1. Minimum Fluidization Velocity
Considering a bed of particles sustained in a distributor for uniform upflow of gas (e.g. synthesized porous metal plate). The onset of fluidization occurs when there is a balance between the drag force promoted by the upflow of gas in motion and the weight of the particles, i.e.:
or even:
Rearranging the Equation (1), we obtain the minimum fluidization conditions:
At the beginning of fluidization, for small particles, the porosity is a little higher than in a fixed bed, corresponding to the expanded state of bed for any solid mass (see details in the minimum fluidization and porosity).
The superficial velocity under conditions of minimum fluidization U_{mf}, is obtained by combination of Equation (2) and the extrapolation of the expression of fixed bed established by Ergun (1952):
Thus:
Or even in the rearranged form:
in which the Archimedes' number is defined as:
In the special case of very small particles, Equation (4) is simplified as:
For very large particles:
When e_{mf} and/or f_{S} is not known, one can also estimate U_{mf}, to a bed of irregular particles, as follows. First, rewrite Equation (5) as:
where K_{1} and K_{2} are constant:
Wen and Yu (1966) were the first to realize that K_{1} and K_{2} remain almost constant for different types of particles in a wide range of conditions (Re = 0.001 to 4000). Thus, other researchers (see Table 2) published values of K_{1} and K_{2}.
Solving the Equation (9) under conditions of minimum fluidization and using the values of K_{1} and K_{2}recommended by Chitester et al. (1984) for coarse particles, is obtained:
or:
For fine particles, the values recommended by Wen and Yu (1966) are:
This expression is useful only as an estimate for U_{mf}. Since U_{mf} is the most important measure necessary for the project, this has been the focus of a large amount of experimental work under a wide variety of conditions (Table 1). Further details are found in Tannous et al. (1994).
Table 1 – Values of the two constants in the Equation (9)
Researchers

K1

K2

Wen e Yu (1966)

33,7

0,0408

Richardson (1971)

25,7

0,0365

Babu et al (1978)

25,3

0,0651

Grace (1982)

27,2

0,0408

Tannous et al. (1998)

25,83

0,043
