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.
Issue Section:
Technical Papers
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
.Copyright © 2003
by ASME
You do not currently have access to this content.