Page 252 - Bird R.B. Transport phenomena

236 Chapter 8 Polymeric Liquids

Fig. 8.1-7. The "acoustical streaming"
near a laterally oscillating rod, show-
ing that the induced secondary flow
goes in the opposite directions for
Newtonian and polymeric fluids.

8.1-7). In a Newtonian fluid, a secondary flow is induced whereby the fluid moves to-
ward the cylinder from above and below (i.e., from the +y and — у directions, and moves
away to the left and right (i.e., toward the — x and +x direction). For the polymeric liquid,
however, the induced secondary motion is in the opposite direction: the fluid moves in-
ward from the left and right along the x axis and outward in the up and down directions
along the у axis. 8
The preceding examples are only a few of many interesting experiments that have
been performed. 9 The polymeric behavior can be illustrated easily and inexpensively
with a 0.5% aqueous solution of polyethylene oxide.
There are also some fascinating effects that occur when even tiny quantities of poly-
mers are present. The most striking of these is the phenomenon of drag reduction. With
10
only parts per million of some polymers ("drag-reducing agents"), the friction loss in
turbulent pipe flow may be lowered dramatically—by 30-50%. Such polymeric drag-
reducing agents are used by fire departments to increase the flow of water, and by oil
companies to lower the costs for pumping crude oil over long distances.
For discussions of other phenomena that arise in polymeric fluids, the reader should
consult the summary articles in Annual Review of Fluid Mechanics. 11

§8.2 RHEOMETRY AND MATERIAL FUNCTIONS

The experiments described in §8.1 make it abundantly clear that polymeric liquids do
not obey Newton's law of viscosity. In this section we discuss several simple, control-
lable flows in which the stress components can be measured. From these experiments
one can measure a number of material functions that describe the mechanical response of
complex fluids. Whereas incompressible Newtonian fluids are described by only one
material constant (the viscosity), one can measure many different material functions for
non-Newtonian liquids. Here we show how a few of the more commonly used material

8
C. F. Chang and W. R. Schowalter, /. Non-Newtonian Fluid Mech., 6,47-67 (1979).
9
The book by D. V. Boger and K. Walters, Rheological Phenomena in Focus, Elsevier, Amsterdam
(1993), contains many photographs of fluid behavior in a variety of non-Newtonian flow systems.
10
This is sometimes called the Toms phenomenon, since it was perhaps first reported in B. A. Toms,
Proc. Int. Congress on Rheology, North-Holland, Amsterdam (1949). The phenomenon has also been
studied in connection with the drag-reducing nature of fish slime [T. L. Daniel, Biol. Bull, 160, 376-382
(1981)], which is thought to explain, at least in part, "Gray's paradox"—the fact that fish seem to be able
to swim faster than energy considerations permit.
11
For example, M. M. Denn, Ann. Rev. Fluid Mech., 22,13-34 (1990); E. S. G. Shaqfeh, Ann. Rev. Fluid
Mech., 28,129-185 (1996); G. G. Fuller, Ann. Rev. Fluid Mech., 22,387-417 (1992).