Page 87 - Engineering Plastics Handbook

Processing 61

ρ ref = reference density
T test = test temperature, K
ρ test = test density

Shear Rate

Shear rate is the rate at which a layer of melt slides over the layer below.
It is observed as velocity. Shear rate applies to nonnewtonian (shear-
dependent) macromolecular polymeric melts and solutions. Newtonian
fluids, typically small molecules such as H O and oil, have constant vis-
2
cosities and are not shear rate–dependent.
Zero shear rate viscosity (the steady-state viscosity at zero shear rate)
is influenced by the type of polymer, MW, MWD, and additives. To calcu-
late the increase of zero shear rate viscosity with increasing MW [3], use
η = KMa
0
where η = zero shear rate viscosity, s −1
0
K = empirical constant
M = molecular weight of macropolymer
a = 3.4 at M > critical molecular weight M c
= 1 at M < critical molecular weight M c
Shear rate viscosity (shear strain or stress) behavior is fundamental
to controlling melt flow rheology. At low strain rate viscosity, the zero
strain rate viscosity is directly related to extensional (stretching) strain
viscosity by [3]
= 3η
η E 0
−1
where η = extensional strain viscosity, s
E
η = zero shear rate viscosity, s −1
0
The effects of shear on viscosity are plotted in three phases (y axis =
log viscosity, x axis = log shear rate): I, a newtonian plateau which is the
initial phase where the viscosity shows no change with increased shear
rate; II, the power law region which shows a rapid drop in viscosity as shear
rate increases; and III, the newtonian plateau which is the final phase
where the viscosity again shows no change with increased shear rate [3].
Newtonian law works with low shear rate, and the power law works with
high shear rate.
At low shear rates, polymeric liquid properties are characterized by two
and recoverable shear
constitutive parameters: zero shear rate viscosity η 0
e
compliance J 0 , which indicates fluid elasticity. At higher shear strain
rates, rheological behavior is measured with a viscometer. Extensional
strain viscosity, associated with extensional flow, occurs with film extrusion,