It is important to understand the operational aspects which affect the continuous fabrication of alginate gel fibers. These can be formed from a cross-linking reaction of an alginate precursor injected into a coaxial annular pipe flow with a calcium chloride solution. This is an example of an emerging solid interface that interacts with the flow in its neighborhood. We advance on earlier works by relaxing assumptions of a fixed spatial domain to explore and observe mechanisms controlling gel radius. We use two different models. The first one represents the gel layer as a capillary interface between two immiscible liquids and captures the effect of surface tension. A second model is introduced to treat the cross-linking chemical reaction and its effect on the viscosity as the alginate gel forms. Through numerical simulations and analytical approximations of the downstream behavior, we determine the shape of the fiber in the pipe flow and its impact on the flow velocity as well as on the total production of gel.

References

References
1.
Park
,
C.-W.
,
1990
, “
Extensional Flow of a Two-Phase Fiber
,”
AIChE J.
,
36
(
2
), pp.
197
206
.
2.
Lipscomb
,
G. G.
,
1994
, “
The Melt Hollow Fiber Spinning Process: Steady-State Behavior, Sensitivity and Stability
,”
Polym. Adv. Technol.
,
5
(
11
), pp.
745
758
.
3.
Barge
,
L. M.
,
Cardoso
,
S. S.
,
Cartwright
,
J. H.
,
Cooper
,
G. J.
,
Cronin
,
L.
,
De Wit
,
A.
,
Doloboff
,
I. J.
,
Escribano
,
B.
,
Goldstein
,
R. E.
,
Haudin
,
F.
,
Jones
,
D. E. H.
,
Mackay
,
A. L.
,
Maselko
,
J.
,
Pagano
,
J. J.
,
Pantaleone
,
J.
,
Russell
,
M. J.
,
Ignacio Sainz-Diaz
,
C.
,
Steinbock
,
O.
,
Stone
,
D. A.
,
Tanimoto
,
Y.
, and
Thomas
,
N. L.
,
2015
, “
From Chemical Gardens to Chemobrionics
,”
Chem. Rev.
,
115
(
16
), pp.
8652
8703
.
4.
Mikkelsen
,
A.
, and
Elgsaeter
,
A.
,
1995
, “
Density Distribution of Calcium-Induced Alginate Gels—A Numerical Study
,”
Biopolymers
,
36
(
1
), pp.
17
41
.
5.
Braschler
,
T.
,
Valero
,
A.
,
Colella
,
L.
,
Pataky
,
K.
,
Brugger
,
J.
, and
Renaud
,
P.
,
2011
, “
Link Between Alginate Reaction Front Propagation and General Reaction Diffusion Theory
,”
Anal. Chem.
,
83
(
6
), pp.
2234
2242
.
6.
Thumbs
,
J.
, and
Kohler
,
H.-H.
,
1996
, “
Capillaries in Alginate Gel as an Example of Dissipative Structure Formation
,”
Chem. Phys.
,
208
(
1
), pp.
9
24
.
7.
Treml
,
H.
, and
Kohler
,
H.-H.
,
2000
, “
Coupling of Diffusion and Reaction in the Process of Capillary Formation in Alginate Gel
,”
Chem. Phys.
,
252
(
1–2
), pp.
199
208
.
8.
Treml
,
H.
,
Woelki
,
S.
, and
Kohler
,
H.-H.
,
2003
, “
Theory of Capillary Formation in Alginate Gels
,”
Chem. Phys.
,
293
(
3
), pp.
341
353
.
9.
Secchi
,
E.
,
Roversi
,
T.
,
Buzzaccaro
,
S.
,
Piazza
,
L.
, and
Piazza
,
R.
,
2013
, “
Biopolymer Gels With “Physical” Cross-Links: Gelation Kinetics, Aging, Heterogeneous Dynamics, and Macroscopic Mechanical Properties
,”
Soft Matter
,
9
(
15
), pp.
3931
3944
.
10.
Wu
,
Z. L.
,
Takahashi
,
R.
,
Sawada
,
D.
,
Arifuzzaman
,
M.
,
Nakajima
,
T.
,
Kurokawa
,
T.
,
Hu
,
J.
, and
Gong
,
J. P.
,
2014
, “
In Situ Observation of Ca2+ Diffusion-Induced Superstructure Formation of a Rigid Polyanion
,”
Macromolecules
,
47
(
20
), pp.
7208
7214
.
11.
Vempati
,
B.
,
Panchagnula
,
M. V.
,
Öztekin
,
A.
, and
Neti
,
S.
,
2007
, “
Numerical Investigation of Liquid-Liquid Coaxial Flows
,”
ASME J. Fluids Eng.
,
129
(
6
), pp.
713
719
.
12.
Govindarajan
,
R.
, and
Sahu
,
K. C.
,
2014
, “
Instabilities in Viscosity-Stratified Flow
,”
Annu. Rev. Fluid Mech.
,
46
(
1
), pp.
331
353
.
13.
Shin
,
S.-J.
,
Park
,
J.-Y.
,
Lee
,
J.-Y.
,
Park
,
H.
,
Park
,
Y.-D.
,
Lee
,
K.-B.
,
Whang
,
C.-M.
, and
Lee
,
S.-H.
,
2007
, “
On the Fly” Continuous Generation of Alginate Fibers Using a Microfluidic Device
,”
Langmuir
,
23
(
17
), pp.
9104
9108
.
14.
Bonhomme
,
O.
,
Leng
,
J.
, and
Colin
,
A.
,
2012
, “
Microfluidic Wet-Spinning of Alginate Microfibers: A Theoretical Analysis of Fiber Formation
,”
Soft Matter
,
8
(
41
), pp.
10641
10649
.
15.
Li
,
S.
,
Liu
,
Y.
,
Li
,
Y.
,
Zhang
,
Y.
, and
Hu
,
Q.
,
2015
, “
Computational and Experimental Investigations of the Mechanisms Used by Coaxial Fluids to Fabricate Hollow Hydrogel Fibers
,”
Chem. Eng. Process.
,
95
, pp.
98
104
.
16.
Li
,
Y.
,
Liu
,
Y.
,
Jiang
,
C.
,
Li
,
S.
,
Liang
,
G.
, and
Hu
,
Q.
,
2016
, “
A Reactor-Like Spinneret Used in 3D Printing Alginate Hollow Fiber: A Numerical Study of Morphological Evolution
,”
Soft Matter
,
12
(
8
), pp.
2392
2399
.
17.
Leal
,
L.
,
2007
, “
Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes
,”
Cambridge Series in Chemical Engineering
,
Cambridge University Press
, Cambridge, UK.
18.
Leonard
,
B. P.
,
1979
, “
A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation
,”
Comput. Methods Appl. Mech. Eng.
,
19
(
1
), pp.
59
98
.
19.
Youngs
,
D. L.
,
1982
, “
Time-Dependent Multi-Material Flow With Large Fluid Distortion
,”
Numer. Methods Fluid Dyn.
,
24
(
2
), pp.
273
285
.
20.
Issa
,
R. I.
,
1986
, “
Solution of the Implicitly Discretised Fluid Flow Equations by Operator-Splitting
,”
J. Comput. Phys.
,
62
(
1
), pp.
40
65
.
21.
Patankar
,
S.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
CRC Press
, Boca Raton, FL.
22.
Bonhomme
,
O.
,
2011
, “
étude de la formation de fibres en microfluidique: Compétition entre mise en forme et gélification de fluides complexes sous écoulement
,” Ph.D. thesis, l'université Bordeaux-I, Bordeaux, France.
23.
Graham
,
M. D.
,
2003
, “
Interfacial Hoop Stress and Instability of Viscoelastic Free Surface Flows
,”
Phys. Fluids
,
15
(
6
), pp.
1702
1710
.
24.
Cohen
,
Y.
, and
Metzner
,
A.
,
1985
, “
Apparent Slip Flow of Polymer Solutions
,”
J. Rheol.
,
29
(
1
), pp.
67
102
.
25.
Denn
,
M. M.
,
2001
, “
Extrusion Instabilities and Wall Slip
,”
Annu. Rev. Fluid Mech.
,
33
(
1
), pp.
265
287
.
26.
Cuadros
,
T.
,
Skurtys
,
O.
, and
Aguilera
,
J.
,
2012
, “
Mechanical Properties of Calcium Alginate Fibers Produced With a Microfluidic Device
,”
Carbohydr. Polym.
,
89
(
4
), pp.
1198
1206
.
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