430
Chapter 10
where
u
is the bulk flow velocity (m s'1).
This results in the following relation between
kt
and the diffusion coefficient:
(
10
.
12
)
where the proportionality factor is a function of the physical properties of the liquid and the liquid
flow rate.
None of these theoretically based models are of much use for calculating the value of
kt
in a real
system, e.g., an agitated and sparged liquid. They do, however, tell us something about how the
physical properties of the liquid influence the liquid mass transfer coefficient. Furthermore, the
relative values of
kt
for various compounds may be evaluated even if the diffUsivities of the
compounds are unknown (see also Note 10.3).
10.1.2.
Interfacial Area and Bubble Behavior
In Eq. (10.7), the specific interfacial area
a
is based on the liquid volume,
Vh
i.e.
a = 4 -
00.13)
where
A
is the total interfacial area in the gas liquid dispersion. This definition of the specific
interfacial area is the most convenient when the volumetric rate of the mass transfer process is to be
used together with mass balances for dissolved components, e.g., the dissolved oxygen. However,
in empirical correlations for the volumetric mass transfer coefficient (see Section 10.1.4), one often
uses the specific interfacial area based on the total volume of the gas-liquid dispersion, i.e.,
A _
A
vd ~ v*+ vg
(10.14)
The two definitions of the specific interfacial area are related by
ad = { \ - £)a
(10.15)
where
£
(10.16)
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