proposed equation, and the values of Umf, 2D were significantly higher
when the particle size to thickness ratio was between 0 and 0.04.
The discrepancies between the experimental data and the
theoretical results are too high to be attributed to uncertainties in
the experimental measurements or to the variety of experimental
techniques used in the studies. Nevertheless, as shown in Table 3, all
of the experimental data that were in accordance with the proposed
correlation (Eq. (2)) were obtained in 2D beds with walls made of
glass. An exception to the aforementioned observation is the data
obtained by Rowe and Everett [23],which is marked with an empty
square. However, based on the thickness of the bed, the study
conducted by Rowe and Everett can be considered a 3D experiment. In
addition, although Busciglio et al. [15] used a bed made from perspex,
the walls of the bed were in direct contact with fluidized particles,
which were made of glass to avoid electrostatic charge interactions. As
a result, the particles were deposited on the surface of the walls,
which precluded the proper observation of the interior of the bed.
Alternatively, Saxena and Jadov [33] ground the walls of the bed to
ensure that static charge did not accumulate on the surface of the
walls. In the present study, problems associated with electrostatic
charge were not observed during the experiments.
In contrast, the rest of data were obtained in 2D beds made of
plastic materials (either perspex or plexiglass). Under these conditions,
electrostatic charge could have a significant effect on the
fluidization velocity. Moreover, Mudde et al. [35] fluidized plastic
particles, and obtained the highest velocity ratio (Umf, 2D/Umf, 3D=1.5)
of all of the data shown in Table 3, for the bed thickness of t=30mm.
The exception to the aforementioned observations is marked with a
filled diamond. However, this data set departs from the other data
obtained by the same authors. As previously mentioned, Saxena and
Jadav [33] attributed the discrepancies in this data set to differences in
particle geometry.
Electrostatic charge in fluidized beds is a complex phenomenon
and is dependent on a number of variables [42–46], including the
bed height, particle size, fluidization velocity, relative humidity of
the fluidizing air, etc. The results of Rojo et al. [42] revealed that the
electrostatic charge increases with an increase in the height of the
fixed bed under bubbling conditions, which may explain the fact
that an increase in the minimum fluidization velocity with an
increase in bed height was observed by Ramos et al. [27] and Geldart
[24]. Moreover, Guardiola et al. [43] observed that electrification
increased with an increase in particle size and air velocity and
suggested that the relative humidity of the air was an important
parameter. Similarly, in a study conducted by Park et al. [44],the
electrostatic charge of glass and polyethylene particles was reduced
when the humidity of the fluidizing air was between 40 and 80%
Alternatively, Mehrani et al. [45] concluded that most of the
electrostatic charge in a fluidized bed was related to the charges
entrained by the finest particles. More recently, Moughrabiah et al.
[46] studied the effect of pressure, temperature and gas velocity on
the electrostatics of a 3D column with a diameter of 15cm, and
evaluated the same particles fluidized by Park et al. [44](glass and
polyethylene). The results obtained from both types of particles
were compared, and the authors demonstrated that the glass
particles accumulated more electrostatic charge than the plastic
particles. Moughrabiah et al. [46] suggested that electrostatic
charges can modify interparticle forces, which could have a
significant effect on the properties of the bed, such as the effective
viscosity. In 2D beds, walls-particle interactions could influence the
electrostatic charge; however, these effects are usually neglected in
3D beds[42]. Thus, electrostatic charge could be considered in the
momentum equation (Eq. (3)), but the multitude of variables and
the experimental conditions of the data summarized in Table 3
preclude the quantification of this force. Kashyap et al. [47] studied
the effect of an electric field on the hydrodynamics of particles in a
rectangular fluidized bed. Thus, if the electrostatic forces can be
quantified, the effects of an electric field could be included in the
correlation as a term that increases the gas pressure drop along the
bed.
According to criteria proposed by Grace, most of the data shown in
Fig. 5 correspond with type B particles [36]. Alternatively, Glicksman
and McAndrews [34] used type D particles, and the polystyrene
spheres fluidized by Mudde et al. [35] are similar to type A particles.
However, the particles used by Mudde et al. are considered type B.
Rowe and Everett [23] did not indicate the density of the alumina
particles used in their study; thus, the particle type could not be
determined.
Based on the experimental conditions shown in Table 3, another
parameter that may affect the bed dynamics is the sphericity ϕp of the
particles [24]. The particle sphericity is directly related to the particle