We study experimentally the stability of micrometer weakly viscoelastic jets produced with transonic flow focusing. Highly stable jets are formed when a low molecular weight polymer is added to water at a given low concentration, and the injected flow rate is reduced to its minimum value. In this case, the capillary instability is delayed, and the jet breakup occurs at distances from the ejector of the order of tens of thousands the jet diameter. The results indicate that the intense converging extensional flow in the ejection point builds up viscoelastic stress that does not relax in the jet even for times much longer than the polymer relaxation time. We hypothesize that the drag (shear) force exerted by the outer gas stream prevents the stress relaxation. It is also possible that partial polymer entanglement at the jet emission point contributes to this effect. We measure the jet length and the diameter at the ejector orifice and breakup point. The diameter takes values just above 2 μm at the breakup point regardless of the liquid flow rate and gas pressure.

1.
D. F.
James
, “
Boger fluids
,”
Annu. Rev. Fluid Mech.
41
,
129
142
(
2009
).
2.
G. H.
McKinley
and
A.
Tripathi
, “
How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer
,”
J. Rheol.
44
,
653
670
(
2000
).
3.
S. L.
Anna
and
G. H.
McKinley
, “
Elasto-capillary thinning and breakup of model elastic liquids
,”
J. Rheol.
45
,
115
138
(
2001
).
4.
R. B.
Bird
,
R. C.
Armstrong
, and
O.
Hassager
,
Dynamics of Polymeric Liquids Volume I: Fluid Mechanics; Volume II: Kinetic Theory
(
Wiley
,
New York
,
1987
).
5.
J. G.
Oldroyd
, “
On the formulation of rheological equations of state
,”
Proc. R. Soc. London, Ser. A
200
,
523
541
(
1950
).
6.
J.
Eggers
and
E.
Villermaux
, “
Physics of liquid jets
,”
Rep. Prog. Phys.
71
,
036601
(
2008
).
7.
A. L.
Yarin
,
B.
Pourdeyhimi
, and
S.
Ramakrishna
,
Fundamentals and Applications of Micro- and Nanofibers
(
Cambridge University Press
,
Cambridge, Great Britain
,
2014
).
8.
T.
Funada
and
D. D.
Joseph
, “
Viscoelastic potential flow analysis of capillary instability
,”
J. Non-Newtonian Fluid Mech.
111
,
87
105
(
2003
).
9.
M.
Goldin
,
J.
Yerushalmi
,
R.
Pfeffer
, and
R.
Shinnar
, “
Breakup of a laminar capillary jet of a viscoelastic fluid
,”
J. Fluid Mech.
38
,
689
711
(
1969
).
10.
Z.
Liu
and
Z.
Liu
, “
Linear analysis of three-dimensional instability of non-Newtonian liquid jets
,”
J. Fluid Mech.
559
,
451
459
(
2006
).
11.
P.
Huerre
and
P. A.
Monkewitz
, “
Local and global instabilites in spatially developing flows
,”
Annu. Rev. Fluid Mech.
22
,
473
537
(
1990
).
12.
J. M.
Montanero
and
A. M.
Gañán-Calvo
, “
Viscoelastic effects on the jetting-dripping transition in co-flowing capillary jets
,”
J. Fluid Mech.
610
,
249
260
(
2008
).
13.
S.
Middleman
, “
Stability of a viscoelastic jet
,”
Chem. Eng. Sci.
20
,
1037
1040
(
1965
).
14.
S. L.
Goren
and
J.
Gavis
, “
Transverse wave motion on a thin capillary jet of a viscoelastic liquid
,”
Phys. Fluids
4
,
575
579
(
1961
).
15.
T.
Han
,
A. L.
Yarin
, and
D. H.
Reneker
, “
Viscoelastic electrospun jets: Initial stresses and elongational rheometry
,”
Polymer
49
,
1651
1658
(
2008
).
16.
S.
Goren
and
M.
Gottlieb
, “
Surface-tension-driven breakup of viscoelastic liquid threads
,”
J. Fluid Mech.
120
,
245
266
(
1982
).
17.
A.-C.
Ruo
,
F.
Chen
,
C.-A.
Chung
, and
M.-H.
Chang
, “
Three-dimensional response of unrelaxed tension to instability of viscoelastic jets
,”
J. Fluid Mech.
682
,
558
576
(
2011
).
18.
Z.
Ding
,
K.
Mu
,
T.
Si
, and
Y.
Jian
, “
Linear instability analysis of a viscoelastic jet in a co-flowing gas stream
,”
J. Fluid Mech.
936
,
A6
(
2022
).
19.
A. S.
Mohamed
,
M. A.
Herrada
,
A. M.
Gañán-Calvo
, and
J. M.
Montanero
, “
Convective-to-absolute instability transition in a viscoelastic capillary jet subject to unrelaxed axial elastic tension
,”
Phys. Rev. E
92
,
023006
(
2015
).
20.
J.
Eggers
, “
Nonlinear dynamics and breakup of free-surface flows
,”
Rev. Mod. Phys.
69
,
865
929
(
1997
).
21.
H.-C.
Chang
,
E. A.
Demekhin
, and
E.
Kalaidin
, “
Iterated stretching of viscoelastic jets
,”
Phys. Fluids
11
,
1717
1737
(
1999
).
22.
M. S. N.
Oliveira
and
G. H.
McKinley
, “
Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of highly-extensible flexible polymers
,”
Phys. Fluids
17
,
071704
(
2005
).
23.
C.
Clasen
,
J.
Eggers
,
M. A.
Fontelos
,
J.
Li
, and
G. H.
McKinley
, “
The beads-on-string structure of viscoelastic threads
,”
J. Fluid Mech.
556
,
283
308
(
2006
).
24.
A. V.
Bazilevsky
,
S. I.
Voronkov
,
V. M.
Entov
, and
A. N.
Rozhkov
, “
Orientational effects in capillary breakup of jets and threads of dilute polymer solutions (English version in vol. 26)
,”
Dokl. Akad. Nauk SSSR
257
,
336
339
(
1981
).
25.
A.
Ponce-Torres
,
J. M.
Montanero
,
E. J.
Vega
, and
A. M.
Gañán-Calvo
, “
The production of viscoelastic capillary jets with gaseous flow focusing
,”
J. Non-Newtonian Fluid Mech.
229
,
8
15
(
2016
).
26.
A. M.
Gañán-Calvo
, “
Generation of steady liquid microthreads and micron-sized monodisperse sprays in gas streams
,”
Phys. Rev. Lett.
80
,
285
288
(
1998
).
27.
A.
Rubio
,
F.
Galindo
,
E. J.
Vega
,
J. M.
Montanero
, and
M. G.
Cabezas
, “
Viscoelastic transition in transonic flow focusing
,” (to be published).
28.
J.
Doshi
and
D. R.
Reneker
, “
Electrospinning process and applications of electrospun fibers
,”
J. Electrost.
35
,
151
160
(
1995
).
29.
M.
Lauricella
,
S.
Succi
,
E.
Zussman
,
D.
Pisignano
, and
A. L.
Yarin
, “
Models of polymer solutions in electrified jets and solution blowing
,”
Rev. Mod. Phys.
92
,
035004
(
2020
).
30.
J. L.
Daristotle
,
A. M.
Behrens
,
A. D.
Sandler
, and
P.
Kofinas
, “
A review of the fundamental principles and applications of solution blow spinning
,”
ACS Appl. Mater. Interfaces
8
,
34951
34963
(
2016
).
31.
D. A.
Saville
, “
Electrohydrodynamics: The Taylor-Melcher leaky dielectric model
,”
Annu. Rev. Fluid Mech.
29
,
27
64
(
1997
).
32.
D. H.
Reneker
,
A.
Yarin
,
H.
Fong
, and
S.
Koombhongse
, “
Bending instability of electrically charged liquid jets of polymer solutions in electrospinning
,”
J. Appl. Phys.
87
,
4531
4547
(
2000
).
33.
C.
van der Walt
,
M. A.
Hulsen
,
A. C. B.
Bogaerds
,
H. E. H.
Meijer
, and
M. J. H.
Bulters
, “
Stability of fiber spinning under filament pull-out conditions
,”
J. Non-Newtonian Fluid Mech.
175–176
,
25
37
(
2012
).
34.
M. G.
Cabezas
,
A.
Bateni
,
J. M.
Montanero
, and
A. W.
Neumann
, “
A new drop-shape methodology for surface tension measurement
,”
Appl. Surf. Sci.
238
,
480
484
(
2004
).
35.
S.
Sur
and
J.
Rothstein
, “
Drop breakup dynamics of dilute polymer solutions: Effect of molecular weight, concentration, and viscosity
,”
J. Rheol.
62
,
1245
1259
(
2018
).
36.
M.
Rubio
,
A.
Ponce-Torres
,
E. J.
Vega
, and
J. M.
Montanero
, “
Experimental analysis of the extensional flow of very weakly viscoelastic polymer solutions
,”
Materials
13
,
192
(
2020
).
37.
R.
Sattler
,
C.
Wagner
, and
J.
Eggers
, “
Blistering pattern and formation of nanofibers in capillary thinning of polymer solutions
,”
Phys. Rev. Lett.
100
,
164502
(
2008
).
38.
T.
Alty
, “
The maximum rate of evaporation of water
,”
London, Edinburgh, Dublin Philos. Mag. J. Sci.
15
,
82
103
(
1933
).
39.
A. H.
Persad
and
C. A.
Ward
, “
Expressions for the evaporation and condensation coefficients in the Hertz-Knudsen relation
,”
Chem. Rev.
116
,
7727
7767
(
2016
).
40.
A. M.
Gañán-Calvo
,
H. N.
Chapman
,
M.
Heymann
,
M. O.
Wiedorn
,
J.
Knoska
,
B.
Gañán-Riesco
,
J. M.
López-Herrera
,
F.
Cruz-Mazo
,
M. A.
Herrada
,
J. M.
Montanero
, and
S.
Bajt
, “
The natural breakup length of a steady capillary jet: Application to serial femtosecond crystallography
,”
Crystals
11
,
990
(
2021
).
41.
T.
Si
,
F.
Li
,
X.-Y.
Yin
, and
X.-Z.
Yin
, “
Modes in flow focusing and instability of coaxial liquid-gas jets
,”
J. Fluid Mech.
629
,
1
23
(
2009
).
42.
D. H.
Reneker
,
A. L.
Yarin
,
E.
Zussman
, and
H.
Xu
, “
Electrospinning of nanofibers from polymer solutions and melts
,”
Adv. Appl. Mech.
41
,
345
346
(
2007
).
43.
N.
Mittal
,
F.
Ansari
,
K.
Gowda
,
C.
Brouzet
,
P.
Chen
,
P. T.
Larsson
,
S. V.
Roth
,
F.
Lundell
,
L.
Wagberg
,
N. A.
Kotov
, and
L. D.
Soderberg
, “
Multiscale control of nanocellulose assembly: Transferring remarkable nanoscale fibril mechanics to macroscale fibers
,”
ACS Nano
12
,
6378
6388
(
2018
).
44.
D. D.
Joseph
,
Fluid Dynamics of Viscoelastic Liquids
(
Springer-Verlag
,
1990
).
45.
P. C.
Hiemenz
and
T.
Lodge
,
Polymer Chemistry
(
CRC
,
New York
,
2007
).
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