The problem of stretching a viscoplastic (yield-stress) thread of a liquid hanging vertically is considered. The length of the thread at later times and the time at which it ruptures is determined. A Lagrangian coordinate system is used to analyze the extension of the thread as it sags under its own weight, with negligible inertial effects. The biviscosity model has been used to characterize viscoplastic fluids; the Newtonian and Bingham models can be recovered as limiting cases. The Bingham limit is of special interest.

1.
Matta
,
J. E.
, and
Titus
,
R. P.
,
1990
, “
Liquid Stretching Using a Falling Cylinder
,”
J. Non-Newtonian Fluid Mech.
,
35
, pp.
215
229
.
2.
Sridhar
,
T.
,
Tirtaatmadja
,
V.
,
Nguyen
,
D. A.
, and
Gupta
,
R. K.
,
1991
, “
Measurement of Extensional Viscosity of Polymer Solutions
,”
J. Non-Newtonian Fluid Mech.
,
40
, pp.
271
280
.
3.
Markovich
,
P.
, and
Renardy
,
M. A.
,
1985
, “
Finite Difference Study of the Stretching and Breakup of Filament of Polymer Solutions
,”
J. Non-Newtonian Fluid Mech.
,
17
, pp.
13
22
.
4.
Renardy
,
M. A.
,
1995
, “
A Numerical Study of the Asymptotic Evolution and Breakup of Newtonian and Viscoelastic Jets
,”
J. Non-Newtonian Fluid Mech.
,
59
, pp.
267
282
.
5.
Denn
,
M. M.
,
1980
, “
Continuous Drawing of Liquids to Form Fibers
,”
Annu. Rev. Fluid Mech.
,
12
, pp.
365
387
.
6.
De Wynne
,
J.
,
Ockendon
,
J. R.
, and
Wilmott
,
P.
,
1989
, “
On a Mathematical Model for Fiber Tapering
,”
SIAM (Soc. Ind. Appl. Math.) J. Appl. Math.
,
49
, pp.
983
990
.
7.
Doyle, P. J., 1994, Glass Making Today, R. A. N. Publishers, OH.
8.
Rekhson, S., Lu, Z., and Day, C., 1991, “Computer Modelling of Glass Processing,” Coll. papers from the 52nd conf. on glass problems, pp. 65–77.
9.
Gaudet
,
S.
,
Mckinley
,
G. H.
, and
Stone
,
H. A.
,
1996
, “
Extensional Deformation of Newtonian Liquid Bridges
,”
Phys. Fluids
,
8
, pp.
2568
2579
.
10.
Canright
,
D.
, and
Morris
,
S.
,
1993
, “
Bouyant Instability of a Viscous Film Over a Passive Fluid
,”
J. Fluid Mech.
,
255
, pp.
349
372
.
11.
Houseman
,
G. A.
, and
Molnar
,
P.
,
1997
, “
Gravitational (Rayleigh-Taylor) Instability of a Layer With Non-Linear Viscosity and Connective Thinning of Continental Lithosphere
,”
Geophys. J. Int.
,
128
, pp.
125
150
.
12.
Stokes
,
Y. M.
,
Tuck
,
E. O.
, and
Schwartz
,
L. W.
,
2000
, “
Extensional Fall of a Very Viscous Fluid Drop
,”
Q. J. Mech. Appl. Math.
,
53
, pp.
565
582
.
13.
Wilson
,
S. D. R.
,
1988
, “
The Slow Dripping of a Viscous Fluid
,”
J. Fluid Mech.
,
190
, pp.
561
570
.
14.
Beverly
,
C. R.
, and
Tanner
,
R. I.
,
1992
, “
Numerical Analysis of Three Dimensional Bingham Plastic Flow
,”
J. Non-Newtonian Fluid Mech.
,
42
, pp.
85
115
.
15.
Wilson
,
S. D. R.
,
1993
, “
Squeezing Flow of a Bingham Material
,”
J. Fluid Mech.
,
47
, pp.
211
219
.
16.
Barnes
,
H. A.
, and
Walters
,
K.
,
1985
, “
The Yield Stress Myth?
Rheol. Acta
,
24
(
4
), pp.
323
326
.
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