The additive manufacturing technology of extrusion of concrete mixtures through a nozzle and deposition layer-by-layer is commonly called three-dimensional concrete printing (3DCP). Such materials are rheologically characterized by yield stress and viscosity. The Bingham model is a good approximation of their rheological behavior. We have developed approximate expressions for determination of pressure for flow through slightly tapered tubes and wedge-shaped extrusion dies, starting from the Buckingham–Reiner equation for flow of a Bingham fluid in a straight tube. The predictions are compared to numerical simulations for convergence half-angles (taper) from 0° to 30° and to analytical solutions available in the literature. Good comparison has been obtained for taper angles up to 15° but the agreement deteriorates as the angle increases. Some experimental data available in the literature have been analyzed, and the challenges for prediction of pressure drop in flow of concrete mixtures through tubes and dies, including entry flow losses, are discussed.
REFERENCES
1.
R.
Lapasin
,
A.
Papo
, and
S.
Rajgelj
, “
Flow behavior of fresh cement pastes. A comparison of different rheological instruments and techniques
,” Cem. Concr. Res
13
(3
), 349
–356
(1983
).2.
A.
Papo
and
L.
Piani
, “
Effect of various superplasticizers on the rheological properties of Portland cement pastes
,” Cem. Concr. Res
34
(11
), 2097
–2101
(2004
).3.
R. J.
Flatt
,
N.
Martys
, and
L.
Bergström
, “
The rheology of cementitious materials
,” MRS Bull.
29
(5
), 314
–318
(2004
).4.
M.
Haist
,
J.
Link
,
D.
Nicia
,
S.
Leinitz
,
C.
Baumert
,
T.
von Bronk
,
D.
Cotardo
,
M.
Eslami Pirharati
,
S.
Fataei
,
H.
Garrecht
,
C.
Gehlen
,
I.
Hauschildt
,
I.
Ivanova
,
S.
Jesinghausen
,
C.
Klein
,
H.-W.
Krauss
,
L.
Lohaus
,
D.
Lowke
,
O.
Mazanec
,
S.
Pawelczyk
,
U.
Pott
,
N. W.
Radebe
,
J. J.
Riedmiller
,
H.-J.
Schmid
,
W.
Schmidt
,
E.
Secrieru
,
D.
Stephan
,
M.
Thiedeitz
,
M.
Wilhelm
, and
V.
Mechtcherine
, “
Interlaboratory study on rheological properties of cement pastes and reference substances: Comparability of measurements performed with different rheometers and measurements geometries
,” Mater. Struct.
53
, 92
(2020
).5.
Understanding the Rheology of Concrete
, edited by
N.
Roussel
(
Woodhead Publishing
,
Philadelphia
, 2012
).6.
G.
De Schutter
,
K.
Lesage
,
V.
Mechtcherine
,
V. N.
Nerella
,
G.
Habert
, and
I.
Agusti-Juan
, “
Vision of 3D printing with concrete–Technical, economic and environmental potentials
,” Cem. Concr. Res.
112
, 25
–36
(2018
).7.
N.
Roussel
, “
Rheological requirements for printable concretes
,” Cem. Concr. Res.
112
, 76
–85
(2018
).8.
A.
Perrot
,
D.
Rangeard
,
V. N.
Nerella
, and
V.
Mechtcherine
, “
Extrusion of cement-based materials - an overview
,” RILEM Tech. Lett.
3
, 91
–97
(2019
).9.
H.
Alghamdi
,
S. A. O.
Nair
, and
N.
Neithalath
, “
Insights into material design, extrusion, rheology, and properties of 3D-printable alkali-activated fly ash-based binders
,” Mater. Des.
167
, 107634
(2019
).10.
J.
Benbow
and
J.
Bridgwater
, Paste Flow and Extrusion
(
Clarendon Press
,
Oxford, UK
, 1993
).11.
R. A.
Basterfield
,
C. J.
Lawrence
, and
M. J.
Adams
, “
On the interpretation of orifice extrusion data for viscoplastic materials
,” Chem. Eng. Sci.
60
(10
), 2599
–2607
(2005
).12.
P.
Shakor
,
S.
Nejadi
, and
G.
Paul
, “
A study into the effect of different nozzle shapes and fibre-reinforcement in 3D printed mortar
,” Materials
12
(10
), 1708
(2019
).13.
M.
Kalthoff
,
M.
Raupach
, and
T.
Matschei
, “
Investigation of rheological test methods for the suitability of mortars for manufacturing of textile-reinforced concrete using a laboratory mortar extruder (LabMorTex)
,” Constr. Mater.
2
, 217
–233
(2022
).14.
J.
Reinold
,
V. N.
Nerella
,
V.
Mechtcherine
, and
G.
Meschke
, “
Extrusion process simulation and layer shape prediction during 3D-concrete-printing using the particle finite element method
,” Autom. Constr.
136
, 104173
(2022
).15.
L.
Yang
,
S. M. E.
Sepasgozar
,
S.
Shirowzhan
,
A.
Kashani
, and
D.
Edwards
, “
Nozzle criteria for enhancing extrudability, buildability and interlayer bonding in 3D printing concrete
,” Autom. Constr.
146
, 104671
(2023
).16.
S. C.
Paul
,
Y. W. D.
Tay
,
B.
Panda
, and
M. J.
Tan
, “
Fresh and hardened properties of 3D printable cementitious materials for building and construction
,” Arch. Civil Mech. Eng.
18
, 311
–319
(2018
).17.
Y.
Weng
,
M.
Li
,
M. J.
Tan
, and
S.
Qian
, “
Design 3D printing cementitious materials via Fuller Thompson theory and Marson-Percy model
,” Constr. Build. Mater.
163
, 600
–610
(2018
).18.
Y.
Zhang
,
Y.
Zhang
,
G.
Liu
,
Y.
Yang
,
M.
Wu
, and
B.
Pang
, “
Fresh properties of a novel 3D printing concrete ink
,” Constr. Build. Mater.
174
, 263
–271
(2018
).19.
H.
Alghamdi
and
N.
Neithalath
, “
Synthesis and characterization of 3D-printable geopolymeric foams for thermally efficient building envelope materials
,” Cem. Concr. Compos.
104
, 103377
(2019
).20.
V. N.
Nerella
,
M.
Näther
,
A.
Iqbal
,
M.
Butler
, and
V.
Mechtcherine
, “
Inline quantification of extrudability of cementitious materials for digital construction
,” Cem. Concr. Compos.
95
, 260
–270
(2019
).21.
R.
Comminal
,
W. R. L.
da Silva
,
T. J.
Andersen
,
H.
Stang
, and
J.
Spangenberg
, “
Modelling of 3D concrete printing based on computational fluid dynamics
,” Cem. Concr. Res.
138
, 106256
(2020
).22.
K.
Manikandan
,
K.
Wi
,
X.
Zhang
,
K.
Wang
, and
H.
Qin
, “
Characterizing cement mixtures for concrete 3D printing
,” Manuf. Lett.
24
, 33
–37
(2020
).23.
S. A. O.
Nair
,
S.
Panda
,
M.
Santhanam
,
G.
Sant
, and
N.
Neithalath
, “
A critical examination of the influence of material characteristics and extruder geometry on 3D printing of cementitious binders
,” Cem. Concr. Compos.
112
, 103671
(2020
).24.
M. K.
Mohan
,
A. V.
Rahul
,
K.
Van Tittelboom
, and
G.
de Schutter
, “
Rheological and pumping behavior of 3D printable cementitious materials with varying aggregate content
,” Cem. Concr. Res.
139
, 106258
(2021
).25.
N.
Zhang
and
J.
Sanjayan
, “
Extrusion nozzle design and print parameter selections for 3D concrete printing
,” Cem. Concr. Compos.
137
, 104939
(2023
).26.
X.
Guo
,
J.
Yang
, and
G.
Xiong
, “
Influence of supplementary cementitious materials on rheological properties of 3D printed fly ash based geopolymer
,” Cem. Concr. Compos.
114
, 103820
(2020
).27.
Z.
Zhao
,
M.
Chen
,
J.
Xu
,
L.
Li
,
Y.
Huang
,
L.
Yang
,
P.
Zhao
, and
L.
Lu
, “
Mix design and rheological properties of magnesium potassium phosphate cement composites based on the 3D printing extrusion system
,” Constr. Build. Mater.
284
, 122797
(2021
).28.
M. A. D.
Najvani
,
D. H.
Murcia
,
E.
Soliman
, and
M. M. R.
Taha
, “
Early-agre strength and failure characteristics of 3D printable polymer concrete
,” Constr. Build. Mater.
394
, 132119
(2023
).29.
A. R.
Arunothayan
,
B.
Nematollahi
,
K. H.
Khayat
,
A.
Ramesh
, and
J. G.
Sanjayan
, “
Rheological characterization of ultra-high performance concrete for 3D printing
,” Cem. Concr. Compos.
136
, 104854
(2023
).30.
R. B.
Bird
,
R. C.
Armstrong
, and
O.
Hassager
, Dynamics of Polymeric Liquids Vol. 1: Fluid Mechanics
, 2nd ed.
(
Wiley
, 1987
).31.
J. F.
Steffe
, Rheological Methods in Food Process Engineering
, 2nd ed.
(
Freeman Press
,
Michigan
, 1996
).32.
J.
Vlachopoulos
and
N. D.
Polychronopoulos
, Understanding Rheology and Technology of Polymer Extrusion
(
Polydynamics Inc
,
Ontario, Canada
, 2019
).33.
S. H.
Bong
,
M.
Xia
,
B.
Nematollahi
, and
C.
Shi
, “
Ambient temperature cured ‘just-add-water’ geopolymer for 3D concrete printing applications
,” Cem. Concr. Compos.
121
, 104060
(2021
).34.
Y.
Chen
,
S.
He
,
Y.
Gan
,
O.
Çopuroğlu
,
F.
Veer
, and
E.
Schlangen
, “
A review of printing strategies, sustainable cementitious materials and characterization methods in the context of extrusion-based 3D concrete printing
,” J. Build. Eng.
45
, 103599
(2022
).35.
D.
Kaplan
,
F.
de Larrard
, and
T.
Sedran
, “
Design of concrete pumping circuit
,” ACI Mater. J.
102
, 110
–117
(2005
).36.
J.
Vlachopoulos
and
P. S.
Scott
, “
Pressure drop for molten polymer flow through tapered dies
,” Adv. Polym. Technol.
5
(2
), 81
–86
(1985
).37.
R. B.
Bird
,
G. C.
Dai
, and
B. J.
Yarusso
, “
The rheology and flow of viscoplastic materials
,” Rev. Chem. Eng.
1
(1
), 1
–70
(1983
).38.
ANSYS Inc
, Ansys Fluent Theory Guide, Release 2022 R1
(
ANSYS Inc.
,
Canonsburg
, 2022
).39.
R. I.
Tanner
and
J. F.
Milthorpe
, “
Numerical simulation of the flow of fluids with yield stress
,” in Proceedings of the Numerical Methods in Laminar and Turbulent Flow
, Seattle (1983
), Vol.
680–690
.40.
E. J.
O'Donovan
and
R. I.
Tanner
, “
Numerical study of the Bingham squeeze film problem
,” J. Non-Newtonian Fluid Mech.
15
(1
), 75
–83
(1984
).41.
C. R.
Beverly
and
R. I.
Tanner
, “
Numerical analysis of extrudate swell in viscoelastic materials with yield stress
,” J. Rheol.
33
, 989
–1009
(1989
).42.
K.
Vasilic
,
W.
Schmidt
,
H. C.
Kühne
,
F.
Haamkens
,
V.
Mechtcherine
, and
N.
Roussel
, “
Flow of fresh concrete through reinforced elements: Experimental validation of the porous analogy numerical method
,” Cem. Concr. Res.
88
, 1
–6
(2016
).43.
S.
Tichko
,
G.
De Schutter
,
P.
Troch
,
J.
Vierendeels
,
R.
Verhoeven
,
K.
Lesage
, and
N.
Cauberg
, “
Influence of the viscosity of self-compacting concrete and the presence of rebars on the formwork pressure while filling bottom up
,” Eng. Struct.
101
, 698
–714
(2015
).44.
J. J.
Taylor-West
and
A. J.
Hogg
, “
The converging flow of viscoplastic fluid in a wedge or cone
,” J. Fluid Mech.
915
, A69
(2021
).45.
S. G.
Hatzikiriakos
and
E.
Mitsoulis
, “
Slip effects in tapered dies
,” Polym. Eng. Sci.
49
, 1960
–1969
(2009
).46.
H. A.
Ardakani
,
E.
Mitsoulis
, and
S. G.
Hatzikiriakos
, “
Thixotropic flow of toothpaste through extrusion dies
,” J. Non-Newtonian Fluid Mech.
166
, 1262
–1271
(2011
).47.
L.
Fusi
,
K. D.
Housiadas
, and
G. C.
Georgiou
, “
Flow of a Bingham fluid in a pipe of variable radius
,” J. Non-Newtonian Fluid Mech.
285
, 104393
(2020
).48.
P.
Panaseti
,
Y.
Damianou
,
G. C.
Georgiou
, and
K. D.
Housiadas
, “
Pressure-driven flow of a Herschel–Bulkley fluid with pressure-dependent rheological parameters
,” Phys. Fluids
30
, 030701
(2018
).49.
O. H.
Wallevik
,
D.
Feys
,
J. E.
Wallevik
, and
K. H.
Khayat
, “
Avoiding inaccurate interpretations of rheological measurements for cement-based materials
,” Cem. Concr. Res.
78
, 100
–109
(2015
).50.
D.
De Kee
, “
Yield stress measurements technique: A review
,” Phys. Fluids
33
, 111301
(2021
).51.
S.
Jacobsen
,
J. H.
Mork
,
S. F.
Lee
, and
L.
Haugan
, “
Pumping of concrete and mortar—State of the art
,” COIN Project Report No. 5, COIN P2 Improved construction technology. SP 2.4 Workability (SINTEF Building and Infrastructure, 2008).52.
B.
Nazari
,
E.
Moghimi
, and
D. W.
Bousfield
, “
Experimental footprints of a water-rich depletion layer in the Herschel–Bulkley pipe flow of solidifying polyelectrolytes
,” Phys. Fluids
35
, 013112
(2023
).53.
C. W.
Macosko
, Rheology: Principles, Measurements and Applications
(
Wiley-VCH
,
New York
, 1994
).54.
R. I.
Tanner
, Engineering Rheology
, 2nd ed.
(
Oxford University Press
,
New York
, 1988
).55.
R.
Alfani
,
N.
Grizzuti
,
G. L.
Guerrini
, and
G.
Lezzi
, “
The use of the capillary rheometer for the rheological evaluation of extrudable cement-based materials
,” Rheol. Acta
46
, 703
–709
(2007
).56.
S. S.
Abdali
,
E.
Mitsoulis
, and
N. C.
Markatos
, “
Entry and exit flows of Bingham fluids
,” J. Rheol.
36
, 389
–407
(1992
).57.
D. J.
Horrobin
and
R. M.
Nedderman
, “
Die entry pressure drops in paste extrusion
,” Chem. Eng. Sci.
53
(18
), 3215
–3225
(1998
).58.
F. A.
Cardoso
,
V. M.
John
, and
R. G.
Pileggi
, “
Rheological behavior of mortars under different squeezing rates
,” Cem. Concr. Res.
39
, 748
–753
(2009
).59.
R. G.
Pileggi
,
A. M.
Betioli
,
F. A.
Cardoso
, and
V. M.
John
, “
Extended rheological characterization of cement pastes: Squeeze flow plus rotational rheometry
,” in 12th International Congress on the Chemistry of Cement, July 8–13
,
Montréal, Canada
, 2007
.60.
F. A.
Cardoso
,
V. M.
John
,
R. G.
Pileggi
, and
P. F. G.
Banfill
, “
Characterisation of rendering mortars by squeeze-flow and rotational rheometry
,” Cem. Concr. Res.
57
, 79
–87
(2014
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
