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124 3. Heterogeneous Processes and Reactor Analysis

35
30 separated chain transition jet
bubbles bubbling regime
25
20

(mm) 15
b
d
10
5 higher orifice
diameter
0
0.0001 0.001 0.01 0.1 1
gas flow rate at orifice opening*orifice diameter
Figure 3.33 Air-bubble formations at the orifice in water (Heijnen and an’t Riet, 1984). V

Addition of solids in the liquid increases the bubble coalescences, and in turn, the b ub-
ble size (K 1996). Fukuyama et al. (1987) proposed the following correlation for
oide,
slurry bubble columns:
0.59   2
d (3.188)
bub  
g h G 

1  h 
h
u (1 ) u h G (3.189)
sG G sL G   h L  
Bubble diameter dbub is also referred to as “volume-surface mean diameter of bubbles” or
“Sauter mean bubble diameter.” SI units are used with this correlation.
The Rayleigh–Taylor instability is the balance of surface tension and gravity acting on
,
a gas bubble. If the latter is greater than the former the bubble will eentually break up. v
According to Bellman and Pennington (1953), if the diameter of a certain spherical cap
,
bubble exceeds a critical diameter it will break up. This critical diameter is referred to as
the maximum stable bubble size and is generally expressed as (Bellman and Pennington,
1953; Behkish, 2004)


 0.5
d 2  L  (3.190)
x bub,ma g (
 L G ) 

Krishna et al. (2001) used a different and simpler approach for determining the bubble ris-
ing velocity and bubble diameter. They employed a two-phase model, analogous to the one