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3.4 Slurry Reactors 125

used for gas–solid bubbling fluidized beds. The single bubble rising velocity is a relation-
ship originating from the equation of Mendelson (Mendelson, 1967; Krishna, 2000):
 2
gd  0.5
u L bub (3.191)
bs   L d bub 2  

For values of the Eotvos number higher than 40 (for the air–water system, this corre-
sponds to d bub 17 mm), the above equation simplifies to the well-known
Davies–Taylor equation:

u bs 0.71( gd ) bub 0.5 (3.192)

Eotvos number is defined as (Krishna, 2000)

g ( d ) 2
Eo L G bub (3.193)

L

The scaling factor accounts for the influence of the column diameter:

d bub
S f 1 f or 0.125 (3.194)
D

 d  d
S 1.13e xp  for 0.125 bub  0.6 bub < (3.195)
f  D  D

 D  0.5 d
S 0.496 for 0.6 bub (3.196)
f  d  bub   D

and the single-bubble rising velocity is

u bs 0.71( gd ) bub S 0.5 f (3.197)

The rise velocity of the bubbles population is

u bub u A f (3.198)
bs
where A is the acceleration factor. For low-viscosity liquids ( 2000): a s) (Krishna, 0.0029 P
f
A f 2.73 4.505( u) s u trans (3.199)

where u is the superficial gas velocity and u , the transition velocity from homoge-
s trans
neous to heterogeneous flow regime. The latter is practically equal to zero for slurries