Page 250 - Bird R.B. Transport phenomena

234 Chapter 8 Polymeric Liquids
is, the fluid snaps back somewhat like a rubber band. However, whereas a rubber band
returns to its original shape, the fluid retreats only part way toward its original configu-
ration.
If we permit ourselves an anthropomorphism, we can say that a rubber band has
"perfect memory/' since it returns to its initial unstressed state. The polymeric fluid, on
the other hand, has a "fading memory/' since it gradually "forgets" its original state.
That is, as it recoils, its memory becomes weaker and weaker.
Fluid recoil is a manifestation of elasticity, and any complete description of poly-
meric fluids must be able to incorporate the idea of elasticity into the expression for the
stress tensor. The theory must also include the notion of fading memory.

'Normal Stress" Effects
Other striking differences in the behavior of Newtonian and polymeric liquids appear in
the "normal stress" effects. The reason for this nomenclature will be given in the next
section.
A rotating rod in a beaker of a Newtonian fluid causes the fluid to undergo a tan-
gential motion. At steady state, the fluid surface is lower near the rotating rod. Intu-
itively we know that this comes about because the centrifugal force causes the fluid to
move radially toward the beaker wall. For a polymeric liquid, on the other hand, the fluid
moves toward the rotating rod, and, at steady state, the fluid surface is as shown in Fig.
4
8.1-3. This phenomenon is called the Weissenberg rod-climbing effect. Evidently some
kinds of forces are induced that cause the polymeric liquid to behave in a way that is
qualitatively different from that of a Newtonian liquid.
In a closely related experiment, we can put a rotating disk on the surface of a fluid in
a cylindrical container as shown in Fig. 8.1-4. If the fluid is Newtonian, the rotating disk
causes the fluid to move in a tangential direction (the "primary flow"), but, in addition,
the fluid moves slowly outward toward the cylinder wall because of the centrifugal
force, then moves downward, and then back up along the cylinder axis. This superposed
radial and axial flow is weaker than the primary flow and is termed a "secondary flow."
For a polymeric liquid, the fluid also develops a primary tangential flow with a weak ra-

Fig. 8.1-4. The secondary flows in a
cylindrical container with a rotating
Fig. 8.1-3. The free surface of a liquid near disk at the liquid surface have the
a rotating rod. The polymeric liquid shows opposite directions for Newtonian
the Weissenberg rod-climbing effect. and polymeric fluids.

4
This phenomenon was first described by F. H. Garner and A. H. Nissan, Nature, 158, 634-635
(1946) and by R. J. Russel, Ph.D. thesis, Imperial College, University of London (1946), p. 58. The
experiment was analyzed by K. Weissenberg, Nature, 159, 310-311 (1947).