saturation of chain deformation, similar to the second Newtonian-fluid region in
shear flow. The extensional-thinning phenomenon has been observed often in
polymer solutions. In polymer melts, the extensional-thinning region is quite
narrow. This phenomenon is not favored in the practical extension flow, because
the fiber-spinning and film-blowing often break down in this region. Therefore, the
practical processing directly enters the later stage of extensional thickening or strain
hardening. The break of stretching causes a constitutive instability even in shear
flows. Recently, by means of the particle-tracing experiments, Wang and his
coworkers observed shear-banding shortly occurring at the starting stage of shear
flow due to extensional break along the shear direction. In other words, the
transverse velocity gradient appears as discontinuous between high speed and low
speed regions, causing the sliding interface (Tapadia et al. 2006 ).
During fiber-spinning and film-blowing, one may expect the extensional viscosity
increases with the increase of dv/dx. As the local increase of dv/dxleads to the
reduction of the fiber diameter, the increase of viscosity could prevent further thinning
and thus makes the fiber more homogeneous in thickness and stronger. Such a
performance of polymer fluids has been described asspinnability(Petrie 2006 ).
Branching polymers are often called “magic polymers”, including LDPE, hyper-
branching, star-shapes, and grafted polymers. This class of polymers tends to
evolve into globules in shear flows, and thus their viscosity decreases with the
increase of shear rates, facilitating extrusion and injection molding. On the other
hand, they display strain-hardening during extensional flow, and thus their viscosity
increase with the increase of extensional rates, facilitating fiber-spinning and film-
blowing. Therefore, a certain amount of branching polymers as an additive in the
melt of linear polymers will benefit various molding processes of the latter.
Fig. 7.12 Illustration of extensional viscosity versus the extensional rate curve predicted by the
molecular theory based on the standard tube model for the stable extensional flow of linear
polymers. Starting from the low extensional rate, the viscosity first keeps in 3 0 , then decays,
after deformation begins to increase, till to saturation (Marrucci and Iannirubertok 2004 )
(Readapted with permission)
7.2 Characteristics of Polymer Flow 139