Analysis of the String Structure Near Break-up of A Slender Jet of An Upper Convected Maxwell Liquid

A. Y. Gunawan, W. S. Budhi


In this paper, we analytically study the string structure near the break-up of a slender jet of a viscoelastic liquid surrounded by air. The governing equations are derived from the conservation laws of mass and momentum, and the rheological equation of the jet. The rheological equation of the jet is assumed to satisfy an Upper Convected Maxwell (UCM) model. Introducing a stretch variable and then applying a transformation, we obtain a coupled system of nonlinear differential equations. Via these equations, we then show that the UCM jet does not break up in finite time, which physically means that it has sufficient time to exhibit the string structure before it breaks up due to the dominant surface force.

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Papageorgiou, D.T., On the breakup of viscous liquid threads, Physics of Fluids, 7, 1529-1544, 1995.

Eggers, J., Nonlinear dynamics and breakup of free-surface flows, Reviews of Modern Physics, 3, 865-927, 1997.

Pozrikidis, Capillary instability and breakup of a viscous thread, J. Engineering Mathematics, 36, 255-275, 1999.

Renardy, M., Finite time breakup of viscous filaments, Zeitschrift Für Angewandte Mathematik und Physik (ZAMP), 52, 881-887, 2001.

Renardy, M., A comment on self-similar breakup for inertialess Newtonian liquid jets, IMA J. Applied Mathematics, 70, 353-358, 2005.

Renardy, M. & Renardy, Y., Similarity solutions for breakup of jets of power law fluids, J. Non-Newtonian Fluid Mechanics, 122, 303-312, 2004.

Renardy, M., Self-similar jet breakup for a generalized PTT model, J. Non-Newtonian Fluid Mechanics, 103, 261-269, 2002.

Renardy, M., Similarity solution for jet breakup for various models of viscoelastic fluids, J. Non-Newtonian Fluid Mechanics, 104, 65-74, 2002.

Renardy, M. & Losh, D., Similarity solutions for jet breakup in a Giesikus fluid with inertia, J. Non-Newtonian Fluid Mechanics, 106, 17-27, 2002.

Renardy, M., Some comments on the surface-tension driven break-up (or lack of it) of viscoelastic jets, J. Non-Newtonian Fluid Mechanics, 51, 97-107,1994.

Li, J, & Fontelos, M.A., Drop dynamics on the beads-on-string structure for viscoelastic jets: A numerical study, Physics of Fluids, 15, 922-937, 2003.

Oliveira, M.S.N, McKinley, G.H., Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of highly extensible flexible polymers, Physics of Fluids,17 (0717 04),1-4, 2005.

Clasen, C., Eggers, J., Fontelos, M.A., Li, J., McKinley, G.H., The beads-on-string structure of viscoelastic threads, Journal of Fluid Mechanics, 556, 283-308, 2006.



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