Page 256 - Bird R.B. Transport phenomena

240 Chapter 8 Polymeric Liquids

рОооо о ОэО о о <
о
6 о - " ооо
1
)
о о
э о
о о
в
о : LDl^fc
5
-6 -4 -2 -3 -2 -1
loge log (-в)
(а)
Fig. 8.2-6. (a) Elongational viscosity for uniaxial stretching of low- and high-density polyeth-
ylene. [From H. Mtinstedt and H. M. Laun, Rheol. Ada, 20,211-221 (1981).] №) Elongational
viscosity for biaxial stretching of low-density polyethylene, deduced from flow-birefringence
data. [From J. A. van Aken and H. Janeschitz-Kriegl, Rheol. Ada, 20,419-432 (1981).] In both
1
graphs the quantity rj is given in Pa • s and s is in s" .

there are many types of mechanical responses in these various experiments. More
complete discussions of the data obtained in rheometric experiments are given else-
where. 5

§83 NON-NEWTONIAN VISCOSITY AND THE
GENERALIZED NEWTONIAN MODELS
This is the first of three sections devoted to empirical stress tensor expressions for non-
Newtonian fluids. One might say, very roughly, that these three sections satisfy three
different groups of people:

§8.3 The generalized Newtonian models are primarily used to describe steady-state
shear flows and have been widely used by engineers for designing flow systems.
§8.4 The linear viscoelastic models are primarily used to describe unsteady-state flows
in systems with very small displacement gradients and have been used mainly
by chemists interested in understanding polymer structure.
§8.5 The nonlinear viscoelastic models represent an attempt to describe all types of
flow (including the two listed above) and have been developed largely by
physicists and applied mathematicians interested in finding an all-inclusive theory.
Actually the three classes of models are interrelated, and each is important for understand-
ing the subject of non-Newtonian flow. In the following discussion of non-Newtonian
models, we assume throughout that the fluids are incompressible.
The generalized Newtonian models^ discussed here are the simplest of the three types of
models to be discussed. However, they can describe only the non-Newtonian viscosity,
and none of the normal stress effects, time-dependent effects, or elastic effects. Nonethe-

5 R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Vol. 1, Fluid Mechanics,
Wiley-Interscience, 2nd edition (1987).
1 K. Hohenemser and W. Prager, Zeits. f. Math. u. Mech., 12, 216-226 (1932); J. G. Oldroyd, Proc.
Camb. Phil. Soc, 45,595-611 (1949), and 47,410-418 (1950). James Gardner Oldroyd (1921-1982), a
professor at the University of Liverpool, made many contributions to the theory of non-Newtonian
fluids, in particular his ideas on the construction of constitutive equations and the principles of
continuum mechanics.