Chemistry Reference
In-Depth Information
in the two regions. (If there were no such forces the liquid would be a gas.) It
seems intuitively plausible that the magnitude of this force should be proportional
to the local velocity gradient and to the interlayer area
A
. That is,
F
5ηð
dv
=
dr
Þ
A
(3-59)
where the proportionality constant
(eta) is the coefficient of viscosity or just the
viscosity. During steady flow the driving force causing the fluid to exit from the
tube will just balance the retarding force
F
. A liquid whose flow fits
Eq. (3-59)
is
called a Newtonian fluid;
η
is independent of the velocity gradient. Polymer solu-
tions used for molecular weight measurements are usually Newtonian. More con-
centrated solutions or polymer melts are generally not Newtonian in the sense
that
η
may be a function of the velocity gradient and sometimes also of the his-
tory of the material.
Now consider a particle suspended in such a flowing fluid, as in
Fig. 3.6b
.
Impingement on the particle of fluid flowing at different rates causes the sus-
pended entity to move down the tube and also to rotate as shown. Since the parti-
cle surface is wetted by the liquid, its rotation brings adhering liquid from a
region with one velocity into a volume element which is flowing at a different
speed. The resulting readjustments of momenta cause an expenditure of energy
that is greater than that which would be required to keep the same volume of fluid
moving with the particular velocity gradient, and the suspension has a higher vis-
cosity than the suspending medium.
Einstein showed that the viscosity increase is given by
η
η5η
0
ð
1
1ωφÞ
(3-60)
where
η
and
η
0
are the viscosities of the suspension and suspending liquid,
respectively,
(omega) is a
factor that depends on the general shape of the suspended species. In general,
rigid macromolecules, having globular or rodlike shapes, behave differently from
flexible polymers, which adopt random coil shapes in solution. Most synthetic
polymers are of the latter type, and the following discussion focuses on their
behavior in solution.
The effects of a dissolved polymer are similar in some respects to those of the
suspended particles described earlier. A polymer solution has a higher viscosity
than the solvent, because solvent that is trapped inside the macromolecular coils
cannot attain the velocities that the liquid in that region would have in the
absence of the polymeric solute. (Appendix 3A provides an example of an indus-
trial application of this concept.) Thus, the polymer coil and its enmeshed solvent
have the same effect on the viscosity of the mixture as an impenetrable sphere,
but this hypothetical equivalent sphere may have a smaller volume than the real
solvated polymer coil because some of the solvent
φ
is the volume fraction of suspended material, and
ω
inside the coil can drain
through the macromolecule.
The radius of the equivalent sphere is considered to be a constant, while the
volume and shape of the real polymer coil will be changing continuously as a
