496
Chapter 11
significant, whereas for larger reactors the contribution can be neglected. In the type of
correlation given by Eq (11.18), this can be seen as a decreasing value of the exponents
a
and
0
with increasing reactor size.
Non-constant power dissipation
Another factor that needs to be considered is that the power dissipation in the reactor is spatially
inhomogeneous. There is a much higher power dissipation, up to a factor 100, close to the
impeller. This gives a difference in bubble size distribution, with smaller bubbles close to the
impeller and bigger bubbles close to the wall. This is particularly true for a coalescing medium.
Again, a lower
kta
than predicted from correlations based on experiments made in smaller scale
bioreactors may result.
Gradients o f other compounds than oxygen
As stated in section 11.3.1, it is not possible to maintain the same mixing time in a large-scale
bioreactor as in a lab-scale bioreactor. Mass transfer in the bulk liquid phase can no longer be
assumed to take place instantaneously, i.e. the assumption of an ideal tank reactor is no longer
valid. The increased circulation times,
tc,
will cause concentration gradients for any component,
which is added during operation. Besides for oxygen, this typically applies when base is added
for pH control (see problem 11.4). In fed-batch or continuous processes, gradients will occur also
for medium components, e.g. the carbon source added.
11.3.5. Rheology of fermentation broths
The flow pattern in a stirred tank reactor is determined by the reactor and impeller geometry, the
power input to the system and the properties of the fluid. Before defining the fundamental
equations governing flow, we will introduce some useful rheological concepts.
Rheology
is the study of flow and deformation of matter. A
fluid
is strictly defined a material
phase, which cannot sustain
shear stress, i.e
. forces acting in the tangential direction of the
surface. (The forces acting in the normal direction of the surface are the pressure forces.) A fluid
will respond to shear stress by continuously deforming, i.e. by flowing. The
shear rate, y
, (s l)
in a two-dimensional flow is defined as
7
duy
dz
(11.19)
where z is the direction perpendicular to the direction of the flow. Isaac Newton was the first to
propose a relation between shear stress and the shear rate in 1687, when he stated that “the
resistance (
sic
the shear stress) which arises from the lack of slipperiness originating in a fluid,
other things being equal, is proportional to the velocity by which parts of the fluid are being
separated from each other (
sic
the shear rate)“. The
dynamic viscosity
,
77
, (kg m s"1) of a fluid is
the fundamental property which relates the
shear stress, z,
(N m‘2) to the shear rate. For the one-
dimensional case described in Eq. (11.19) we get:
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