Chemistry Reference
In-Depth Information
is not appropriate for non-Newtonian substances, and it
is common practice to plot “flow curves” of such materials in terms of
A single figure for
η
η
a
(appar-
ent viscosity) against corresponding values of
. Many equations have been pro-
posed to describe non-Newtonian behavior. Generally, however, the mathematics
involved is not worth the effort except for the simplest problems. It is most effi-
cient to read the required viscosity values from experimental
γ
plots. These
relations can usually be described over limited shear rate ranges by power law
expressions of the form:
η
a
2 γ
n
τ 5
C
ð γÞ
(4-86)
where
n
is the power law index. If
n
1, it
is shear-thickening. The constant
C
has no real physical significance because its
units will vary with
n
.
Equation (4-86)
indicates that a log
,
1 the material is shear-thinning; if
n
.
log plot of
τ
vs.
γ
is
linear over the shear rate range of applicability. An alternative expression is
n2
1
η
a
5μð γÞ
(4-87)
where
, sometimes called the consistency, has limited significance since its units
also are dependent on
n
. This problem can be circumvented by referencing the
apparent viscosity to that at a specified shear rate,
μ
γ
aref
, which is conveniently
taken as 1 sec
2
1
. Then
n2
1
η
a
5η
aref
j γ
a
=γ
aref
j
(4-88)
Substances that do not flow at shear stresses less than a certain level exhibit
yield properties. Then
γ 5
τ 2τ
y
η
(4-89)
where
τ
y
is the yield stress. The yield stress may be of no significance, as in
high-speed extrusion of plastics, or it could be an important property of materials,
as in the application of architectural paints and in rotational molding.
Most polymeric substances are time dependent to some extent and
,
where
t
here refers to the time under shear. If shearing causes a decrease in vis-
cosity the material is said to be
thixotropic
; the opposite behavior characterizes a
rheopectic
substance. These patterns are sketched in
Fig. 4.29
. After shearing has
been stopped, time-dependent fluids recover their original condition in due
course. PVC plastisols [mixtures of poly(vinyl chloride) emulsion polymers and
plasticizers] and some mineral suspensions often exhibit rheopexy. Thixotropy is
a necessary feature of house paints, which must be reasonably fluid when they
are applied by brushing or rolling, but have to be viscous in the can and shortly
after application, in order to minimize pigment settling and sagging, respectively.
A variety of laboratory instruments have been used to measure the viscosity of
polymer melts and solutions. The most common types are the coaxial cylinder,
cone-and-plate, and capillary viscometers.
Figure 4.30
shows a typical flow curve
for a thermoplastic melt of a moderate-molecular-weight polymer, along with
η5ηð γ;
t
Þ
