One of the most striking effects in polymeric fluids is their strong resistance to elongational stretching. As a result, polymers have a strong stabilizing effect on thin jets and filaments. This has many practical uses; for instance it makes it easier to spin polymeric fluids into fibers than would be the case for a Newtonian fluid. Another application is the addition of polymeric additives to inhibit atomization in fire fighting, crop dusting and other situations involving spraying of liquids from the air.
The surface-tension driven instability of fluid jets evolves quite differently for polymeric fluids than for Newtonian fluids. While Newtonian jets break rapidly, polymeric fluids tend to form a ``beads on a string" structure, where drops of fluid remain connected by thin filaments which break only after a long time, if at all. A combination of numerical and asymptotic methods is used to study the approach to breakup, or, if no breakup occurs, the long time evolution of the jet. The paper compares the Newtonian fluid and several models of viscoelastic behavior.
For very viscous fluids, such as polymer melts, surface tension is often negligible until filaments become extremely thin. It is therefore appropriate to look at the idealized problem of stretching a filament without surface tension. This is pursued in the paper, and again the issue is whether there is breakup in finite time. It can be proved that a Newtonian filament will not break in finite time in the absence of surface tension, even though nonuniformities always increase with time. Two viscoelastic models are also considered, one leads to healing of defects, i.e. filaments evolve to uniform thickness; the other has a nonmonotone force-stretch relationship which leads to failure.