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206 3. Heterogeneous Processes and Reactor Analysis

determine the fluidization pattern, for both liquid and gas–solid systems (Liu et al ., 1996;
Li et al ., 2003).
 Ar   p f 
D (3.486)
n  Re     
 
fm f
In this equation, Ar is based on the particle and not on the hydraulic density . Experiments
showed that

• Particulate fluidization exists for 0 < D n < 10 4 .
• Transitional fluidization exists for 10 4 < D n < 10 6 . “Transitional fluidization” includes
the behavior of Type A fluidization.
• Type B fluidization exists for D n > 10 6 .

To distinguish between particulate and bubbling fluidization, the Romero and Johnson
criterion is useful (Kwauk and Liu, 2000):

particulate fluidization exists if

Z
Fr Re fm fm h f fm 100 (3.487)
f D

bubbling fluidization exists if
Z
Fr Re fm fm h f fm 100 (3.488)
f D

where Fr fm is the Froude number at incipient fluidization:

u fm 2
Fr fm (3.489)
dg p
where:
d p the particle diameter
D the bed diameter
Z fm the fed bed height at incipient fluidization. ix
W Another simpler criterion is that of ilhelm and Kwauk (Kwauk and Liu, 2000), which is
based solely on the Fr fm number–if it is lower than 0.13, particulate fluidization e xists and
if it is higher than 1.3, bubbling fluidization e xists.
Finally, in gas–solid fluidization, slugging will not occur provided the following crite-
rion is satisfied (Beyens and Geldart, 1974):

Z 1.9
fm (3.490)
D ( d ) 0.3
pp