The dripping problem of a viscoplastic (yield-stress) liquid running slowly out of a narrow vertical tube is considered. The volume of the drops which break away is determined. A Lagrangian coordinate system is used to analyze the extension of the thread as it sags under its own weight, neglecting inertia and capillarity. 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.
Rezanka
, I.
, and Eschbach
, R.
, 1996, Recent Progress in Ink Jet Technologies
, IST Press
, Springfield, VA.2.
Pappen
, R.
, 1998, Procee. of IBC Int. Conf. on Massively Parallel DNA Analysis
, San Francisco.3.
4.
Ambravaneswaran
, B.
, Phillips
, S. D.
, and Basaran
, O. A.
, 2000, “Theoretical Analysis of a Dripping Faucet
,” Phys. Rev. Lett.
0031-9007, 85
, pp. 5332
–3325
.5.
Wilkes
, E. D.
, Phillips
, S. D.
, and Basaran
, O. A.
, 1999, “Computational and Experimental Analysis of Dynamics of Drop Formation
,” Phys. Fluids
1070-6631 11
, pp. 3577
–3598
.6.
Chen
, A. U.
, Notz
, P. K.
, and Basaran
, O. A.
, 2002, “Computational and Experimental Analysis of Pinch-off and Scaling
,” Phys. Rev. Lett.
0031-9007 88
, pp. 174501
–174504
.7.
Wilson
, S. D. R.
, 1999, “The Slow Dripping of a Viscous Fluid
,” J. Fluid Mech.
0022-1120 190
, pp. 561
–570
.8.
Fuchikami
, N.
, Ishioka
, S.
and Kiyono
, K.
, 1999, “Simulation of a Dripping Faucet
,” J. Phys. Soc. Jpn.
0031-9015 68
, pp. 1185
–1196
.9.
Coullet
, P.
, Mahadevan
, L.
and Riera
, C.
, 2000, “Return Map for the Chaotic Dripping Faucet
,” Prog. Theor. Phys. Suppl.
0375-9687 139
, pp. 507
–516
.10.
Renardy
, M.
, 1994, “Some Comments on the Surface-Tension Driven Break-up (or the Lack of it) of Viscoelasticets
,” J. Non-Newtonian Fluid Mech.
0377-0257 51
, pp. 97
–107
.11.
Renardy
, M.
, 1995, “A Numerical Study of the Asymptotic Evolution and Breakup of Newtonian and Viscoelastic Jets
,” J. Non-Newtonian Fluid Mech.
0377-0257 59
, pp. 267
–282
.12.
Eggers
, J.
, 1997, “Nonlinear dynamics and breakup of free-surface flows
,” Rev. Mod. Phys.
0034-6861 69
(3
), pp. 865
–929
.13.
Barnes
, H. A.
, and Walters
, K.
, 1985, “The Yield Stress Myth
?” Rheol. Acta
0035-4511 24
(4
), pp. 323
–326
.14.
Beverly
, C. R.
, and Tanner
, R. I.
, 1992, “Numerical Analysis of Three Dimensional Bingham Plastic Flow
,” J. Non-Newtonian Fluid Mech.
0377-0257 42
, pp. 85
–115
.15.
Wilson
, S. D. R.
, 1993, “Squeezing flow of a Bingham material
,” J. Non-Newtonian Fluid Mech.
0377-0257 47
, pp. 211
–219
.16.
Al Khatib
, M. A. M.
, 2003, “The Stretching of a Viscoplastic Thread of Liquid
,” ASME J. Fluids Eng.
0098-2202 125
, pp. 946
–951
.Copyright © 2005
by American Society of Mechanical Engineers
You do not currently have access to this content.