Biomedical Engineering Reference
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coefficients. In mechanically agitated gas-liquid contactors for both Newtonian and non-
Newtonian aerated liquids, a typical correlation is expressed in the form (Markopoulos et al.,
2007):
α
P
k
=
C
·
·
u
β
(12)
La
4
g
V
where k La is the gas-liquid mass transfer coefficient (s -1 ), C 4 , α and β are empirical
coefficients.
For all types of airlift reactors, k La increases with gas velocity (Lazarova et al., 1997;
Masoud et al., 2001) and, usually, a power function law of gas velocity is used:
k
=
C
·
u
δ
g
(13)
La
5
being C 5 and δ are empirical coefficients.
Nevertheless, in liquid-gas mixing systems when the gas and liquid phases are forced to
circulate together, Kouakou et al. (2005) proposed to describe the combined action of air and
forced liquid superficial velocities on k La by:
γ
g
k
=
(
C
·
u
+
C
u
(14)
La
6
l
7
being C 6 , C 7 and γ are empirical coefficients.
The liquid-solid mass transfer coefficient is estimated by correlations which give the
Sherwood number (Sh), as a function of the Reynolds number (Re) and the Schmidt number
(Sc). The equations of Ranz and Marshall (1952) and Brian and Hales (1969) are the most
used for the estimation of k c :
k
c ·
d
p
(15)
Sh
=
D
d
·
u
·
ρ
(16)
p
s
l
Re
=
μ
μ
(17)
Sc
=
ρ
D
1
1
(18)
Sh
=
2
+
0
·Re
2
Sc
2
(19)
Sh
=
4
.
0
+
1
.
21
·(Re·
Sc
)
3
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