Chemistry Reference
In-Depth Information
, was introduced in connection with
Eq. (3-59) as the quotient of the shearing force per unit area divided by the veloc-
ity gradient. The numerator here is the shearing stress,
The coefficient of viscosity concept,
η
τ
, and the denominator is
termed the shear rate,
γ
(
γ
is the strain and
γ
d
γ=
dt
). With these changes,
Eq. (3-59) reads:
η5
ð
F
=
A
Þ
Þ
5 τ γ
(4-85)
ð
d
ν=
dr
The viscosity of water at room temperature is 10
2
3
Pa
5
1 centipoise
(cP)], while that of molten thermoplastics at their processing temperatures is in
the neighborhood of 103
sec [
η
104 Pa
sec. Lubricating oils are characterized by
values up to about 1 Pa
sec. In SI units, the dimensions of viscosity are N
sec/m
2
5
Pa
sec.
is independent of shear history, the material is said to be time indepen-
dent. Such liquids can exhibit different behavior patterns, however, if, as is fre-
quently the case with polymers,
If
η
varies with shear rate. A material whose
viscosity is independent of shear rate, e.g., water, is a Newtonian fluid.
Figure 4.28
illustrates shear-thickening, Newtonian, and shear-thinning
η
rela-
tions. Most polymer melts and solutions are shear-thinning. (Low-molecular-
weight polymers and dilute solutions often exhibit Newtonian characteristics.)
Wet sand is a familiar example of a shear-thickening substance. It feels hard if
you run on it, but you can sink down while standing still.
η2 γ
Newtonian
Shear rate
FIGURE 4.28
Time-independent fluids.
