# Minimum Fluidization Velocity

### 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.:

(1)

or even:

(2)

Re-arranging the Equation (1), we obtain the minimum fluidization conditions:

(3)

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 Umf, is obtained by combination of Equation (2) and the extrapolation of the expression of fixed bed established by Ergun (1952):

(4)

Thus:

(5)

Or even in the rearranged form:

(6)

in which the Archimedes' number is defined as:

(7)

In the special case of very small particles, Equation (4) is simplified as:

(8)

For very large particles:

(9)

When emf and/or fS is not known, one can also estimate Umf, to a bed of irregular particles, as follows. First, re-write Equation (5) as:

(10)

where K1 and K2 are constant:

(11)

Wen and Yu (1966) were the first to realize that K1 and K2 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 K1 and K2.

Solving the Equation (9) under conditions of minimum fluidization and using the values of K1 and K2recommended by Chitester et al. (1984) for coarse particles, is obtained:

(12)

or:

(13)

For fine particles, the values recommended by Wen and Yu (1966) are:

(14)

This expression is useful only as an estimate for Umf. Since Umf 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