We analyze different flow regimes of a filament formed by extrusion of a material through a cylindrical die. We deduce that the elongational yield stress of a simple yield stress fluid (i.e., with negligible thixotropy effects) can be determined from the mass of the droplet after filament breakage and an estimation of the critical radius at pinch-off at the solid-liquid regime transition. We demonstrate that such a simple characterization is relevant in a relatively wide range of extrusion velocities, i.e., this velocity slightly affects the drop mass in this range. For the simple yield stress fluids used, Carbopol gel, clay-water paste at different concentrations, and emulsion, covering a large range of yield stress values (50–1000 Pa), the elongational yield stress appears to be equal to the simple shear yield stress times a factor equal to about 1.53. As a consequence, this simple test may be used to obtain, almost instantaneously and without sophisticated apparatus (a syringe and a balance are sufficient), a good estimate of the shear yield stress of simple yield stress fluids. In that case, the main source of uncertainty (up to about 20%) is the value of the critical radius at the solid-liquid transition. Finally, we review the operating conditions (material properties and extrusion characteristics) for which we can expect this approach to be valid.

1.
Nguyen
,
D. Q.
, and
D. V.
Boger
, “
Yield stress measurement for concentrated suspensions
,”
J. Rheol.
27
,
321
349
(
1983
).
2.
Moller
,
P. C. F.
,
J.
Mewis
, and
D.
Bonn
, “
Yield stress and thixotropy: On the difficulty of measuring yield stresses in practice
,”
Soft Matter
2
,
274
(
2006
).
3.
Dinkgreve
,
M.
,
J.
Paredes
,
M. M.
Denn
, and
D.
Bonn
, “
On different ways of measuring ‘the’ yield stress
,”
J. Non-Newtonian Fluid Mech.
238
,
233
241
(
2016
).
4.
Coleman
,
B. D.
,
H.
Markowitz
, and
W.
Noll
,
Viscometric Flows of Non-Newtonian Fluids
(
Springer
,
Berlin
,
1966
).
5.
Coussot
,
P.
,
Rheometry of Pastes, Suspensions and Granular Materials
(
Wiley
,
New York
,
2005
).
6.
Ovarlez
,
G.
,
S.
Cohen-Addad
,
K.
Krishan
,
J.
Goyon
, and
P.
Coussot
, “
On the existence of a simple yield stress fluid behavior
,”
J. Non-Newtonian Fluid Mech.
193
,
68
79
(
2013
).
7.
Balmforth
,
N. J.
,
I. A.
Frigaard
, and
G.
Ovarlez
, “
Yielding to stress: Recent developments in viscoplastic fluid mechanics
,”
Annu. Rev. Fluid Mech.
46
,
121
146
(
2014
).
8.
Coussot
,
P.
, “
Yield stress fluid flows: A review of experimental data
,”
J. Non-Newtonian Fluid Mech.
211
,
31
49
(
2014
).
9.
Townsend
,
J. M.
,
E. C.
Beck
,
S. H.
Gehrke
,
C. J.
Berkland
, and
M. S.
Detamore
, “
Flow behavior prior to crosslinking: The need for precursor rheology for placement of hydrogels in medical applications and for 3D bioprinting
,”
Prog. Polym. Sci.
91
,
126
140
(
2019
).
10.
M’Barki
,
A.
,
L.
Bocquet
, and
A.
Stevenson
, “
Linking rheology and printability for dense and strong ceramics by direct ink writing
,”
Sci. Rep.
7
,
6017
(
2017
).
11.
Jeong
,
H.
,
S.-J.
Han
,
S.-H.
Choi
,
Y.
Lee
,
S.
Yi
, and
K.
Kim
, “
Rheological property criteria for buildable 3D printing concrete
,”
Materials
12
,
657
(
2019
).
12.
Mechtcherine
,
V.
,
F. P.
Bos
,
A.
Perrot
,
W. R. L.
da Silva
,
V. N.
Nerella
,
S.
Fataei
,
R. J. M.
Wolfs
,
M.
Sonebi
, and
N.
Roussel
, “
Extrusion-based additive manufacturing with cement-based materials—Production steps, processes, and their underlying physics: A review
,”
Cem. Concr. Res.
132
,
106037
(
2020
).
13.
Daalkhaijav
,
U.
,
O. D.
Yirmibesoglu
,
S.
Walker
, and
Y.
Menguc
, “
Rheological modification of liquid metal for additive manufacturing of stretchable electronics
,”
Adv. Mater. Technol.
3
,
1700351
(
2018
).
14.
Tiwari
,
M. K.
,
A. V.
Bazilevsky
,
A. L.
Yarin
, and
C. M.
Megaridis
, “
Elongational and shear rheology of carbon nanotube suspensions
,”
Rheol. Acta
48
,
597
609
(
2009
).
15.
Mackay
,
M. E.
, “
The importance of rheological behavior in the additive manufacturing technique material extrusion
,”
J. Rheol.
62
,
1549
1561
(
2018
).
16.
Nelson
,
A. Z.
,
K. S.
Schweizer
,
B. M.
Rauzan
,
R. G.
Nuzzo
,
J.
Vermant
, and
R. H.
Ewoldt
, “
Designing and transforming yield-stress fluids
,”
Curr. Opin. Solid State Mater. Sci.
23
,
100758
(
2019
).
17.
Oldroyd
,
J. G.
, “
A rational formulation of the equations of plastic flow for a Bingham solid
,”
Math. Proc. Camb. Philos. Soc.
43
,
100
105
(
1947
).
18.
Hohenemser
,
K.
, and
W.
Prager
, “
Über die ansätze der mechanik isotroper kontinua
,”
Z. Angew. Math. Mech.
12
,
216
226
(
1932
).
19.
Coussot
,
P.
, and
S. A.
Rogers
, “
Oldroyd's model and the foundation of modern rheology of yield stress fluids
,”
J. Non-Newtonian Fluid Mech.
295
,
104604
(
2021
).
20.
Niedzwiedz
,
K.
,
H.
Buggisch
, and
N.
Willenbacher
, “
Extensional rheology of concentrated emulsions as probed by capillary breakup elongational rheometry (CaBER)
,”
Rheol. Acta
49
,
1103
1116
(
2010
).
21.
German
,
G.
, and
V.
Bertola
, “
Formation of viscoplastic drops by capillary breakup
,”
Phys. Fluids
22
,
033101
(
2010
).
22.
Martinie
,
L.
,
H.
Buggisch
, and
N.
Willenbacher
, “
Apparent elongational yield stress of soft matter
,”
J. Rheol.
57
,
627
646
(
2013
).
23.
Sadek
,
S. H.
,
H. H.
Najafabadi
, and
F. J.
Galindo-Rosales
, “
Capillary breakup extension electrorheometry (CaBEER)
,”
J. Rheol.
64
,
43
54
(
2020
).
24.
Sadek
,
S. H.
,
H. H.
Najafabadi
, and
F. J.
Galindo-Rosales
, “
Capillary breakup extension magnetorheometry
,”
J. Rheol.
64
,
55
65
(
2020
).
25.
Boujlel
,
J.
, and
P.
Coussot
, “
Measuring the surface tension of yield stress fluids
,”
Soft Matter
9
,
5898
(
2013
).
26.
Zhang
,
X.
,
O.
Fadoul
,
E.
Lorenceau
, and
P.
Coussot
, “
Yielding and flow of soft-jammed systems in elongation
,”
Phys. Rev. Lett.
120
,
048001
(
2018
).
27.
Louvet
,
N.
,
D.
Bonn
, and
H.
Kellay
, “
Nonuniversality in the pinch-off of yield stress fluids: Role of nonlocal rheology
,”
Phys. Rev. Lett.
113
,
218302
(
2014
).
28.
Varchanis
,
S.
,
S. J.
Haward
,
C. C.
Hopkins
,
A.
Syrakos
,
A. Q.
Shen
,
Y.
Dimakopoulos
, and
J.
Tsamopoulos
, “
Transition between solid and liquid state of yield-stress fluids under purely extensional deformations
,”
Proc. Natl. Acad. Sci. U. S. A.
117
,
12611
12617
(
2020
).
29.
Geffrault
,
A.
,
H.
Bessaies-Bey
,
N.
Roussel
, and
P.
Coussot
, “
Extensional gravity-rheometry (EGR) for yield stress fluids
,”
J. Rheol.
65
,
887
901
(
2021
).
30.
Ducoulombier
,
N.
,
R.
Mesnil
,
P.
Carneau
,
L.
Demont
,
H.
Bessaies-Bey
,
J. F.
Caron
, and
N.
Roussel
, “
The ‘slugs-test’ for extrusion-based additive manufacturing: Protocol, analysis and practical limits
,”
Cem. Concr. Compos.
121
,
104074
(
2021
).
31.
Coussot
,
P.
,
H.
Tabuteau
,
X.
Chateau
,
L.
Tocquer
, and
G.
Ovarlez
, “
Aging and solid or liquid behavior in pastes
,”
J. Rheol.
50
,
975
994
(
2006
).
32.
N’gouamba
,
E.
,
J.
Goyon
, and
P.
Coussot
, “
Elastoplastic behavior of yield stress fluids
,”
Phys. Rev. Fluids
4
,
123301
(
2019
).
33.
Planchette
,
C.
,
F.
Marangon
,
W. K.
Hsiao
, and
G.
Brenn
, “
Breakup of asymetric liquid ligaments
,”
Phys. Rev. Fluids
4
,
124004
(
2019
).
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