Mass Transfer
433
\ ! /
-
^
Primary eddies
intermediate eddies
Terminal eddies
Figure 10.4. Energy transfer from primary eddies to terminal eddies.
'T0'6
(10.23)
Thus the maximum stable bubble diameter is reduced (giving a higher specific interfacial area) if
the power input is increased. Based on theoretical predictions in the turbulent regime, Lehrer (1971)
states
k ~
1.93 (with all parameters in SI units), whereas several researchers specify & as a function
of the gas holdup
£.
For pure water Lee and Mevrick (1970) suggest
In the case of highly viscous media, also the viscous resistance needs to be taken into account and
Eq. (10.23) is therefore less accurate.
Note 10.1, Calculation of maximum stable bubble diameter using the statistical theory of turbulence
A turbulent flow field is normally described by the statistical theory of turbulence, where the flow field is
regarded as a distribution of superimposed
eddies
or velocity fluctuations characterized by their direction
and magnitude. According to this theory, large
primary eddies
emerge due to the impeller action. The scale
of these primary eddies is on the order of magnitude of the impeller diameter. These primary eddies are
unstable and disintegrate into smaller eddies (called
intermediate eddies),
which are again unstable and
therefore disintegrate further into still smaller eddies (called
terminal eddies).
The terminal eddies have
completely lost their unidirectional nature and are therefore isotropic. Thus kinetic energy flows through the
cascade of eddies until ultimately the energy is dissipated as heat (see Fig. 10.4). The size of the terminal
eddies is (see, e.g., Moo-Young and Blanch, 1981)
k = 4.25s2
(10.24)
-i
(
1
)
where ti is the viscosity of the liquid.
Any given location will be passed by eddies of widely different velocities, and it is appropriate to introduce
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