Power I aw index, n
500
Chapter 11
0 ■*-- ■■■
1
------L
-------- '-------- J-------
-- ■
......
...........
..........
•--------- ^
0,0 1
0
5
10
1 5
20
2 5
30
35
4 0
4 5
5 0
Biom as (gkg')
Figure 11. 9. Power law constants as functions of the biomass concentration of
P. chrysogenum
(pellet
morphology). The data are taken from Pedersen
etal.
(1993).
In a stirred bioreactor there are large variations in the shear rate throughout the tank, with a high
shear rate found close to the impeller and a low shear rate close to the walls. It is therefore not
possible to specify a value of the viscosity for a medium with non-Newtonian properties. The
average shear rate
, however, is approximately proportional to the stirrer rate,
N, i.e.
t av=kN
(11.24)
where
k
is a characteristic empirical constant for the system being,
k
is reported to be in the range 4-
13, depending on the system, and with a standard Rushton turbine impeller
k
= 10 may be used
(Nienow and Elson, 1988). The
maximum shear
rate, on the other hand, is approximately
proportional to the impeller tip speed, i.e.
f ^ = k 'N d s
(11.25)
The stirrer rate is typically lower in a large-scale reactor than in a small scale. This means that the
average shear rate is lower in the large-scale reactor. The tip speed is, however, normally higher,
which means that the maximum shear rate is higher in the large-scale reactor. For a pseudoplastic
fluid, the decreasing shear rate when moving towards the reactor wall will give an increased
viscosity. In extreme situations an inner core of medium is agitated while a shell of liquid at the wall
does not move at all.
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