Tissue regeneration with scaffolds has proven promising for the repair of damaged tissues or organs. Dispensing-based printing techniques for scaffold fabrication have drawn considerable attention due to their ability to create complex structures layer-by-layer. When employing such printing techniques, the flow rate of the biomaterial dispensed from the needle tip is critical for creating the intended scaffold structure. The flow rate can be affected by a number of variables including the material flow behavior, temperature, needle geometry, and dispensing pressure. As such, model equations can play a vital role in the prediction and control of the flow rate of the material dispensed, thus facilitating optimal scaffold fabrication. This paper presents the development of a model to represent the flow rate of medium viscosity alginate dispensed for the purpose of scaffold fabrication, by taking into account the shear and slip flow from a tapered needle. Because the fluid flow behavior affects the flow rate, model equations were also developed from regression of experimental data to represent the flow behavior of alginate. The predictions from both the flow behavior equation and flow rate model show close agreement with experimental results. For varying needle diameters and temperatures, the slip effect occurring at the needle wall has a significant effect on the flow rate of alginate during scaffold fabrication.

References

References
1.
den Braber
,
E. T.
,
de Ruijter
,
J. E.
,
Smits
,
H. T.
,
Ginsel
,
L. A.
,
von Recum
,
A. F.
, and
Jansen
,
J. A.
,
1996
, “
Quantitative Analysis of Cell Proliferation and Orientation on Substrata With Uniform Parallel Surface Micro-Grooves
,”
Biomaterials
,
17
(
11
), pp.
1093
1099
.
2.
Kruyt
,
M. C.
,
de Bruijn
,
J. D.
,
Wilson
,
C. E.
,
Oner
,
F. C.
,
van Blitterswijk
,
C. A.
,
Verbout
,
A. J.
, and
Dhert
,
W. J. A.
,
2003
, “
Viable Osteogenic Cells Are Obligatory for Tissue-Engineered Ectopic Bone Formation in Goats
,”
Tissue Eng.
,
9
(
2
), pp.
327
336
.
3.
Snyder
,
J.
,
Rin Son
,
A.
,
Hamid
,
Q.
, and
Sun
,
W.
,
2015
, “
Fabrication of Microfluidic Manifold by Precision Extrusion Deposition and Replica Molding for Cell-Laden Device
,”
ASME J. Manuf. Sci. Eng.
,
138
(
4
), p.
041007
.
4.
Wüst
,
S.
,
Müller
,
R.
, and
Hofmann
,
S.
,
2011
, “
Controlled Positioning of Cells in Biomaterials—Approaches Towards 3D Tissue Printing
,”
J. Funct. Biomater.
,
2
(
4
), pp.
119
154
.
5.
Sarker
,
M.
,
Chen
,
X. B.
, and
Schreyer
,
D. J.
,
2015
, “
Experimental Approaches to Vascularisation Within Tissue Engineering Constructs
,”
J. Biomater. Sci. Polym. Ed.
,
26
(
12
), pp.
683
734
.
6.
Lanzotti
,
A.
,
Martorelli
,
M.
, and
Staiano
,
G.
,
2015
, “
Understanding Process Parameter Effects of RepRap Open-Source Three-Dimensional Printers Through a Design of Experiments Approach
,”
ASME J. Manuf. Sci. Eng.
,
137
(
1
), p.
011017
.
7.
Nicodemus
,
G. D.
, and
Bryant
,
S. J.
,
2008
, “
Cell Encapsulation in Biodegradable Hydrogels for Tissue Engineering Applications
,”
Tissue Eng., Part B: Rev.
,
14
(
2
), pp.
149
165
.
8.
Selmi
,
M.
,
Khemiri
,
R.
,
Echouchene
,
F.
, and
Belmabrouk
,
H.
,
2016
, “
Enhancement of the Analyte Mass Transport in a Microfluidic Biosensor by Deformation of Fluid Flow and Electrothermal Force
,”
ASME J. Manuf. Sci. Eng.
,
138
(
8
), p.
081011
.
9.
Nakamura
,
M.
,
Iwanaga
,
S.
,
Henmi
,
C.
,
Arai
,
K.
, and
Nishiyama
,
Y.
,
2010
, “
Biomatrices and Biomaterials for Future Developments of Bioprinting and Biofabrication
,”
Biofabrication
,
2
(
1
), p.
014110
.
10.
Malda
,
J.
,
Visser
,
J.
,
Melchels
,
F. P.
,
Jüngst
,
T.
,
Hennink
,
W. E.
,
Dhert
,
W. J. A.
,
Groll
,
J.
, and
Hutmacher
,
D. W.
,
2013
, “
25th Anniversary Article: Engineering Hydrogels for Biofabrication
,”
Adv. Mater.
,
25
(
36
), pp.
5011
5028
.
11.
Schuurman
,
W.
,
Levett
,
P. A.
,
Pot
,
M. W.
,
van Weeren
,
P. R.
,
Dhert
,
W. J. A.
,
Hutmacher
,
D. W.
,
Melchels
,
F. P. W.
,
Klein
,
T. J.
, and
Malda
,
J.
,
2013
, “
Gelatin-Methacrylamide Hydrogels as Potential Biomaterials for Fabrication of Tissue-Engineered Cartilage Constructs
,”
Macromol. Biosci.
,
13
(
5
), pp.
551
561
.
12.
Jia
,
J.
,
Richards
,
D. J.
,
Pollard
,
S.
,
Tan
,
Y.
,
Rodriguez
,
J.
,
Visconti
,
R. P.
,
Trusk
,
T. C.
,
Yost
,
M. J.
,
Yao
,
H.
,
Markwald
,
R. R.
, and
Mei
,
Y.
,
2014
, “
Engineering Alginate as Bioink for Bioprinting
,”
Acta Biomater.
,
10
(
10
), pp.
4323
4331
.
13.
Rouwkema
,
J.
,
Rivron
,
N. C.
, and
van Blitterswijk
,
C. A.
,
2008
, “
Vascularization in Tissue Engineering
,”
Trends Biotechnol.
,
26
(
8
), pp.
434
441
.
14.
Murphy
,
C. M.
,
Haugh
,
M. G.
, and
O'Brien
,
F. J.
,
2010
, “
The Effect of Mean Pore Size on Cell Attachment, Proliferation and Migration in Collagen-Glycosaminoglycan Scaffolds for Bone Tissue Engineering
,”
Biomaterials
,
31
(
3
), pp.
461
466
.
15.
Karageorgiou
,
V.
, and
Kaplan
,
D.
,
2005
, “
Porosity of 3D Biomaterial Scaffolds and Osteogenesis
,”
Biomaterials
,
26
(
27
), pp.
5474
5491
.
16.
Martinez-Padilla
,
L. P.
, and
Hardy
,
J.
,
1989
, “
Quantifying Thixotropy of Béchamel Sauce Under Constant Shear Stress by Phenomenological and Empirical Models
,”
J. Texture Stud.
,
20
(
1
), pp.
71
85
.
17.
Cheng
,
D. C.-H.
, and
Evans
,
F.
,
1965
, “
Phenomenological Characterization of the Rheological Behaviour of Inelastic Reversible Thixotropic and Antithixotropic Fluids
,”
Br. J. Appl. Phys.
,
16
(
11
), pp.
1599
1617
.
18.
De Kee
,
D.
,
1983
, “
Flow Properties of Time-Dependent Foodstuffs
,”
J. Rheol.
,
27
(
6
), pp.
581
604
.
19.
Fong
,
C. F. C. M.
,
Turcotte
,
G.
, and
De Kee
,
D.
,
1996
, “
Modelling Steady and Transient Rheological Properties
,”
J. Food Eng.
,
27
(
1
), pp.
63
70
.
20.
Taghizadeh
,
M.
, and
Razavi
,
S. M. A.
,
2009
, “
Modeling Time-Independent Rheological Behavior of Pistachio Butter
,”
Int. J. Food Prop.
,
12
(
2
), pp.
331
340
.
21.
Chen
,
X. B.
, and
Ke
,
H.
,
2006
, “
Effects of Fluid Properties on Dispensing Processes for Electronics Packaging
,”
IEEE Trans. Electron. Packag. Manuf.
,
29
(
2
), pp.
75
82
.
22.
Tian
,
X. Y.
,
Li
,
M. G.
,
Cao
,
N.
,
Li
,
J. W.
, and
Chen
,
X. B.
,
2009
, “
Characterization of the Flow Behavior of Alginate/Hydroxyapatite Mixtures for Tissue Scaffold Fabrication
,”
Biofabrication
,
1
(
4
), p.
045005
.
23.
Kwong
,
C. K.
, and
Bai
,
H.
,
2005
, “
Fuzzy Regression Approach to Process Modelling and Optimization of Epoxy Dispensing
,”
Int. J. Prod. Res.
,
43
(
12
), pp.
2359
2375
.
24.
Chen
,
X. B.
,
Zhang
,
W. J.
,
Schoenau
,
G.
, and
Surgenor
,
B.
,
2003
, “
Off-Line Control of Time-Pressure Dispensing Processes for Electronics Packaging
,”
IEEE Trans. Electron. Packag. Manuf.
,
26
(
4
), pp.
286
293
.
25.
Chen
,
X. B.
,
Shoenau
,
G.
, and
Zhang
,
W. J.
,
2000
, “
Modeling of Time-Pressure Fluid Dispensing Processes
,”
IEEE Trans. Electron. Packag. Manuf.
,
23
(
4
), pp.
300
305
.
26.
Razban
,
A.
, and
Davies
,
B. L.
,
1995
, “
Analytical Modelling of the Automated Dispensing of Adhesive Materials
,”
J. Adhes. Sci. Technol.
,
9
(
11
), pp.
1435
1450
.
27.
Chen
,
X. B.
,
Schoenau
,
G.
, and
Zhang
,
W. J.
,
2002
, “
On the Flow Rate Dynamics in Time-Pressure Dispensing Processes
,”
ASME J. Dyn. Syst., Meas., Control
,
124
(
4
), pp.
693
698
.
28.
Zhao
,
Y.-X.
,
Li
,
H.-X.
,
Ding
,
H.
, and
Xiong
,
Y.-L.
,
2005
, “
Integrated Modelling of a Time-Pressure Fluid Dispensing System for Electronics Manufacturing
,”
Int. J. Adv. Manuf. Technol.
,
26
(
1–2
), pp.
1
9
.
29.
Zohdi
,
T. I.
,
2015
, “
On Necessary Pumping Pressures for Industrial Process-Driven Particle-Laden Fluid Flows
,”
ASME J. Manuf. Sci. Eng.
,
138
(
3
), p.
031009
.
30.
Cohen
,
Y.
,
1985
, “
Apparent Slip Flow of Polymer Solutions
,”
J. Rheol.
,
29
(
1
), pp.
67
102
.
31.
Yilmazer
,
U.
,
1989
, “
Slip Effects in Capillary and Parallel Disk Torsional Flows of Highly Filled Suspensions
,”
J. Rheol.
,
33
(
8
), pp.
1197
1212
.
32.
Kalyon
,
D. M.
,
1993
, “
Rheological Behavior of a Concentrated Suspension: A Solid Rocket Fuel Simulant
,”
J. Rheol.
,
37
(
1
), pp.
35
53
.
33.
Smay
,
J. E.
,
Cesarano
,
J.
, and
Lewis
,
J. A.
,
2002
, “
Colloidal Inks for Directed Assembly of 3-D Periodic Structures
,”
Langmuir
,
18
(
14
), pp.
5429
5437
.
34.
Li
,
M.
,
Tian
,
X.
,
Schreyer
,
D. J.
, and
Chen
,
X.
,
2009
, “
Effect of Needle Geometry on Flow Rate and Cell Damage in the Dispensing-Based Biofabrication Process
,”
Biotechnol. Prog.
,
27
(
6
), pp.
1777
1784
.
35.
Chen
,
X. B.
,
Li
,
M. G.
, and
Ke
,
H.
,
2008
, “
Modeling of the Flow Rate in the Dispensing-Based Process for Fabricating Tissue Scaffolds
,”
ASME J. Manuf. Sci. Eng.
,
130
(
2
), p.
021003
.
36.
Kozicki
,
W.
,
Chou
,
C. H.
, and
Tiu
,
C.
,
1966
, “
Non-Newtonian Flow in Ducts of Arbitrary Cross-Sectional Shape
,”
Chem. Eng. Sci.
,
21
(
8
), pp.
665
679
.
37.
Chang
,
G. S.
,
Koo
,
J. S.
, and
Song
,
K. W.
,
2003
, “
Wall Slip of Vaseline in Steady Shear Rheometry
,”
Korea Aust. Rheol. J.
,
15
(
2
), pp.
55
61
.
38.
You
,
F.
,
Wu
,
X.
,
Zhu
,
N.
,
Lei
,
M.
,
Eames
,
B. F.
, and
Chen
,
X.
,
2016
, “
3D Printing of Porous Cell-Laden Hydrogel Constructs for Potential Applications in Cartilage Tissue Engineering
,”
ACS Biomater. Sci. Eng.
,
2
(
7
), pp.
1200
1210
.
39.
Devi
,
D. A.
,
Smitha
,
B.
,
Sridhar
,
S.
,
Jawalkar
,
S. S.
, and
Aminabhavi
,
T. M.
,
2007
, “
Novel Sodium Alginate/Polyethyleneimine Polyion Complex Membranes for Pervaporation Dehydration at the Azeotropic Composition of Various Alcohols
,”
J. Chem. Technol. Biotechnol.
,
82
(
11
), pp.
993
1003
.
40.
Johann
,
R. M.
, and
Renaud
,
P.
,
2007
, “
Microfluidic Patterning of Alginate Hydrogels.
,”
Biointerphases
,
2
(
2
), pp.
73
79
.
41.
Izadifar
,
M.
,
Kelly
,
M. E.
,
Haddadi
,
A.
, and
Chen
,
X.
,
2015
, “
Optimization of Nanoparticles for Cardiovascular Tissue Engineering
,”
Nanotechnology
,
26
(
23
), p.
235301
.
42.
Nichetti
,
D.
, and
Manas-Zloczower
,
I.
,
1998
, “
Viscosity Model for Polydisperse Polymer Melts
,”
J. Rheol.
,
42
(
4
), pp.
951
969
.
43.
Gupta
,
R. K.
,
2000
,
Polymer and Composite Rheology
,
2nd ed.
,
Marcel Dekker
,
New York
.
44.
Khan
,
A. U.
,
Briscoe
,
B. J.
, and
Luckham
,
P. F.
,
2001
, “
Evaluation of Slip in Capillary Extrusion of Ceramic Pastes
,”
J. Eur. Ceram. Soc.
,
21
(
4
), pp.
483
491
.
45.
Cogswell
,
F. N.
,
1972
, “
Converging Flow of Polymer Melts in Extrusion Dies
,”
Polym. Eng. Sci.
,
12
(
1
), pp.
64
73
.
46.
Sahai
,
N.
, and
Tewari
,
R. P.
,
2015
, “
Characterization of Effective Mechanical Strength of Chitosan Porous Tissue Scaffolds Using Computer Aided Tissue Engineering
,”
Int. J. Biomed. Eng. Sci.
,
2
(
1
), pp. 21–28.
47.
Du
,
Y.
,
Ghodousi
,
M.
,
Qi
,
H.
,
Haas
,
N.
,
Xiao
,
W.
, and
Khademhosseini
,
A.
,
2011
, “
Sequential Assembly of Cell-Laden Hydrogel Constructs to Engineer Vascular-Like Microchannels
,”
Biotechnol. Bioeng.
,
108
(
7
), pp.
1693
1703
.
48.
Barnes
,
H. A.
,
1995
, “
A Review of the Slip (Wall Depletion) of Polymer Solutions, Emulsions and Particle Suspensions in Viscometers: Its Cause, Character, and Cure
,”
J. Nonnewtonian Fluid Mech.
,
56
(
3
), pp.
221
251
.
49.
Franco
,
J. M.
,
Gallegos
,
C.
, and
Barnes
,
H. A.
,
1998
, “
On Slip Effects in Steady-State Flow Measurements of Oil-in-Water Food Emulsions
,”
J. Food Eng.
,
36
(
1
), pp.
89
102
.
50.
Chen
,
L.
,
Duan
,
Y.
,
Zhao
,
C.
, and
Yang
,
L.
,
2009
, “
Rheological Behavior and Wall Slip of Concentrated Coal Water Slurry in Pipe Flows
,”
Chem. Eng. Process.: Process Intensif.
,
48
(
7
), pp.
1241
1248
.
51.
Granick
,
S.
,
Zhu
,
Y.
, and
Lee
,
H.
,
2003
, “
Slippery Questions About Complex Fluids Flowing Past Solids
,”
Nat. Mater.
,
2
(
4
), pp.
221
227
.
52.
Graham
,
M. D.
,
1995
, “
Wall Slip and the Nonlinear Dynamics of Large Amplitude Oscillatory Shear Flows
,”
J. Rheol.
,
39
(
4
), pp.
697
712
.
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