Chemistry Reference
In-Depth Information
continually dissipated and we can calculate the rate from the force and the
distance moved per second:
E
¼
sg
ð
3
:
1
Þ
Now the constitutive equation or equation of state for our Newtonian fluid is:
s
¼
Zg
ð
3
:
2
Þ
and so the rate of energy dissipation for a Newtonian material is now:
E
¼
Zg
2
ð
3
:
3
Þ
We can take as an example a Newtonian oil, hexadecane say, which has a visco-
sity of 3.34
10
-3
Pa s at 20 1C, in our rheometer with a sample size of 2 g of oil.
We are going to shear this sample at 300 s
-1
for 100 s. The energy input is
500 Jmole
-1
K the temperature
rise would be 6.7 1C if our rheometer was a very poor heat conductor (i.e. an
adiabatic system). The viscosity reduces exponentially with temperature and so
clearly there is a requirement for good thermostatting so that the experiment is
isothermal. But even if the rheometer is a good heat conductor, large samples of
viscous organic materials may not remain at a uniform temperature across the
sample!
The energy changes that occur when a fluid flows are due to the sum
3340 J. Now, as the heat capacity of the oil is
B
1. changes in potential energy (e.g. changes in height);
2. changes in pressure (reversible pressure volume term);
3. changes in kinetic energy (from the momentum changes);
4. the viscous or ''frictional'' losses.
Formally this is expressed by the Bernoulli equation (see for example Ref. 1),
but in the laboratory we have the ability to work under conditions where we
can minimise some of these. For example, in a small sample in our simple
viscometer pictured in Figure 3.1, a small volume element of fluid would not be
expected to change in height in the cup. We usually regard liquids as incom-
pressible but we should bear in mind that this is not strictly the case. The faster
a fluid flows, the lower is the pressure. The best example of this is the lift
generated by an aerofoil moving through a fluid. This will also not raise any
problems in our simple viscometric flow so let us focus for a moment on 3 and 4
above for a flowing liquid. The amount of energy dissipated in one second due
to the flow is the force multiplied by the velocity. The force being given by the
momentum of the fluid element, which is simply the mass times the velocity.
The mass of fluid that we are considering is calculated from the density, r, and
the volume of fluid passing through the element. Hence, we can say that the
force due to the momentum is:
F
m
/
mv
