Numerical study on oblique stretching of viscoelastic polymer film
,” J. Non-Newtonian Fluid Mech.
295
, 104597
(2021
).50.
51.
J. M.
López-Herrera
,
S.
Popinet
, and
A. A.
Castrejón-Pita
, “
An adaptive solver for viscoelastic incompressible two-phase problems applied to the study of the splashing of weakly viscoelastic droplets
,” J. Non-Newtonian Fluid Mech.
264
, 144
–158
(2019
).52.
S. C.
Xue
,
N.
Phan-Thien
, and
R. I.
Tanner
, “
Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method
,” J. Non-Newtonian Fluid Mech.
59
, 191
–213
(1998
).53.
R.
Comminal
,
F.
Pimenta
,
J. H.
Hattel
,
M. A.
Alves
, and
J.
Spangenberg
, “
Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods
,” J. Non-Newtonian Fluid Mech.
252
, 1
–18
(2018
).54.
R.
Fattal
and
R.
Kupferman
, “
Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation
,” J. Non-Newtonian Fluid Mech.
126
, 23
–37
(2005
).55.
Y.
Li
,
W.
Yuan
,
Q.
Ba
,
M.
Mei
, and
W.
Wu
, “
Numerical investigation on the bubble rising dynamics in ratchet channels filled with viscoelastic liquids
,” Phys. Fluids
35
, 083116
(2023
).56.
M.
Nooranidoost
,
D.
Izbassarov
, and
M.
Muradoglu
, “
Droplet formation in a flow focusing configuration: Effects of viscoelasticity
,” Phys. Fluids
28
, 123102
(2016
).57.
P.
Garstecki
,
H. A.
Stone
, and
G. M.
Whitesides
, “
Mechanism for flow-rate controlled breakup in confined geometries: A route to monodisperse emulsions
,” Phys. Rev. Lett.
94
, 164501
(2005
).58.
V.
van Steijn
,
M. T.
Kreutzer
, and
C. R.
Kleijn
, “
μ-PIV study of the formation of segmented flow in microfluidic T-junctions
,” Chem. Eng. Sci.
62
, 7505
–7514
(2007
).59.
D.
Funfschilling
,
H.
Debas
,
H. Z.
Li
, and
T. G.
Mason
, “
Flow-field dynamics during droplet formation by dripping in hydrodynamic-focusing microfluidics
,” Phys. Rev. E
80
, 015301
(2009
).60.
T.
Fu
,
Y.
Ma
, and
H. Z.
Li
, “
Breakup dynamics of slender droplet formation in shear-thinning fluids in flow-focusing devices
,” Chem. Eng. Sci.
144
, 75
–86
(2016
).61.
C.
Zhou
,
P.
Yue
, and
J. J.
Feng
, “
Formation of simple and compound drops in microfluidic devices
,” Phys. Fluids
18
, 092105
(2006
).62.
B.
Rostami
and
G. L.
Morini
, “
Generation of Newtonian and non-Newtonian droplets in silicone oil flow by means of a micro cross-junction
,” Int. J. Multiphase Flow
105
, 202
–216
(2018
).63.
W.
Yuan
,
M.
Zhang
,
B. C.
Khoo
, and
N.
Phan-Thien
, “
Hydrodynamic interaction and coalescence of two inline bubbles rising in a viscoelastic liquid
,” Phys. Fluids
33
, 083102
(2021
).64.
B.
Steinhaus
,
A. Q.
Shen
, and
R.
Sureshkumar
, “
Dynamics of viscoelastic fluid filaments in microfluidic devices
,” Phys. Fluids
19
, 073103
(2007
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
